Level I Math Black Line Masters Toolkit

Level I Math Black Line Masters Toolkit NSSAL (Draft) C. David Pilmer 2012 (Last Updated: February, 2013)

This resource is the intellectual property of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. The following are permitted to use and reproduce this resource for classroom purposes. Nova Scotia instructors delivering the Nova Scotia Adult Learning Program Canadian public school teachers delivering public school curriculum Canadian non-profit tuition-free adult basic education programs The following are not permitted to use or reproduce this resource without the written authorization of the Adult Education Division of the Nova Scotia Department of Labour and Advanced Education. Upgrading programs at post-secondary institutions Core programs at post-secondary institutions Public or private schools outside of Canada Basic adult education programs outside of Canada Individuals, not including teachers or instructors, are permitted to use this resource for their own learning. They are not permitted to make multiple copies of the resource for distribution. Nor are they permitted to use this resource under the direction of a teacher or instructor at a learning institution. Acknowledgments The Adult Education Division would like to thank the following ALP instructors for piloting this resource and offering suggestions during its development. Andre Davey (Metroworks) Shannon Davis (YCLA) Andrea Fitzgerald (CLANS) Elizabeth Grzesik (EHALA) Cheryl Mycroft (GALA) Joyce Power (Metroworks) David Sweeny (YCLA) Kirsteen Thomson (Can-U)

Table of Contents Introduction iv Difficulty Game or Puzzle Number Magnitude (Whole Numbers).... 1 Expanded Form (A and B) 2 Write the Number (A to C) 4 Write the Number (D and E) 8 Place Value 12 Before, After, or Between (A and B) 13 Closer To, and Odd or Even (A and B) 15 Whole Numbers and Number Lines (A and B) 17 Give an Example.. 19 Closer To (A and B).. 20 Operations with Whole Numbers. 22 Connect Four Addition Game (A to C).... 23 Connect Four Subtraction Game (A to D)... 26 Subtraction Search..... 30 Multiplication Models 31 Multiplication Array Game 33 Connect Four Multiplication Game (A to E). 34 Connect Four Multiples Game (A to C) 39 Capture the Flag Multiplication Game. 42 Random Multiplication Facts Quizzes.. 44 Multiplying on Your Hands... 46 Put the Number in the Right Box... 50 Investigation: Multiplying by Multiples of 10, 100, and 1000. 51 Multiplying by Multiples of 10, 100, and 1000. 52 Multiplying Two Digit Numbers, Part 1 (Expanded Form).. 54 Multiplying Two Digit Numbers, Part 2 (Lattice Method) 59 Multiplying Multi-Digit Numbers.. 65 Connect Four Division Game.... 69 Division Search.. 70 Divisibility Chart 71 More Divisibility (A and B).. 72 Divisibility or Prime Connect Four Game 75 Division with Remainders. 76 Long Division (Partial Quotient Method). 80 Prime Factorization 88 Multiple Operations (Whole Numbers)... 90 Express the Number in Multiple Ways.. 91 Name the Preceding or Next.. 92 One of these Things is Not Like the Others.. 93 NSSAL i Draft

Fact Family Puzzle.... 95 Pathways.... 97 Two of These Boxes Just Don't Belong (A and B).. 98 Equivalent.. 100 Venn Diagrams and Whole Numbers 101 Whole Number Crossword Puzzle (A to D). 103 KenKen Puzzles (A and B) 107 KenKen Puzzles (C and D) 110 KenKen Puzzles (E).. 112 Find the Two Numbers.. 113 Which Combination of Numbers Works?. 114 Magic Squares... 115 Addition Pyramids 116 Row Factors and Column Factors. 118 Letter and Number Sentences 119 Math Logic Puzzles 120 Number Sentences (A).. 121 Number Sentences (B). 122 Order of Operations (A) 123 Order of Operations (B) 126 Order of Operations (C) 129 Patterns. 132 What's the Pattern? (A).. 133 What's the Pattern? (B).. 134 Toothpick Patterns. 135 Create the Pattern (A and B).. 137 Number Patterns (A and B) 139 Row, Column, and Diagonal Pattern. 141 What's the Relationship? 142 Input Output (A to D) 144 Filling or Draining. 148 Travelling Towards or Away From Home 153 Weight of the Water.. 160 Word Problems 165 Describing the Relationships with Words. 166 List the Numbers Based on the Written Description 167 Addition and Subtraction Crossword 168 Multiplication and Division Crossword 170 Operations Crossword 172 Word Sentence to Number Sentence to Answer (A to C) 174 What are the Possibilities? (A). 177 What are the Possibilities? (B). 180 Does It Make Sense?. 182 Insert Your Own Numbers and Words. 184 NSSAL ii Draft

Put the Numbers in Where It Makes Sense (A to B) 185 Put the Numbers in Where It Makes Sense (C) 187 Put the Numbers in Where It Makes Sense (D) 188 Not Enough Information is Provided 190 Word Problems with Too Much Information 191 Create Your Own Math Statement 193 Word Problems (A and B) 195 Same Numbers, Similar Context, Different Math (A). 200 Same Numbers, Similar Context, Different Math (B). 202 More than One Question 204 Food Chart (A and B) 206 Keeping Track of the New Stock (A and B) 209 Consumer Math 211 How Much Do They Have? (A to E). 212 Emptying the Junk Drawer. 217 Connect Four Money Game.. 219 Find the Price. 220 Name a Product near that Price. 221 Least to Most Expensive 222 What are the Three Items Worth?.. 223 What Is It Worth? (A and B). 224 Purchasing Groceries. 226 Measurement 228 Which Measurement Is Reasonable? 229 Telling Time (A to F) 230 Connect Four Time Ahead Game (A and B) 236 How Much Time Has Passed? (A to C) 238 Geometry (From 3D to 2D) 244 Isoball 245 Orthographic Projections (A) 246 Orthographic Projections (B). 250 Transfer Image to Dot Paper. 252 Isometric Projections 253 Orthographic Isometric Challenge 257 Edges, Faces, and Vertices (A and B)..... 259 Construct the Geometric Figure 261 Nets 266 Describe the Faces. 268 Geometry Terminology Crossword 277 Reflections (A to C)... 279 Base Ten Blocks.. 282 What's the Number?.. 283 NSSAL iii Draft

Express the Number Different Ways 285 Express with the Fewest Number of Manipulatives. 287 Adding 295 Adding with Regrouping 299 Subtracting. 305 Subtracting with Regrouping. 310 Answers 317 NSSAL iv Draft

Introduction The concepts covered in Level I Math fit into one of the following five categories. Number and Operations Patterns and Relations Statistics and Probability Shape, Space, and Measurement Consumer Math The specific outcomes aligned with each of these categories can be found in the ALP Level I Math Curriculum Guide. Over the years, Community-Learning Organizations have collected, and the Adult Education Division have supplied, a variety of print resources used in the delivery of Level I Math. Many of those resources can still be used with this new curriculum but we emphasize that there is a much greater emphasis on mathematical understanding and multiple representations of concepts in this new program. Although we want our learners to develop a level of automaticity as it pertains to operations with whole numbers, we do not want this math course, or any other ALP math course, to focus primarily on the mastery of skills. Unfortunately many of the "traditional" textbooks used in adult basic education programs do have this as their primary focus. For this reason, the Adult Education division would like all instructors to use the following ALP resources in the delivery of Level I Math, and to supplement that material with the more traditional resources they have collected over the years. Level I Math Black Line Masters Mental Math Customized Practice Number Sense These resources include activities, exercises, investigations, and games that encourage understanding and thinking, rather than solely focussing on the mastery of algorithms. Learners are ultimately better served when mathematical concepts are examined and taught in this matter. We do not expect all Level I learners to complete all the worksheets or activities in the resources above, rather instructors will use their professional judgement to choose the items that are most appropriate for their individual learners. By supplying these materials the LAE is providing a greater variety of education tools for ALP instructors; the instructors have to decide what tools are best suited for their learners, at what times, and in what sequence. For example, let's consider multiplication of two multi-digit numbers. Most instructors are familiar with the traditional algorithm for such multiplication, but some instructors are unfamiliar with multiplication of multi-digit numbers using the expanded forms of the numbers and/or lattice multiplication. These latter two techniques are found in this resource. Does that mean that all learners need to know all three methods? Definitely not; chose the technique that works best for your learner. Please do not view this specific resource as a textbook. Although within sections, the activity sheets are generally arranged from easiest to hardest, a seamless flow from one activity to the NSSAL v Draft

next was not created. This booklet is merely a collection of black line masters to be used as the instructor sees fit. All of these materials are available at the NSSAL site (http://gonssal.ca/documents/nssaldevelopedresources.pdf) NSSAL Practitioners Website (http://instructors.gonssal.ca/login) NSSAL vi Draft

Number Magnitude (Whole Numbers) NSSAL 1 Draft

Expanded Form (A) 1. Write the multi-digit number in its expanded form. Two examples have been done for you. Number Expanded Form Number Expanded Form e.g. 396 300 + 90 + 6 e.g. 2056 2000 + 50 + 6 (a) 42 (b) 694 (c) 3985 (d) 569 (e) 78 (f) 4281 (g) 867 (h) 31 (i) 6497 (j) 528 (k) 826 (l) 5923 (m) 59 (n) 3045 (o) 4808 (p) 703 (q) 6420 (r) 5099 (s) 810 (t) 9603 2. Given the expanded form, write the multi-digit number. The last eight have had their expanded forms scrambled. Expanded Form Number Expanded Form Number (a) 50 + 8 (b) 600 + 20 + 9 (c) 5000 + 800 + 70 + 4 (d) 200 + 80 + 6 (e) 8000 + 300 + 80 + 7 (f) 30 + 5 (g) 400 + 90 + 3 (h) 700 + 20 + 1 (i) 600 + 10 + 9 (j) 7000 + 80 + 2 (k) 800 + 50 (l) 500 + 3 (m) 1000 + 700 + 8 (n) 6000 + 80 + 9 (o) 5000 + 300 + 40 (p) 8000 + 600 + 50 + 7 (q) 8 + 50 (r) 50 + 300 + 2 (s) 200 + 50 + 1000 + 9 (t) 9 + 600 + 40 (u) 8000 + 7 + 300 + 60 (v) 500 + 80 + 7000 (w) 4 + 6000 + 80 (x) 8000 + 5 + 30 NSSAL 2 Draft

Expanded Form (B) 1. Write the multi-digit number in its expanded form. An example has been done for you. Number Expanded Form e.g. 132 794 100 000 + 30 000 + 2000 + 700 + 90 + 4 (a) 54 982 (b) 5685 (c) 746 173 (d) 27 959 (e) 306 781 (f) 43 908 (g) 372 080 (h) 50 736 (i) 270 480 (j) 908 704 2. Given the expanded form, write the multi-digit number. The last four have had their expanded forms scrambled. Expanded Form (a) 60 000 + 7000 + 500 + 90 + 1 Number (b) 500 000 + 60 000 + 2000 + 700 + 10 + 3 (c) 40 000 + 1000 + 200 + 70 + 8 (d) 800 000 + 50 000 + 300 + 70 + 4 (e) 600 000 + 2000 + 800 + 90 + 2 (f) 90 000 + 5000 + 40 + 3 (g) 500 000 + 30 000 + 900 + 5 (h) 600 000 + 80 000 + 4000 + 700 + 10 (i) 6 + 700 + 20 000 + 50 + 9000 (j) 30 000 + 5000 + 700 000 + 60 + 200 + 9 (k) 400 + 200 000 + 8 + 90 000 + 60 (l) 900 000 + 5 + 7000 + 30 + 100 NSSAL 3 Draft

Write the Number (A) 1. Write the number that has been described using words. Word Description Number Word Description Number e.g. fifty-seven 57 e.g. nineteen 19 (a) eighty-two (b) forty-nine (c) sixteen (d) ten (e) forty-six (f) twenty-seven (g) seventy-four (h) thirteen (i) fifty-six (j) eleven (k) thirty-eight (l) twenty-three (m) eight (n) ninety-nine (o) seventeen (p) eighty-three (q) twelve (r) fifty-two (s) ninety (t) thirty-one (u) seven (v) sixty-three (w) fifteen (x) sixty-eight 2. Write out the number using words. Number Word Description e.g. 72 seventy-two (a) 59 (b) 42 (c) 18 (d) 37 (e) 61 (f) 95 (g) 21 NSSAL 4 Draft

Write the Number (B) 1. Write the number that has been described using words. Word Description Number Word Description Number e.g. three hundred forty-nine 349 e.g. six hundred eight 608 (a) nine hundred thirty-two (b) two hundred forty-six (c) seven hundred twelve (d) three hundred sixty (e) seventy-nine (f) six hundred twenty-one (g) one hundred seven (h) five hundred eighty-nine (i) four hundred ninety (j) forty-two (k) eight hundred eleven (l) two hundred seventy-six (m) seven hundred two (n) three hundred nineteen (o) twelve (p) five hundred thirty-one (q) six hundred seventy (r) nine (s) one hundred eighty-six (t) nine hundred (u) two hundred sixteen (v) sixty-five (w) seven hundred twenty (x) four hundred sixty-two 2. Write out the number using words. Number Word Description e.g. 452 four hundred fifty-two (a) 578 (b) 352 (c) 79 (d) 217 (e) 906 (f) 740 (g) 541 NSSAL 5 Draft

Write the Number (C) 1. Write the number that has been described using words. Word Description Number e.g. three thousand, two hundred ninety-one 3 291 e.g. six thousand, fourteen 6 014 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) eight thousand, three hundred twenty-two four thousand, six hundred eighty-three seven thousand, five hundred thirteen four hundred eleven nine thousand, five hundred twelve three thousand, four hundred twenty-nine two thousand, nine hundred fifty one thousand, seventy-eight two hundred seven five thousand, nine hundred eighty-three six thousand, eight hundred seven nine thousand, forty-six (m) five hundred ninety-seven (n) (o) (p) (q) (r) (s) (t) (u) (v) (w) eight thousand, two hundred seventy-four fifteen four thousand, nine hundred twenty-eight one thousand, three hundred eighteen thirty-eight three thousand, seventy-six six thousand, nine hundred seven thousand, three hundred eight seven hundred sixteen nine thousand, five hundred seventy NSSAL 6 Draft

2. Write out the number using words. Number Word Description e.g. 3 612 three thousand, six hundred twelve (a) 4 567 (b) 2 351 (c) 547 (d) 9 189 (e) 6 911 (f) 63 (g) 8 063 (h) 1 904 (i) 708 (j) 7 850 NSSAL 7 Draft

Write the Number (D) 1. Write the number that has been described using words. Word Description Number e.g. twenty-three thousand, eight hundred two 23 802 e.g. one hundred fifty thousand, six hundred twenty-three 150 623 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) fifty-six thousand, seven hundred forty-six two hundred thirty-nine thousand, one hundred fifteen forty thousand, three hundred seventy-one three thousand six hundred five five hundred twenty-three thousand, ninety sixty thousand, two hundred eight ninety-three three hundred five thousand, sixty-eight nine hundred one thirteen thousand, seven hundred fifteen five hundred thirty-six thousand four hundred seven thousand, fifty-two (m) nine thousand, four hundred sixty (n) (o) (p) (q) (r) (s) (t) (u) (v) (w) fifty thousand, six hundred nine seven hundred thirteen thousand, three hundred ninety-one twelve thousand, ninety-six six hundred thirty two hundred thousand, five hundred sixteen eighty thousand, five hundred seventy ten thousand, four hundred three hundred six thousand, one hundred eleven nine hundred fifteen eight hundred seven thousand, two NSSAL 8 Draft

2. Write out the number using words. Number Word Description e.g. 254 703 two hundred fifty-four thousand, seven hundred three (a) 34 781 (b) 245 359 (c) 780 (d) 12 692 (e) 304 562 (f) 7 023 (g) 70 650 (h) 634 904 (i) 53 011 (j) 940 060 NSSAL 9 Draft

Write the Number (E) 1. Write the number that has been described using words. Word Description Number e.g. six million, fifty-three thousand, eight hundred seven 6 053 807 e.g. twenty-four million, one hundred thousand, fifty 24 100 050 (a) ten million, ninety-six thousand, eight hundred two (b) one million, two hundred five thousand, sixteen (c) seven hundred thirty-four million (d) eighty million, five hundred twenty-nine thousand, seventy (e) four hundred twelve million, six hundred seventy thousand (f) eighty-five million, fifteen thousand, nine hundred (g) ninety-seven thousand, eight hundred twelve (h) six hundred twenty-seven million, seven hundred fifty (i) forty million, sixty-five thousand, ninety (j) five hundred six million, seventy thousand, nine hundred (k) three hundred two thousand, twenty-eight (l) eleven million, three thousand, forty-seven (m) nine million, three hundred thirteen thousand, four (n) five hundred twenty million, six hundred seventy-two NSSAL 10 Draft

2. Write out the number using words. Number Word Description e.g. 8 290 043 Eight million, two hundred ninety thousand, forty-three (a) 7 305 411 (b) 23 078 600 (c) 328 109 000 (d) 13 436 500 (e) 6 009 740 (f) 498 315 (g) 540 679 020 (h) 95 811 002 NSSAL 11 Draft

Place Value Complete each of the following. 1. For 2 345, what number is in the: (a) tens' place? (b) thousands' place? (c) ones' place? 3. For 7 890, what number is in the: (a) ones' place? (b) thousands' place? (c) hundreds' place? 5. For 423 719, what number is in the: (a) ten thousands' place? (b) hundred thousands' place? (c) ones' place? 7. For 65 807, what number is in the: (a) thousands' place? (b) hundreds' place? (c) tens' place? 9. For 8 143 625, what number is in the: (a) hundreds' place? (b) hundred thousands' place? (c) millions' place? 11. For 6 324 857, what number is in the: (a) tens' place? (b) ten thousands' place? (c) hundred thousands' place? 2. For 65 721, what number is in the: (a) ten thousands' place? (b) hundreds' place? (c) thousands' place? 4. For 48 156, what number is in the: (a) hundreds' place? (b) ten thousands' place? (c) tens' place? 6. For 120 693, what number is in the: (a) tens' place? (b) thousands' place? (c) hundred thousands' place? 8. For 835 270, what number is in the: (a) ten thousands' place? (b) ones' place? (c) hundred thousands' place? 10. For 7 015 428, what number is in the: (a) tens' place? (b) millions' place? (c) ten thousands' place? 12. For 5 391 207, what number is in the: (a) millions' place? (b) hundreds' place? (c) thousands' place? NSSAL 12 Draft

Before, After, or Between (A) Your Answers: Number Word Description e.g. What number is before 8? 7 seven e.g. What number is between 12 and 14? 13 thirteen e.g. What number is after 29? 30 thirty 1. What number is after 6? 2. What number is before 11? 3. What number is between 18 and 20? 4. What number is after 15? 5. What number is between 23 and 25? 6. What number is before 27? 7. What number is between 28 and 30? 8. What number is after 34? 9. What number is before 37? 10. What number is after 11? 11. What number is between 46 and 48? 12. What number is after 59? 13. What number is before 70? 14. What number is between 81 and 83? 15. What number is after 42? 16. What number is between 90 and 92? 17. What number is before 77? 18. What number is after 99? 19. What number is between 73 and 74? 20. What number is before 80? NSSAL 13 Draft

Before, After, or Between (B) Your Answers: Number Word Description e.g. What number is before 120? 119 one hundred nineteen e.g. What number is between 456 and 458? 457 four hundred fifty-seven e.g. What number is after 599? 600 six hundred 1. What number is after 325? 2. What number is before 421? 3. What number is between 188 and 190? 4. What number is after 239? 5. What number is between 356 and 358? 6. What number is before 650? 7. What number is between 286 and 288? 8. What number is before 700? 9. What number is before 998? 10. What number is after 437? 11. What number is between 638 and 640? 12. What number is after 399? 13. What number is before 900? 14. What number is between 513 and 515? 15. What number is after 661? 16. What number is before 712? 17. What number is between 600 and 602? 18. What number is after 807? 19. What number is after 999? 20. What number is between 499 and 501? NSSAL 14 Draft

Closer to, and Odd or Even (A) For each of the following, write the number based on the description, indicate whether it is closer to 0 or 100, and state whether it is an odd or even number. Word Description Number Closer to 0 or 100 Odd or Even e.g. fifty-nine 59 100 odd e.g. thirty-six 36 0 even (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) (t) (u) (v) eighteen seventy-six eighty-three forty twenty-four thirty-nine ninety-three sixty-five forty-six seventy-one eleven thirty-eight forty-nine seventy-two ninety-six twenty-seven sixteen twelve forty-four eighty-five fifty-eight thirty-seven NSSAL 15 Draft

Closer to, and Odd or Even (B) For each of the following, write the number based on the description, indicate whether it is closer to 0 or 100, and state whether it is an odd or even number. Word Description Number Closer to 0 or 1000 Odd or Even e.g. three hundred seventy-two 372 0 even e.g. eight hundred eleven 811 1000 odd (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) (t) (u) (v) two hundred forty-nine six hundred twenty-three seven hundred ninety-four one hundred eighty-six five hundred twelve three hundred seven four hundred sixty ninety-nine two hundred seventy-six five hundred forty-seven one hundred eighty-four nine hundred eight fifty-three three hundred fifty nine hundred ninety-six six hundred forty-five one thousand, thirty-one two hundred seventy-seven three thousand, ten seven hundred sixty-nine two thousand, three hundred eight hundred fifteen NSSAL 16 Draft

Whole Numbers and Number Lines (A) 1. Place each number at its approximate location on the number line. 7 18 5 21 12 0 20 2. Place each number at its approximate location on the number line. 62 30 24 11 56 0 60 3. Place each number at its approximate location on the number line. 14 18 36 9 22 10 30 4. Place each number at its approximate location on the number line. 32 27 37 21 17 5. Place each number at its approximate location on the number line. 62 20 40 95 48 20 40 0 100 NSSAL 17 Draft

Whole Numbers and Number Lines (B) 1. Place each number at its approximate location on the number line. 72 183 5 148 96 0 200 2. Place each number at its approximate location on the number line. 99 270 304 213 52 0 300 3. Place each number at its approximate location on the number line. 215 240 369 285 196 200 400 4. Place each number at its approximate location on the number line. 321 362 329 348 357 5. Place each number at its approximate location on the number line. 192 31 905 699 560 300 360 0 1000 NSSAL 18 Draft

Give an Example e.g. Give an example where the number 365 is used to represent something. Answer: There are 365 days in one year. 1. Give an example where the number 10 is used to represent something. 2. Give an example where the number 12 is used to represent something. 3. Give an example where the number 18 is used to represent something. 4. Give an example where the number 24 is used to represent something. 5. Give an example where the number 25 is used to represent something. 6. Give an example where the number 30 is used to represent something. 7. Give an example where the number 50 is used to represent something. 8. Give an example where the number 60 is used to represent something. 9. Give an example where the number 100 is used to represent something. 10. Give an example where the number 1000 is used to represent something. NSSAL 19 Draft

Closer To (A) Three whole numbers are provided. You are asked to determine whether the first number is closer to the second number or closer to the third number. Circle the correct answer. Two examples have been provided. e.g. Is 8 closer to 5 or 10? Answer: 10 e.g. Is 43 closer to 40 or 50? Answer: 40 1. Is 6 closer to 5 or 8? 2. Is 3 closer to 1 or 7? 3. Is 4 closer to 0 or 6? 4. Is 7 closer to 4 or 9? 5. Is 5 closer to 1 or 8? 6. Is 8 closer to 4 or 10? 7. Is 6 closer to 3 or 10? 8. Is 2 closer to 0 or 3? 9. Is 9 closer to 7 or 12? 10. Is 8 closer to 3 or 12? 11. Is 6 closer to 0 or 11? 12. Is 7 closer to 5 or 11? 13. Is 9 closer to 6 or 13? 14. Is 10 closer to 7 or 15? 15. Is 11 closer to 10 or 14? 16. Is 10 closer to 6 or 12? 17. Is 15 closer to 13 or 19? 18. Is 13 closer to 10 or 15? 19. Is 16 closer to 14 or 20? 20. Is 12 closer to 8 or 15? 21. Is 19 closer to 15 or 21? 22. Is 18 closer to 16 or 22? 23. Is 24 closer to 20 or 30? 24. Is 27 closer to 20 or 30? 25. Is 39 closer to 30 or 40? 26. Is 46 closer to 40 or 50? 27. Is 73 closer to 70 or 80? 28. Is 94 closer to 90 or 100? 29. Is 28 closer to 20 or 30? 30. Is 60 closer to 0 or 100? 31. Is 40 closer to 0 or 100? 32. Is 70 closer to 0 or 100? 33. Is 30 closer to 20 or 50? 34. Is 70 closer to 50 or 100? NSSAL 20 Draft

Closer To (B) Three whole numbers are provided. You are asked to determine whether the first number is closer to the second number or closer to the third number. Circle the correct answer. Two examples have been provided. e.g. Is 34 closer to 30 or 40? Answer: 30 e.g. Is 459 closer to 400 or 500? Answer: 500 1. Is 36 closer to 30 or 40? 2. Is 44 closer to 40 or 50? 3. Is 67 closer to 60 or 70? 4. Is 50 closer to 20 or 60? 5. Is 60 closer to 10 or 90? 6. Is 80 closer to 70 or 100? 7. Is 100 closer to 80 or 150? 8. Is 150 closer to 130 or 160? 9. Is 270 closer to 250 or 300? 10. Is 420 closer to 400 or 500? 11. Is 200 closer to 0 or 300? 12. Is 500 closer to 400 or 800? 13. Is 700 closer to 600 or 750? 14. Is 600 closer to 550 or 700? 15. Is 640 closer to 600 or 700? 16. Is 870 closer to 800 or 900? 17. Is 81 closer to 20 or 100? 18. Is 67 closer to 30 or 80? 19. Is 58 closer to 0 or 90? 20. Is 37 closer to 0 or 100? 21. Is 99 closer to 0 or 200? 22. Is 230 closer to 100 or 300? 23. Is 341 closer to 300 or 350? 24. Is 789 closer to 750 or 800? 25. Is 699 closer to 600 or 750? 26. Is 219 closer to 100 or 250? 27. Is 224 closer to 200 or 300? 28. Is 547 closer to 500 or 550? 29. Is 839 closer to 800 or 900? 30. Is 658 closer to 650 or 700? 31. Is 2399 closer to 2000 or 3000? 32. Is 1837 closer to 1000 or 2000? 33. Is 5643 closer to 5000 or 6000? 34. Is 2845 closer to 2000 or 4000? NSSAL 21 Draft

Operations with Whole Numbers NSSAL 22 Draft

Connect Four Addition Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 4 0 8 2 3 5 2 6 7 6 0 3 1 4 5 4 8 2 7 3 6 0 4 5 6 4 1 7 3 6 2 5 8 3 5 1 Addend Strip: 0 1 2 3 4 NSSAL 23 Draft

Connect Four Addition Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 10 12 7 13 8 11 9 11 10 12 6 13 6 14 9 11 10 9 8 11 12 7 14 11 13 10 8 6 9 10 9 7 14 10 12 8 Addend Strip: 3 4 5 6 7 NSSAL 24 Draft

Connect Four Addition Game (C) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Addend Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the addend strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 12 11 18 14 16 14 15 14 13 16 12 13 16 12 15 10 14 17 15 17 14 18 15 13 13 10 13 16 11 18 15 12 11 17 14 10 Addend Strip: 5 6 7 8 9 NSSAL 25 Draft

Connect Four Subtraction Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 7 8 5 7 6 9 4 9 7 3 10 5 5 6 8 4 6 7 10 8 5 3 7 8 6 4 7 9 5 6 9 8 3 10 6 4 Value 1: Value 2: 10 9 8 7 6 0 1 2 3 NSSAL 26 Draft

Connect Four Subtraction Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 5 4 2 4 6 3 3 6 7 3 0 5 0 4 1 5 2 1 4 2 6 3 7 4 3 5 4 0 3 2 2 7 2 1 5 6 Value 1: Value 2: 10 9 8 7 6 3 4 5 6 NSSAL 27 Draft

Connect Four Subtraction Game (C) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3 2 5 4 6 4 7 4 6 2 3 5 6 0 1 0 5 6 3 5 3 7 2 4 4 3 2 4 1 0 1 7 0 5 3 6 Value 1: Value 2: 13 12 11 10 9 6 7 8 9 NSSAL 28 Draft

Connect Four Subtraction Game (D) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate difference (i.e. Value 1 subtract Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same difference but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that difference using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3 5 4 5 6 5 6 8 7 9 10 7 9 7 6 3 5 9 7 10 5 7 8 4 8 6 9 4 9 3 4 7 8 10 5 6 Value 1: Value 2: 15 14 13 12 5 6 7 8 9 NSSAL 29 Draft

Subtraction Search There are twenty subtraction facts (e.g. 12-8 = 4) hidden in this grid. Check for three adjoining numbers that produce this fact. These numbers could be oriented horizontally, vertically, or diagonally. Circle the three adjoin numbers and record the fact below. Some of the facts cross over each other (e.g. vertical facts intersect with horizontal facts). 14 0 20 9 11 5 12 1 18 28 6 6 2 8 1 9 5 4 10 3 8 30 4 9 16 22 7 0 8 14 5 12 4 2 9 15 19 7 1 6 15 4 11 3 3 7 0 19 2 8 3 4 5 11 6 1 5 10 0 16 6 8 10 13 2 5 10 3 20 9 17 11 6 15 4 20 1 8 13 7 3 0 7 9 20 8 12 7 2 8 28 2 17 6 1 9 9 0 5 23 Subtraction Facts: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. NSSAL 30 Draft

Multiplication Models There are three common models used to represent the operation of multiplication. These are the area model, set model and number line model. An example of each has been provided below for the product of 3 and 4. Example: Mathematic al Sentence 3 4 12 Area Model Set Model Number Line Model A rectangle measuring 3 units by 4 units. 12 Three sets of four For each of the following, complete the mathematical statement and draw the three models. (a) 2 7 Area Model: Set Model: Number Line Model: (b) 6 3 Area Model: Set Model: Number Line Model: NSSAL 31 Draft

(c) 5 5 Area Model: Set Model: Number Line Model: (d) 7 4 Area Model: Set Model: Number Line Model: (e) 3 6 Area Model: Set Model: Number Line Model: NSSAL 32 Draft

Multiplication Array Game Roll two dice. Multiply the two numbers that are rolled and write down the mathematical sentence (e.g. 3 4 = 12) in the space provided. In the circular array recording sheet that has been provided, create an array using the rolled numbers. (e.g. 3 rows of 4, or 3 columns of 4). Once this is done, roll the dice again and repeat the procedure. The only thing is that the new array cannot overlap other array. Continue to roll the dice, write the sentences and draw the arrays until you are unable to draw new arrays (i.e. cannot be drawn without overlapping existing arrays). See how many arrays you can draw on the recording. It is a combination of luck and skill. Mathematical Sentence: Circular Array Recording Sheet: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Number of Arrays Drawn: NSSAL 33 Draft

Connect Four Multiplication Game A Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 9 2 5 45 15 0 3 0 15 6 18 45 0 18 9 27 10 5 18 27 2 10 9 3 3 10 0 15 4 6 45 2 6 3 10 27 Factor Strip: 0 1 2 3 5 9 NSSAL 34 Draft

Connect Four Multiplication Game B Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 45 27 5 45 8 10 0 36 18 20 15 36 8 12 4 0 36 2 18 45 27 6 12 20 4 15 0 10 9 27 12 3 6 36 20 Factor Strip: 0 1 2 3 4 5 9 NSSAL 35 Draft

Connect Four Multiplication Game C Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 18 2 30 8 12 24 9 54 12 18 10 6 24 5 8 6 54 20 10 30 18 5 24 3 24 4 20 12 2 18 12 54 9 30 5 8 Factor Strip: 1 2 3 4 5 6 9 NSSAL 36 Draft

Connect Four Multiplication Game D Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 14 63 6 28 15 30 42 12 30 63 14 10 8 21 54 18 54 21 35 15 8 28 42 12 18 54 14 63 6 35 10 28 42 12 21 18 Factor Strip: 2 3 4 5 6 7 9 NSSAL 37 Draft

Connect Four Multiplication Game E Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers on the Factor Strip whose product is that desired square. Once they have chosen the two numbers, they can capture one square with that appropriate product. They either mark the square with an X or place a colored counter on the square. There may be other squares with that same product but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on the Factor Strip. They then mark the square with that product using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved on the fraction strip in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 42 12 16 8 24 48 6 72 45 54 15 18 56 24 21 16 56 20 14 30 10 40 6 27 54 18 36 12 42 21 15 72 27 14 35 10 Factor Strip: 2 3 4 5 6 7 8 9 NSSAL 38 Draft

Connect Four Multiples Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place one paper clip on the appropriate "Multiple of" Strip and one paper clip on the appropriate "Range for Multiple" Strip. For example to capture a 32, the first paper clip could be on the "2" or "4" (because 32 is a multiple of 2 or 4), while the second paper clip must be on the "30 to 39" range (because 32 is within this range). They either mark the square with an X or place a colored counter on the square. Only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 27 12 38 28 15 22 26 30 14 36 34 10 35 24 33 20 16 25 18 10 12 32 24 32 38 21 35 25 12 18 15 32 27 16 21 36 "Multiple of" Strip: "Range for Multiple" Strip: 2 3 4 5 6 10 to 19 20 to 29 30 to 39 NSSAL 39 Draft

Connect Four Multiples Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place one paper clip on the appropriate "Multiple of" Strip and one paper clip on the appropriate "Range for Multiple" Strip. For example to capture a 45, the first paper clip could be on the "5" or "9" (because 45 is a multiple of 5 or 9), while the second paper clip must be on the "40 to 49" range (because 45 is within this range). They either mark the square with an X or place a colored counter on the square. Only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 28 36 45 44 25 36 45 24 35 21 30 27 30 49 32 40 48 42 48 42 20 49 36 24 36 27 45 35 21 32 20 35 24 42 30 28 "Multiple of" Strip: "Range for Multiple" Strip: 4 5 6 7 9 20 to 29 30 to 39 40 to 49 NSSAL 40 Draft

Connect Four Multiples Game (C) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place one paper clip on the appropriate "Multiple of" Strip and one paper clip on the appropriate "Range for Multiple" Strip. For example to capture a 56, the first paper clip could be on the "7" or "8" (because 56 is a multiple of 7 or 8), while the second paper clip must be on the "50 to 59" range (because 56 is within this range). They either mark the square with an X or place a colored counter on the square. Only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that product using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 36 49 64 42 36 45 66 32 45 56 35 63 40 54 63 30 66 48 60 64 42 54 36 56 48 30 35 63 40 42 36 56 54 32 60 35 "Multiple of" Strip: "Range for Multiple" Strip: 6 7 8 9 30 to 39 40 to 49 50 to 59 60 to 69 NSSAL 41 Draft

Capture the Flag Multiplication Game Mission: The winner is the first player to capture the opposing player's flag on the opposite side of the board. Rules: With this game each player starts with six markers on opposing sides of the board at the designated spots. Coins can be used as markers. For example, six pennies for one player, and six nickels for the other player. Each round a player can only move one marker one square either forwards, backwards, diagonally, or sideways. However, the player must know the multiplication fact to make that move. For example if the marker is first on a "2" square and wishes to move to a "5" square, then they must tell the other player that "2 times 5 is 10." If they do not know the fact, then they must choose another marker to move. Markers can move two spaces if they are jumping an opponent's marker and thus eliminating that marker. Again the player must know the multiplication fact associated with their starting square and their landing square. Each player is required to move a marker each round. Two markers cannot share the same square. There are a few squares that have "blockers" that limit movement and the opportunities to jump and eliminate markers. You are not permitted to guard your flag by placing one of your markers on your own flag. NSSAL 42 Draft

Player 2 Start Player 2 Start Player 2 Start Player 2 Start Player 2 Start Player 2 Start 2 6 7 10 7 6 2 3 8 4 5 9 5 4 8 3 0 10 1 6 4 6 1 10 0 9 3 2 7 2 3 9 3 4 5 6 7 6 5 4 3 8 7 10 4 4 10 7 8 3 4 5 6 7 6 5 4 3 9 3 2 7 2 3 9 0 10 1 6 4 6 1 10 0 3 8 4 5 9 5 4 8 3 2 6 7 Player 1 Start Player 1 Start Player 1 Start 10 7 6 2 Player 1 Start Player 1 Start Player 1 Start NSSAL 43 Draft

Random Multiplication Facts Quizzes Please note that there are three different types of quizzes (A, B & C). These three types correspond to the suggested order that the multiplication facts are taught. Quiz A1 Name: Quiz A2 Name: 2 7 5 8 4 1 5 0 9 2 5 2 0 1 9 7 0 8 6 3 Quiz A3 Name: Quiz A4 Name: 9 6 3 4 7 9 2 1 5 0 1 5 9 2 0 6 8 1 3 7 Quiz B1 Name: Quiz B2 Name: 8 3 2 7 6 5 3 4 1 9 4 9 0 3 5 8 2 4 7 6 NSSAL 44 Draft

Quiz B3 Name: Quiz B4 Name: 8 6 7 1 3 9 2 4 5 3 3 5 1 4 9 7 6 2 4 8 Quiz C1 Name: Quiz C2 Name: 8 7 5 6 3 6 4 8 2 7 6 9 2 8 7 4 8 6 9 7 Quiz C3 Name: Quiz C4 Name: 1 6 9 7 3 5 8 4 7 6 2 7 6 9 3 3 7 4 8 9 NSSAL 45 Draft

Multiplying on Your Hands Most people are OK with the multiplication facts with the numbers 0, 1, 2, 3, 4, and 5. Examples: 1 8 8 2 3 6 3 7 21 4 6 24 5 9 45 However, many people struggle remembering the facts for larger numbers (6, 7, 8, and 9). Examples: 6 7 42 7 7 49 8 6 48 8 8 64 9 7 63 There is a neat way to get these multiplication facts using your hands. First we need to identify the numbers associated with the fingers on your hands. 10 10 9 9 8 8 7 7 6 6 Example 1 Complete the following operation. 8 8? Step 1 Touch the appropriate fingers to find the multiplication fact. For example, if you wanted to work out 8 8, take finger eight from the left hand and touch it to finger eight from the right hand. NSSAL 46 Draft

Step 2 Count the number of fingers above the touching fingers on the left hand. In this case there are 2. Count the number of fingers above the touching fingers on the right hand. In this case there are 2. Now multiply these two numbers together ( 2 2 4 ) Step 3 Count the two touching fingers and all the fingers dangling below the touching fingers. In this case we have 6 fingers. Now multiply this number by 10 ( 6 10 60 ) Step 4 Add the two numbers that were generated in steps 2 and 3. 4 60 64 Therefore: 8 8 64 NSSAL 47 Draft

Example 2 Complete the following operation. 7 9? Step 1 Touch the correct fingers. Step 2 Count the fingers above the touching fingers left hand and count the fingers above the touching fingers on the right hand. Multiply these two numbers. 3 1 3 Step 3 Count the two touching fingers and all the fingers dangling below the touching fingers. Now multiply this number by 10. 6 10 60 Step 4 Add the numbers from steps 2 and 3 ( 3 60 63). Therefore: 7 9 63 NSSAL 48 Draft

Example 3 Complete the following operation. 6 7? Step 1 Step 2 4 3 12 Step 3 3 10 30 Step 4 Since12 30 42, then 6 7 42 "Hand" clipart by scarlett was downloaded on April 5, 2011 from http://www.clker.com/cliparthand-11.html NSSAL 49 Draft

Put the Number in the Right Box With each question you have been provided with a list of numbers. Place those numbers in the appropriate box found on the right. A sample question has been provided. e.g. List of Numbers Multiple of 4 Not a Multiple of 4 16, 12, 9, 5, 20, 6, Multiple of 3 12, 24, 36 9, 6, 27 24, 17, 8, 27, 22, 36 Not a Multiple of 3 16, 20, 8 5, 17, 22 1. List of Numbers Multiple of 2 Not a Multiple of 2 15, 4, 11, 6, 19, 18, 10, 14, 7, 12, 9, 21 Multiple of 3 Not a Multiple of 3 2. List of Numbers Multiple of 2 Not a Multiple of 2 19, 15, 10, 9, 16, 30, 22, 25, 18, 40, 45, 21 Multiple of 5 Not a Multiple of 5 3. List of Numbers Multiple of 3 Not a Multiple of 3 24, 20, 8, 15, 30, 9, 28, 25, 27, 40, 45, 26 Multiple of 5 Not a Multiple of 5 4 List of Numbers Multiple of 4 Not a Multiple of 4 16, 24, 21, 30, 9, 12, 8, 18, 6, 28, 15, 36 Multiple of 6 Not a Multiple of 6 5. List of Numbers Multiple of 5 Not a Multiple of 5 27, 25, 20, 12, 10, 40, 12, 19, 32, 80, 35, 28 Multiple of 4 Not a Multiple of 4 NSSAL 50 Draft

Investigation: Multiplying by Multiples of 10, 100, and 1000 Numbers are multiples of 10 if they can be expressed as a whole number multiplied by 10 e.g. 30 = 3 10 e.g. 70 = 7 10 e.g. 340 = 34 10 Numbers are multiples of 100 if they can be expressed as a whole number multiplied by 100. e.g. 300 = 3 100 e.g. 700 = 7 100 e.g. 3400 = 34 100 Numbers are multiples of 1000 if they can be expressed as a whole number multiplied by 1000. e.g. 3000 = 3 1000 e.g. 7000 = 7 1000 e.g. 34000 = 34 1000 In this section we will discover how we can multiply numbers that are multiples of 10, 100 and 1000. (e.g. 60 400 ). Use a calculator to work out the answers to the following two sets of questions. Look for a pattern. (Hint: Look at the number of zeros in each question.) First Set of Questions 4 2 40 2 4 20 40 20 400 2 4 200 400 20 40 200 4000 2 4 2000 Second Set of Questions 5 7 50 7 5 70 50 70 500 7 5 700 500 70 50 700 5000 7 5 7000 Questions 1. Based on the work that you have done above, what do you think the answers to each of these is. (Only use a calculator to check your answers.) (a) 4000 200 (b) 40 2000 (c) (e) (g) 5000 7000 (d) 500 7000 60 3 (f) 60 300 900 8 (h) 90 8000 2. Explain the rule that you have discovered. It may be easiest to do by looking at a specific question or questions (e.g. 40 70 2800, 400 7000 2800000, ) NSSAL 51 Draft

Multiplying by Multiples of 10, 100, and 1000 In the previous investigation, you discovered how to multiply numbers that are multiples of 10, 100, and 1000 (e.g. 60 400 24000). Here are two examples that cover the material that you learned in that investigation. Example 1 Evaluate 400 70. Answer: To work out 400 70, it is a three step process (i) Omitting the zeros, multiply the two numbers ( 4 7 28) (ii) Next count the number of zeros in the original question (There are 3; two from the number 400 and one from the 70) (iii) Take the product from step (a) and tack on the number of zeros from step (b). Therefore: 400 70 = 28 000 Example 2 Evaluate 800 6000. Answer: To work out 800 6000, it is a three step process. (i) Omitting the zeros, multiply the two numbers ( 8 6 48) (ii) Next count the number of zeros in the original question (There are 5; two from the number 800 and three from the 6000) (iii) Take the product from step (a) and tack on the number of zeros from step (b). Therefore: 800 6000 = 4 800 000 Questions: 1. Complete the operation and express the answer in written form. Two sample questions has been completed for you. Answer in Written Form e.g. e.g. (a) (b) (c) (d) (e) (f) 90 6000 540 000 five hundred forty thousand 70 30 2 100 two thousand one hundred 2000 600 9 4000 300 500 80 400 60 60 800 5 NSSAL 52 Draft

2. Complete the following operations. Do not use a calculator. (a) 20 70 (b) 9 60 (c) 400 30 (d) 5 5000 (e) 300 8 (f) 1000 400 (g) 90 7000 (h) 2000 6000 (i) 40 8 (j) 700 700 (k) 9 80 (l) 500 60 (m) 3000 90 (n) 7000 4 (o) 2000 900 (p) 80 500 (q) 800 6 (r) 1000 1000 (s) 2 4000 (t) 90 90 (u) 700 8000 (v) 80 800 (w) 5000 2000 (x) 90 8 (y) 100 900 (z) 7 5000 NSSAL 53 Draft

Multiplying Two Digit Numbers, Part 1 (Expanded Form) In order to complete this activity sheet, you should already know: 1. How to express a number in its expanded form e.g. 47 40 7 e.g. 392 300 90 2 2. How to multiply numbers that are multiples of 10, 100, or 1000. e.g. To work out 400 70 : (a) Omitting the zeros, multiply the two numbers ( 4 7 28) (b) Next count the number of zeros in the original question (There are 3; two from the number 400 and one from the 70) (c) Take the product from step (a) and tack on the number of zeros from step (b). Therefore: 400 70 = 28 000 e.g. To work out 800 6000 : (a) Omitting the zeros, multiply the two numbers ( 8 6 48) (b) Next count the number of zeros in the original question (There are 5; two from the number 800 and three from the 6000) (c) Take the product from step (a) and tack on the number of zeros from step (b). Therefore: 800 6000 = 4 800 000 Let's look at multiplying two digit numbers. The easiest way to do this is work through a sample problem. You may wish to view the following video that corresponds to the examples below. http://www.youtube.com/watch?v=gec_7v_upb4 (or Google Search: YouTube Multiplying Two Digit Numbers Part 1 (Expanded Form)) Example 1 Complete the following operation. 73 24 Answer: We first need to express the two numbers in their expanded forms. 73 = 70 + 3 24 = 20 + 4 Next we set the numbers up so that we can do the multiplication. Note that the 20 and the 4 must both be multiplied by the 70 and the 3. That means we have to do four sets of multiplication. 1 1 2 4 7 70 3 20 4 1 8 6 0 5 2 0 0 0 2 4 3; first set of multiplication 4 70 ; second set of multiplication 20 3; third set of multiplication 20 70 ; fourth set of multiplication Therefore: 73 24 1752 NSSAL 54 Draft

Example 2 Complete the following operation. 67 49 Answer: We first need to express the two numbers in their expanded forms. 67 = 60 + 7 49 = 40 + 9 Next we set the numbers up so that we can do the multiplication. 2 3 5 2 4 2 60 7 40 9 6 4 8 0 8 3 0 0 0 3 Therefore: 67 49 3283 Example 3 Complete the following operation. 84 57 Answer: 80 4 4 4 5 2 0 7 50 7 2 6 0 0 8 8 0 0 0 8 Example 4 Complete the following operation. 91 35 Answer: 90 1 2 3 4 7 1 30 5 8 5 3 0 5 5 0 0 0 The 9 must be multiplied by both the 60 and the 7. The 40 must be multiplied by both the 60 and the 7. The 7 must be multiplied by both the 80 and the 4. The 50 must be multiplied by both the 80 and the 4. The 5 must be multiplied by both the 90 and the 1. The 30 must be multiplied by both the 90 and the 1. NSSAL 55 Draft

Questions 1. The answer to 63 95 is partially completed. Fill in the four missing components. 60 3 90 5 The 5 must be multiplied by both the 60 and the 3. The 90 must be multiplied by both the 60 and the 3. 5 9 8 5 2. The answer to 74 38 is partially completed. Fill in the five missing components. 70 4 30 8 The 8 must be multiplied by both the 70 and the 4. The 30 must be multiplied by both the 70 and the 4. 3 Complete each of the operations. Only use a calculator to check your answers. (a) 26 43 (b) 57 35 NSSAL 56 Draft

(c) 29 71 (d) 53 83 (e) 79 36 (f) 83 41 (g) 48 61 (h) 72 79 NSSAL 57 Draft

4. In this section we have focused on multiplying two digit numbers using a specific technique. This technique, however, can be used to multiply even larger numbers. An example has been provided below. Look at this example and then multiply the numbers 436 and 72 on your own. Example: 651 37 =? 600 50 30 1 7 The two numbers are written in their expanded forms. 3 5 7 0 The 7 must be multiplied by the 600, 50, and 1. 4 2 0 0 1 5 3 0 0 0 The 30 must be multiplied by the 600, 50, and 1. 1 8 0 0 0 2 4 0 8 7 Now work out 436 72 in the space provided. NSSAL 58 Draft

Multiplying Two Digit Numbers, Part 2 (Lattice Method) Up to this point if we wanted to multiply two digit numbers, we had to write both numbers in their expanded form and then do the four sets of multiplication, and add the four numbers. For example, if we wanted to multiply 82 and 53, we would have to do the following. 4 82 = 80 + 2 Expanded Forms 53 = 50 + 3 80 2 Remember that the 3 must be multiplied by both the 80 and 2. The same is true with the 50; it must also be multiplied by the 50 3 80 and 2. 6 2 1 0 4 0 0 0 0 0 4 3 4 6 Therefore: 82 53 4346 There is an alternate method that is directly tied to the technique but it is much easier and faster. It involves using a two column two row chart where each cell is divided in two by a diagonal. You can view explanations that correspond to examples 1 and 2 by going to the following website. http://www.youtube.com/watch?v=yt2atjulffy (or Google Search: YouTube Multiplying Two Digit Numbers (Lattice Method)) Example 1 Complete the following operation. 82 53 We can use the following chart to multiply two digit numbers. We put the 82 along the top of the chart, and the 53 along the right side of the chart 8 2 5 3 NSSAL 59 Draft

Multiply the 5 by the 8, and place the two digits of the product (40) in the two spaces in the upper left hand corner of the chart. 8 2 4 0 5 3 Now multiply the 5 by the 2, and place the two digits of the product (10) in the two spaces in the upper right hand corner of the chart. 8 2 4 0 1 0 5 3 Repeat this procedure by multiplying the 3 by the 8 (product: 24), the 3 by 2 (product: 6), and fill in the appropriate spaces in the chart. 8 2 4 0 1 0 5 2 0 4 6 3 NSSAL 60 Draft

Now ignore the 82 and 53 along the outside of our chart. Starting at the bottom, add the numbers along each diagonal placing the answer along the outer edge of the chart. If a sum exceeds 9, carry the tens digit up to the next diagonal (This does not occur in this example.). 4 4 0 1 0 3 2 0 4 6 Start here and work your way up to the next diagonal. 4 6 These numbers along the outside, starting at the upper left, represent the digits of your product. Therefore: 82 53 4346 Example 2 Complete the following operation. 34 26 3 4 6 3 4 0 0 2 2 6 8 1 2 8 4 0 6 8 34 26 = 884 0 6 1 8 8 0 8 2 4 4 carry 1 Example 3 Complete the following operation. 71 65 7 1 4 0 6 6 2 6 5 7 1 3 0 5 5 4 5 6 71 65 = 4615 4 2 3 5 1 0 6 0 5 5 carry 1 NSSAL 61 Draft

Example 4 Complete the following operation. 68 95 carry 1 6 8 5 6 8 5 7 9 9 4 2 3 4 0 0 6 5 4 68 95 = 6460 5 4 3 0 6 7 2 4 0 0 Why Does this Work? Let's take the last example and do it another way where we express 68 as 60 + 8, and 95 as 90 + 5. When we multiply these expanded forms of the numbers, make sure the 5 is multiplied by both the 60 and 8, and similarly the 90 must be multiplied by both the 60 and 8. 5 6 3 7 4 4 60 8 90 5 4 0 2 0 6 0 0 0 0 0 Notice how the columns in the first technique match up to the diagonals in the second technique. The nice thing about the second technique is that it takes care of the place values (units, tens, hundreds, and thousands) for us. 6 4 5 3 6 4 0 7 4 2 0 0 68 95 = 6460 NSSAL 62 Draft

Questions 1. Multiply the numbers using the chart provided. (a) 32 75 (b) 41 36 (c) 92 81 (d) 74 24 (e) 67 18 (f) 58 36 NSSAL 63 Draft

2. Work out 57 38 using both techniques (The chart has not been provided; you must draw your own.). Which technique do you prefer? 3. Complete the following operations. (a) 42 46 (b) 52 71 (c) 39 72 (d) 84 37 NSSAL 64 Draft

Multiplying Multi-Digit Numbers On previous activity sheets, you learned how to multiple two digit numbers using two techniques. Those same techniques can be used with numbers having three or more digits, and as before, the second technique (i.e. chart method) is far easier and faster. You may wish to view the following video. http://www.youtube.com/watch?v=vzohbbtvs-0 (or Google Search: YouTube Multiplying Multi-Digit Numbers (Lattice Method)) Example 1 Complete the operation. 382 57 Answer: First Technique (Expanded Form with Repeated Multiplication) 300 1 2 4 5 80 50 5 1 1 0 0 1 6 0 0 0 0 2 7 4 0 0 0 0 0 The two numbers are written in their expanded forms. The 7 must be multiplied by the 300, 80, and 2. The 50 must be multiplied by the 300, 80, and 2. 2 1 7 7 4 Therefore: 382 57 21 774 Answer: Second Technique (Chart Method) Our chart will have three columns because one number is a three digit number. The chart will have two rows because the other number is a two digit number. Remember that each cell is divided in two by a diagonal. 3 8 2 5 7 We could have set the chart up so that it had two columns and three rows. If that was the case, then 57 would be along the top and 382 would be down along the right side. NSSAL 65 Draft

We will now multiply the numbers. 3 8 2 1 5 4 0 1 0 5 2 1 5 6 1 4 7 Now ignore the 382 and 57 along the outside of our chart. Starting at the bottom, add the numbers along each diagonal placing the answer along the outer edge of the chart. If a sum exceeds 9, carry the tens digit up to the next diagonal. Carry 1 2 1 5 4 0 1 0 1 2 1 5 6 1 4 7 7 4 Therefore: 382 57 21 774 Example 2 Complete the following operation using the chart method. 725 613 Answer: Set up the chart with the three digit numbers along the sides and do the multiplication. 4 7 2 2 5 1 3 2 0 6 0 0 0 7 2 5 1 2 1 0 6 1 5 3 NSSAL 66 Draft

Ignore the numbers along the sides, and add the numbers along the diagonals. Carry 1 4 1 3 Carry 1 4 2 2 0 4 0 0 0 7 2 5 4 2 1 0 6 1 5 Therefore: 725 613 = 444 425 Example 3 Complete the following operation using the chart method. 9271 46 Answer: 4 2 5 9 2 7 1 3 6 0 2 8 8 0 4 4 5 1 4 0 4 2 2 6 6 Carry 1 Carry 1 Carry 1 4 3 6 0 2 8 8 0 4 5 1 4 0 2 4 2 2 6 6 4 6 6 Therefore: 9271 46 = 426 466 NSSAL 67 Draft

Questions: 1. Complete the following operations using the chart provided. (a) 453 62 (b) 571 245 (c) 4372 59 2. Complete the operations. (a) 45 623 (b) 341 908 NSSAL 68 Draft

Connect Four Division Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place two paper clips on two numbers; one from Value 1 and one from Value 2. Once they have chosen the two numbers, they can capture one square with that appropriate quotient (i.e. Value 1 divided by Value 2). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same quotient but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that quotient using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 24 12 15 12 2 8 3 6 30 4 15 18 12 10 9 8 12 6 8 2 24 6 9 30 4 15 12 4 3 6 18 9 2 10 18 Value 1: Value 2: 30 24 18 12 6 1 2 3 NSSAL 69 Draft

Division Search There are twenty division facts (e.g. 12 6 = 2) hidden in this grid. Check for three adjoining numbers that produce this fact. These numbers could be oriented horizontally, vertically, or diagonally. Circle the three adjoin numbers and record the fact below. Some of the facts cross over each other (e.g. vertical facts intersect with horizontal facts). 30 2 48 6 8 0 18 14 5 9 5 28 15 11 2 33 9 13 3 9 32 4 8 5 9 17 2 27 6 1 11 7 1 5 3 10 5 2 31 0 24 64 45 3 45 4 19 1 42 23 21 8 9 25 7 16 4 4 6 7 1 8 3 0 5 12 43 8 7 36 20 4 5 27 1 5 4 1 5 6 4 56 8 7 22 9 8 0 12 6 3 0 18 5 36 8 18 2 9 25 Division Facts: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. NSSAL 70 Draft

Divisibility Chart You need three colored pencils (red, yellow, and blue) to complete this activity. Each number between 1 and 60 has three blocks below it. Using a calculator, determine whether the number is divisible by 2, 3, and/or 5. If the number is divisible by 2, shade the first block below the number red. If the number is divisible by 3, shade the second block below the number yellow. If the number is divisible by 5, shade the third block below the number blue. For example, the number 15 is both divisible by 3 and 5, therefore its second block is shaded yellow, and its third block is shaded blue. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Now that the chart is complete, look for patterns. Look at all the numbers that are divisible by 2. How can you determine if a number is divisible by 2 by just looking at the number (versus using a calculator)? Look at all the numbers that are divisible by 3. How can you determine if a number is divisible by 3 by just looking at the number (versus using a calculator)? (Hint: Consider adding the digits.) Look at all the numbers that are divisible by 5. How can you determine if a number is divisible by 5 by just looking at the number (versus using a calculator)? NSSAL 71 Draft

More Divisibility (A) You have already learned how to identify numbers that are divisible by 2, 3, and 5. Numbers that are divisible by 2 are even numbers. e.g. 6, 34, 798, 2050, and 3942 are all divisible by 2 Questions: If the sum of the digits of a multi-digit number produces a number that is divisible by three, then the original multi-digit number is divisible by 3. e.g. 561 is divisible by 3 because 5 + 6 + 1 = 12 and 12 is divisible by 3. If the ones digit is a 0 or a 5, then the number is divisible by 5. e.g. 75, 120, 375, and 2960 are all divisible by 5. 1. Beside each number you will find a box corresponding to a number that might divide evenly into the original number. Check off the appropriate boxes to identify whether the original number is divisible by 2, 3, and/or 5. Do not use a calculator. 2 3 5 2 3 5 e.g. 78 e.g. 345 (a) 64 (b) 35 (c) 81 (d) 90 (e) 40 (f) 42 (g) 105 (h) 307 (i) 208 (j) 635 (k) 915 (l) 410 (m) 720 (n) 816 (o) 1245 (p) 2036 (q) 4109 (r) 7281 (s) 9130 (t) 3075 (u) 8374 (v) 7320 2. (a) Create 4 three-digit numbers that are divisible by 2 and 5 (but not 3). Do not use numbers encountered in question 1. (b) Create 4 three-digit numbers that are divisible by 2 and 3 (but not 5). Do not use numbers encountered in question 1. NSSAL 72 Draft

More Divisibility (B) You have already learned how to identify numbers that are divisible by 2, 3, and 5. Numbers that are divisible by 2 are even numbers. If the sum of the digits of a multi-digit number produces a number that is divisible by three, then the original multi-digit number is divisible by 3. If the ones digit is a 0 or a 5, then the number is divisible by 5. Did you know that if a number is divisible by both 2 and 3, then that number is also divisible by 6? Did you know that if a number is divisible by both 2 and 5, then that number is also divisible by 10? Did you know that if a number is divisible by both 3 and 5, then that number is also divisible by 15? Questions: 1. Beside each number you will find a box corresponding to a number that might divide evenly into the original number. Check off the appropriate boxes to identify whether the original number is divisible by 2, 3, 5, 6, 10, and/or 15. Do not use a calculator. 2 3 5 6 10 15 e.g. 220 e.g. 315 (a) 12 (b) 45 (c) 30 (d) 14 (e) 36 (f) 19 (g) 430 (h) 114 (i) 207 (j) 96 (k) 225 (l) 600 (m) 704 (n) 425 NSSAL 73 Draft

(o) 408 (p) 570 (q) 615 (r) 1078 (s) 2310 (t) 7131 (u) 8706 (v) 5603 (w) 4700 (x) 6125 (y) 3210 2 3 5 6 10 15 2. (a) Create 4 three-digit numbers that are divisible by 2, 3, and 6 (but not 5, 10, or 15). Do not use numbers encountered in question 1. (b) Create 4 three-digit numbers that are divisible by 3, 5, and 15 (but not 2, 6, or 10). Do not use numbers encountered in question 1. (c) Create 4 four-digit numbers that are divisible by 3 (but not 2, 5, 6, 10, or 15). Do not use numbers encountered in question 1. 3. Fill in the blanks. (a) If a number is divisible by both 2 and 7, then that number is also divisible by. (b) If a number is divisible by both 3 and 11, then that number is also divisible by. (c) If a number is divisible by both 5 and 6, then that number is also divisible by. NSSAL 74 Draft

Divisibility or Prime Connect Four Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place one paper clip on the Tens strip and one paperclip on the Ones strip. They have now generated a two digit number. That two digit number is either divisible by a single digit whole number greater than 1 (i.e. 2, 3, 4, 5, 6, 7, 8, 9), or the number is a prime. The player captures a single square that describes the number. For example if the two digit number is 14, it is divisible by 2 or 7 (of the choices we are given), then the player can capture either a square with a 2 on it, or a square with a 7 on it. If the number is prime, then a square marked P can be captured. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips on either the Tens or Ones strip. They then mark the square that describes that number using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 6 4 7 2 6 3 P 9 6 8 P 2 5 3 P 5 4 9 4 8 9 7 3 2 7 2 4 6 8 P 6 P 9 3 2 5 Tens Strip: Ones Strip 1 2 3 1 2 4 5 6 8 NSSAL 75 Draft

Division with Remainders Up to this point, we have only worked with division questions that worked out evenly (i.e. no remainders). Examples of this are shown below. 14 7 2 21 3 7 45 5 9 64 8 8 70 10 7 But what happens when division questions do not work out evenly. 19 7? 22 3? 44 5? 67 8? 78 10? With these types of questions, we have to talk about remainders. Consider the examples that follow. Example 1 Complete the operation: 9 4 Answer: We are going to show you three ways to solve this question. You are only required to learn the third method (i.e. most efficient method). We have shown the first two methods so that you understand why the third method works. Method 1: Sharing Items Suppose you had 9 apples that you had to share evenly between 4 people. How many apples would each person get? Are there any apples left over? Each person gets 2 apples, and 1 apple is left over. This 1 apple is what remains. Therefore we can conclude that: 9 4 2 with a remainder of 1. This can also be written as 9 4 2, R:1 Method 2: Using Cuisenaire Rods Take the Cuisenaire rod for 9 (color: blue) and figure out how many Cuisenaire rods for 4 (color: purple) fit into it. Since your exercise sheet is photocopied in black and white, we have used two different textures so that you can distinguish the two types of rods Rod Representing 9: Rod Representing 4: We can place two purple rods (i.e. rods representing 4) on top of the blue rod (i.e. rod representing 9), but they don't cover the whole thing. A small portion, which is 1 unit long, is sticking out. 4 4 NSSAL 76 Draft

So 2 sets of 4 fit into 9, with 1 left over. That means that 9 4 is equal to 2 with a remainder of 1. This is written as 9 4 2, R:1 (Same answer that we got when we used the sharing items method.) Method 3: Using the Rule Four does not divide evenly into 9, so start by finding the closest number to 9 that is smaller than 9 which 4 does divide evenly into. That number is 8 8 4 2. Now find the difference between the 8 and 9. The difference is 1 9 8 1. This difference is our remainder. Therefore: 9 4 2, R:1 Example 2 Complete the operation: 10 3 Answer: Method 1: Sharing Items Suppose you had 10 apples that you had to share evenly between 3 people. How many apples would each person get? Are there any apples left over? Method 2: Using Cuisenaire Rods Take the Cuisenaire rod for 10 (color: orange) and figure out how many Cuisenaire rods for 3 (color: lime green) fit into it. Since your exercise sheet is photocopied in black and white, we have used two different textures so that you can distinguish the two types of rods Rod Representing 10: Rod Representing 3: Each person gets 3 apples, and 1 apple is left over. This 1 apple is what remains. Therefore we can conclude that: 10 3 3 with a remainder of 1. This can also be written as 10 3 3, R:1 We can place three lime green rods (i.e. rods representing 3) on top of the orange rod (i.e. rod representing 10), but they don't cover the whole thing. A small portion, which is 1 unit long, is sticking out. 3 3 3 So 3 sets of 3 fit into 10, with 1 left over. That means that 10 3 is equal to 3 with a remainder of 1. This is written as 10 3 3, R:1 (Same answer that we got when we used the sharing items method.) NSSAL 77 Draft

Method 3: Using the Rule Three does not divide evenly into 10, so start by finding the closest number to 10 that is smaller than 10 which 3 does divide evenly into. That number is 9 9 3 3. Now find the difference between the 9 and 10. The difference is 1 10 9 1. This difference is our remainder. Therefore: 10 3 3, R:1 For the remaining examples, we will use the "Rule" to obtain our answer. This is the method we would like you to use when you complete the exercise questions. Example 3 Complete the following division questions. (a) 19 7 (b) 22 3 (c) 44 5 (d) 67 8 Answers: (a) Start by finding the closest number to 19 that is smaller than 19 which 7 does divide evenly into. That number is 14 14 7 2. Now find the difference between the 19 and 14. The difference is 5 19 14 5. This difference is our remainder. Therefore: 19 7 2, R:5 (b) If 21 3 7, and 22 21 1, then 22 3 7, R:1 (c) If 40 5 8, and 44 40 4, then 44 5 8, R:4 (d) If 64 8 8, and 67 64 3, then 67 8 8, R:3 Questions: 1. Complete the following division. Most, but not all, of these questions involve remainders. (a) 13 5 (b) 7 2 (c) 14 3 (d) 18 3 (e) 33 7 (f) 43 8 (g) 25 6 (h) 19 2 (i) 29 3 NSSAL 78 Draft

(j) 40 6 (k) 42 7 (l) 22 5 (m) 60 9 (n) 31 8 (o) 13 4 (p) 38 5 (q) 48 9 (r) 32 4 (s) 18 4 (t) 19 6 (u) 54 5 (v) 35 8 (w) 50 7 (x) 69 9 2. There are twenty apples to share equally between six people. How many apples does each person get? How many apples are left over? NSSAL 79 Draft

Long Division (Partial Quotient Method) Division can be thought as "splitting a number into equal parts." Another way of thinking about division is to say "how many times can one number be subtracted from another number" (i.e. repeated subtraction). e.g. 12 4 =? "Splitting a Number into Equal Parts" "Repeated Subtraction" 12-4 - 4-4 = 0 We were able to split the number 12 into four equal parts of three; therefore 12 4 = 3 Taking these approaches with larger numbers is far too difficult and time-consuming. e.g. 52 4 =? We were able to subtract 4 from 12, three times. Therefore 12 4 = 3 "Splitting a Number into Equal Parts" We were able to split the number 52 into four equal parts of thirteen; therefore 52 4 = 13 NSSAL 80 Draft

"Repeated Subtraction" 52-4 - 4-4 - 4-4 - 4-4 - 4-4 - 4-4 - 4-4 = 0 We were able to subtract 4 from 52, thirteen times. Therefore 52 4 = 13 Now there is the traditional algorithm for long division that some of you may have learned in the past, but we are going to use a different approach called the Partial Quotient Method. The biggest problem with the traditional method is that on it is very easy to make a mistake, there is only one way to complete the question, and that learners often do not understand why the procedure works. The Partial Quotient Method tends to make more sense because it relies on repeated subtraction, and allows learners to use multiple ways to obtain the correct answer. To use this technique, you must have a good grasp of your multiplication facts, be able to multiply by multiples of 10, 100, and 1000, and be able to subtract multi-digit numbers. These are all things that we have done in previous lessons. Example 1 Solve 2856 8 Answer: 8 8 2856 1600 2856 1600 1256 200 200 How many times does 8 go into 1600? This learner goes with 200 because he/she knows that 8 200 1600. (The learner could have gone with a larger number like 300, but it does not matter with this method.) Now he/she subtracted 1600 from 2856. 8 2856 1600 1256 800 8 2856 1600 1256 800 456 200 100 200 100 How many times does 8 go into 1256. This learner goes with 100 because he/she knows that 8 100 800. Now he/she subtracted 800 from 1256. NSSAL 81 Draft

8 2856 1600 1256 800 456 400 8 2856 1600 1256 800 456 400 56 200 100 50 200 100 50 How many times does 8 go into 456. This learner goes with 50 because he/she knows that 8 50 400. Now he/she subtracted 400 from 456. 8 2856 1600 1256 800 456 400 56 56 0 200 100 50 7 How many times does 8 go into 56. This learner goes with 7 because he/she knows that 8 7 56. After we filled in the 56, we did the subtraction and found that we had a remainder of 0. That means 8 divides evenly into 2856. 357 In our last step the learner simply adds 200, 100, 50, and 7. That 8 2856 means that the quotient is 357. 1600 1256 800 456 400 56 56 0 200 100 50 7 2856 8 = 357 NSSAL 82 Draft

View the following YouTube video that walks you through Examples 2 and 3. http://www.youtube.com/watch?v=yx4vru233zu (or Google Search: YouTube Long Division (Partial Quotient Method) nsccalpmath) Example 2 Solve 4785 7 Answer: We have shown you three solutions to this question. The first student was the most efficient because he/she did the question in the fewest number of steps, however, all of the students have correct answers. That is the great thing about the partial quotient method; there is more than one way to do it right. In this case, 7 does not go evenly into 4785; we have a remainder of 4 when we complete the division. First Learner: Second Learner: Third Learner: 683 R: 4 683 R: 4 683 R: 4 7 4785 7 4785 7 4785 4200 585 560 25 21 4 600 80 3 2800 1985 1400 585 560 25 21 4 400 200 80 3 4200 585 350 235 210 25 21 4 600 50 30 3 NSSAL 83 Draft

Example 3 Solve 31 654 9 Answer: We have again supplied multiple solutions; all of them are correct. First Learner Second Learner: Third Learner: 3517 R: 1 3517 R: 1 3517 R: 1 9 31654 9 31654 9 31654 27000 4654 4500 154 90 64 63 1 3000 500 10 7 18000 13654 9000 4654 3600 1054 900 154 90 64 63 1 2000 1000 400 100 10 7 27000 4654 4500 154 90 64 45 19 18 1 3000 500 10 5 2 Questions Complete each of the division questions. Show all of your work. 1. 2. 5 3185 4 2064 NSSAL 84 Draft

3. 4. 3 2256 6 1524 5. 6. 4 1489 5 4642 7. 8. 9 3479 7 4609 NSSAL 85 Draft

9. 10. 8 4664 6 5236 11. 12. 4 3833 3 2903 13. 14. 5 13705 3 12651 NSSAL 86 Draft

15. 16. 4 22945 6 28581 17. 18. 7 25144 9 58712 19. 20. 8 41738 9 65745 NSSAL 87 Draft

Prime Factorization Prime numbers are numbers that are only divisible by one or itself. The first eight prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. Factors are numbers that multiply together to get another number. For example, the numbers 3 and 4 are factors of 12 because 3 4 12. The numbers 2 and 6 are also factors of 12 because 2 6 12. Prime factorization is the process of finding the prime numbers that multiply together to make another number. Example Determine the prime factors of each of the following. (a) 12 (b) 40 (c) 150 Answers: We these questions, there are often multiple ways of arriving at the final answer. (a) Method 1: In this case the learner starts by expressing 12 as the product of 2 and 6. 12 2 6 The learner then realizes that 6 is not a prime number, so proceeds to factor the 6. 12 2 6 12 2 2 3 12 2 2 3 Final Answer Method 2: In this case the learner starts by expressing 12 as the product of 3 and 4. 12 3 4 The learner then realizes that 4 is not a prime number, so proceeds to factor the 4. 12 3 4 12 3 2 2 12 2 2 3 Final Answer The two learners got the same answer even though they started out on slightly different paths. (b) 40 8 5 40 2 4 5 8 is not prime so it's expressed as 2 4 40 2 4 5 40 2 2 2 5 4 is not prime so it's expressed as 2 2 40 2 2 2 5 Final Answer (c) 150 15 10 150 3 5 2 5 Neither 15 nor 10 is a prime number 150 2 3 5 5 Final Answer NSSAL 88 Draft

Questions 1. Determine the prime factors for each of the following. (a) 6 (b) 21 (c) 10 (d) 35 (e) 49 (f) 26 (g) 33 (h) 20 (i) 44 (j) 42 (k) 45 (l) 66 (m) 30 (n) 70 (o) 27 (p) 63 (q) 110 (r) 18 (s) 16 (t) 100 (u) 36 (v) 250 (w) 81 (x) 24 NSSAL 89 Draft

Multiple Operations (Whole Numbers) NSSAL 90 Draft

Express the Number in Multiple Ways For each number, express it as: At least two number sentences involving addition, At least two number sentences involving subtraction, At least two number sentences involving multiplication, At least two number sentences involving division, and At least three written sentences. (Please note that answers will vary from learner to learner.) Example: Number 10 Two number sentences involving addition: 6 4 10, 5 5 10 Two number sentences involving subtraction: 12 2 10, 29 19 10 Two number sentences involving multiplication: 1 10 10, 2 5 10 Two number sentences involving division: 30 3 10, 80 8 10 Three written sentences: The number is three more than seven The number is half of twenty. The number is five times bigger than two. Questions (a) Number 4 (b) Number 6 (c) Number 8 (d) Number 9 NSSAL 91 Draft

Name the Preceding or Next Fill in the blank with the missing number. Two examples have been completed to assist you. e.g. Name the next even number to each of the following. (a) 36 : (b) 74 : (c) 88 : Answers: (a) 36 : 38 (b) 74 : 76 (c) 88 : 90 e.g. Name the preceding multiple of five. (a) 45 : (b) 30 : (c) 100 : Answers: (a) 45 : 40 (b) 30 : 25 (c) 100 : 95 1. Name the next odd number to each of the following (a) 47 : (b) 63 : (c) 29 : 2. Name the preceding even number to each of the following. (a) 36 : (b) 58 : (c) 50 : 3. Name the preceding multiple of five to each of the following. (a) 35 : (b) 20 : (c) 55 : 4. Name the next multiple of ten to each of the following. (a) 60 : (b) 30 : (c) 90 : 5. Name the next multiple of three to each of the following. (a) 21 : (b) 15 : (c) 27 : 6. Name the preceding multiple of four to each of the following. (a) 36 : (b) 28 : (c) 16 : 7. Name the preceding multiple of three to each of the following. (a) 15 : (b) 9 : (c) 27 : 8. Name the next multiple of four to each of the following. (a) 28 : (b) 20 : (c) 4 : 9. Name the next multiple of six to each of the following. (a) 24 : (b) 42 : (c) 18 : NSSAL 92 Draft

One of these Things is Not Like the Others With each of these questions, you must identify which one of the four does not belong. You must also explain why that one does not belong and why the remaining three belong together. (Hint: Think about odd and even, prime and composite, divisibility, patterns, perfect squares ) e.g. 13 15 2 9 The 2 does not belong because it is an even number and the remaining numbers, 13, 15, and 9, are all odd numbers. 1. 10 7 12 4 2. 5 12 6 9 3. 15 6 8 11 4. 3, 5, 7, 9, 11 1, 2, 4, 8, 16, 2, 7, 12, 17, 22, 1, 4, 7, 10, 13, 5. 25 9 16 6 NSSAL 93 Draft

6. 22 15 40 55 7. 17 7 9 19 8. 31, 34, 37, 40, 18, 21, 24, 27 66, 63, 60, 57, 52, 55, 58, 61, 9. dozen 4 + 4 + 4 2 6 fourteen 10. one hundred five twenty-six eighty-seven fifty-two 11. 8 + 7 10-5 5 3 17-2 12. ninety-nine 90 +9 9 9 one less than 100 NSSAL 94 Draft

Fact Family Puzzle (Multiplications and Division) Print the following onto rigid paper, cut each fact family into four puzzle pieces, shuffle all the family facts together, and ask the learners to sort them into their appropriate families. 3 4 4 3 2 7 7 2 12 3 12 4 14 2 14 7 5 6 6 5 8 1 1 8 30 5 30 6 8 8 8 1 2 9 9 2 4 6 6 4 18 2 18 9 24 4 24 6 NSSAL 95 Draft

3 5 5 3 6 9 9 6 15 3 15 5 54 6 54 9 8 4 4 8 3 7 7 3 32 8 32 4 21 3 21 7 8 6 6 8 6 7 7 6 48 8 48 6 42 6 42 7 NSSAL 96 Draft

Pathways Find the pathway from the upper left hand corner to the lower right hand corner of each grid by moving to equivalent and adjacent squares (i.e. squares to the left, right, top, or bottom). Start Start 2 4 7 3 9 1 9 7 24 8 12 2 9 3 3 2 24 3 7 1 16 2 6 2 6 4 3 6 11 1 5 3 4 3 10 4 4 4 8 8 7 2 12 4 8 3 19 7 18 2 6 1 18 3 5 1 7 7 9 2 9 2 4 2 3 5 12 4 3 2 0 6 18 6 4 5 8 1 7 5 7 6 16 4 32 4 8 1 9 1 15 9 3 3 30 5 8 2 4 2 Finish Finish Start Start 15 3 8 2 9 6 15 3 25 5 9 2 21 3 18 1 17 6 2 8 6 6 10 2 7 9 8 6 15 3 1 19 3 3 9 9 24 6 6 6 12 1 7 8 8 4 12 1 2 6 32 4 0 6 36 9 13 5 27 3 18 6 3 4 20 8 7 4 0 12 28 9 35 7 4 10 6 3 19 4 7 6 21 7 8 9 18 4 9 3 10 8 12 7 17 1 7 11 18 0 Finish Finish NSSAL 97 Draft

Two of These Boxes Just Don't Belong (A) Three boxes in each row have the same answers; the remaining two boxes just don't belong. Circle the three boxes in each row that have the same answers. 1. 5 1 10 2 2 3 6 + 1 9-4 2. 4 + 3 5-2 21 3 8 + 1 11-4 3. 8-5 10-4 24 4 3 2 9 + 6 4. 20-2 17-7 3 3 40 4 2 5 5. 4 4 5 + 3 4 2 12-2 40 5 6. 15-4 8 + 6 33 3 11 1 3 4 7. 13 + 4 30 2 7 3 20-5 5 3 8. 6 2 12-2 4 3 7 + 8 9 + 3 9. 19-6 5 4 14 + 6 40 2 22 2 10. 21-3 8 2 6 + 7 3 6 9 + 9 NSSAL 98 Draft

Two of These Boxes Just Don't Belong (B) Three boxes in each row have the same answers; the remaining two boxes just don't belong. Circle the three boxes in each row that have the same answers. 1. 3 3 8 3 36 4 12-5 4 + 5 2. 30 + 20 4 10 15 2 5 8 80 2 3. 8 2 20-4 24 4 4 4 15-1 4. 9 + 5 12-2 28 2 2 7 14 0 5. 4 7 90 3 26+4 40-20 5 6 6. 25 + 25 60-20 40 + 20 100 2 5 10 7. 100-20 90-30 20 3 120 2 70 + 10 8. 20-4 40 4 240 3 10 8 50 + 30 9. 0 + 0 50-50 9 1 7 7 0 8 10. 50 + 60 2 + 45 3 30 450 5 100-10 NSSAL 99 Draft

Equivalent Determine the missing number. Example 1: 5 6 3 The answer is 10 because 5 6 and 3 10 both equal 30. Example 2: 6 8 2 The answer is 7 because 6 8 and 7 2 both equal 14. Part 1 (a) 4 6 2 (b) 9 3 7 (c) 8 8 12 (d) 5 4 3 (e) 6 8 7 (f) 5 8 11 Part 2 (a) 12 2 14 (b) 14 7 11 (c) 9 3 1 (d) 24 3 29 (e) 18 3 20 (f) 17 6 4 Part 3 (a) 2 6 3 (b) 5 4 2 (c) 8 2 4 (d) 5 8 4 (e) 6 4 8 (f) 4 9 6 Part 4 (a) 24 3 16 (b) 30 5 2 (c) 14 2 28 (d) 42 7 5 (e) 27 9 15 (f) 70 7 4 Part 5 (a) 4 7 20 (b) 16 4 9 (c) 5 7 39 (d) 72 9 11 (e) 6 6 32 (f) 4 5 54 (g) 15 10 30 (h) 9 7 64 (i) 1 6 3 (j) 19 3 8 (k) 39 3 6 (l) 15 7 32 (m) 7 3 26 (n) 56 8 3 (o) 18 3 3 (p) 8 0 9 (q) 7 5 4 (r) 32 8 10 (s) 45 9 3 (t) 7 7 4 (u) 23 7 6 (v) 9 1 16 (w) 42 7 6 (x) 9 3 5 NSSAL 100 Draft

Venn Diagrams and Whole Numbers A Venn diagram, which is normally comprised of overlapping circles, is used to show relationships between different things. For this activity we are going to use them to illustrate relationships between different whole numbers. Suppose a learner is given the numbers 3, 5, 6, 9, 12, 11, 14, 16, 20, 21, and 23. They are asked to take those numbers and identify those that are divisible by 2, and those that are divisible by 3. Now some of these numbers (e.g. 5, 11, 23) are not divisible by either 2 or 3. Some numbers (e.g. 14, 16, 20) are only divisible by 2, others (e.g. 3, 9, 21) are divisible by only 3, and still others (e.g. 6, 12) are divisible by both 2 and 3. A Venn diagram, like the shown on the right, can be used to illustrate this. With the questions below, you have been given an incomplete Venn diagram and a list of numbers. Your mission is to place the numbers correctly in the Venn diagram. 1. List: 4, 5, 8, 9, 10, 14, 15, 20, 21, 22, 25, 30 11 23 16 3 6 Divisible by 2 Divisible by 3 14 20 12 9 21 5 Divisible by 2 Divisible by 5 2. List: 6, 9, 10, 11, 12, 15, 16, 18, 20, 25, 27, 30 Divisible by 3 Divisible by 5 NSSAL 101 Draft

3. List: 2, 3, 4, 7, 9, 10, 13, 15, 18, 20, 21, 23, 25 Note: A prime number is a number that can be divided evenly only by 1 or itself. (e.g. The number 11 is a prime number because it is only divisible by 1 and 11.) Odd Prime 4. List: 3, 4, 7, 9, 10, 15, 16, 18, 25, 27, 28, 30, 36 Note: For our purposes, a perfect square is a number that can be expressed as a whole number squared. (e.g. 81 is a perfect square because 81 = 9 2 ) Perfect Square Even 5. List: 7, 9, 10, 13, 15, 18, 30, 36, 45, 48, 55, 90 Multiple of 9 Multiple of 5 NSSAL 102 Draft

Whole Number Crossword Puzzle (A) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. Next even number after 384 C. 22 + 10 + 10 G. one thousand, four hundred twenty I. 5 more than 228 J. Double 25 L. The product of 4 and 8 O. 196 + 231 Q. 143-87 R. 5 times 7 T. The number of minutes in 1 hour and 34 minutes V. 4 2 W. A number between 10 and 20 that is divisible by both 5 and 3 Down: B. 8 10 D. 2000 + 100 + 30 + 9 E. 337-10 F. 8 90 H. 7 less than 470 K. Next number in the following sequence. 70, 74, 78, 82, M. 3 sets of 9 N. increase 734 by 20 P. 11 + 5 + 3 + 9 S. Next number in the following sequence. 63, 60, 57, 54, U. The number of cents in 2 quarters, 1 dime, and 1 nickel NSSAL 103 Draft

Whole Number Crossword Puzzle (B) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. 50 9 C. 5 more than 81 G. 4000 + 800 + 10 + 5 I. increase 153 by 30 J. 63-29 L. 7 = 4 O. The number of minutes in 6 hours and 4 minutes Q. A number between 10 and 20 that is divisible by 2, 3, 6, and 9 R. decrease 70 by 7 T. The product of 2 and 7 V. 5 + 10 + 2 + 30 W. The even number before 88 Down: B. The next odd number after 51 D. six thousand, four hundred thirty-nine E. 213 rounded to the nearest tens F. Next number in the following sequence 394, 399, 404, 409, H. 156 + 316 K. 7 2 M. Double 12 N. 1542 3 P. 6 sets of 11 S. 6 less than double 20 U. Next number in the following sequence 60, 54, 48, 42, NSSAL 104 Draft

Whole Number Crossword Puzzle (C) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. 70 8 C. Triple 6 plus 1 G. 7558 rounded to the nearest hundreds I. increase 361 by 40 J. Number of cents in 3 quarters and 2 dimes L. 9 times 6 O. 800 + 70 + 4 Q. 37 + 56 R. 581 7 T. Double 13 V. Next number in the following sequence 50, 47, 44, 41, W. 6 = 8 Down: B. 6 + 20 + 2 + 40 D. nine thousand, seven hundred twelve E. Next number in the following sequence 886, 890, 894, 898, 902, F. 15 23 H. The next multiple of 5 that follows 130 K. 8 sets of 4 M. 8 2 N. Number of minutes in 3 hours and 16 minutes P. 161-87 S. 39 decreased by 6 U. A number between 20 and 30 that is divisible by 2, 4, 7, and 14 NSSAL 105 Draft

Whole Number Crossword Puzzle (D) A B C D E F G H I J K L M N O P Q R S T U V W Across: A. The next odd number after 769 C. 6 sets of 3 G. six thousand, three hundred seven I. Next number in the following sequence 338, 344, 350, 356, J. 444 6 L. 25+47 O. 1 + 30 + 4 + 100 + 50 Q. 6 times 7 R. 9 = 4 T. Number of cents in 2 quarters and 3 dimes V. A number between 40 and 50 that is a multiple of 3, 5, 9, and 15 W. The product of 8 and 9 Down: B. 87 decreased by 9 D. 8000 + 600 + 20 + 9 E. 746 increased by 60 F. 50 less than 784 H. Number of minutes in 2 hours and 37 minutes K. triple 8 plus 4 M. Next number in the following sequence 107, 104, 101, 98, N. 24 35 P. 9 2 S. Double 32 U. 119-37 NSSAL 106 Draft

KenKen Puzzles (A) KenKen puzzles were invented in 2004 by Japanese math teacher Tetsuya Miyamoto. The goal is to fill a grid with numbers such that no number is repeated in the same row or column. For a 3 by 3 KenKen grid, one can only use the numbers 1, 2, and 3. For a 4 by 4 KenKen grid, one can only use the digits 1, 2, 3, and 4. In addition to this, grids are divided into heavily outlined groups of cells, called cages. The numbers in these cages have to produce the target number using the indicated operation. For example if two cells are within a cage and 5+ is shown in an upper corner, then one find two numbers that add to 5. If working with a 3 by 3 grid where we are restricted to the numbers 1, 2, and 3, the only possible numbers are 2 and 3. All of this will make more sense after viewing the following online video. http://www.youtube.com/watch?v=eik2syomwsm (or Google Search: YouTube KenKen Will Shortz Introduces New Puzzle) Questions: Complete the following KenKen Puzzles. Since these are 3 by 3 puzzles, you can only use the numbers 1, 2, and 3. Work in pencil and make sure you have a good eraser. (a) 5+ 4+ (b) 3+ 4+ 1 5+ 2 5+ 3+ 4+ (c) 5+ 3+ (d) 6+ 3+ 3+ 4+ 5+ 3 4+ NSSAL 107 Draft

(e) 5+ 3+ (f) 4+ 3 4+ 8+ 3+ 2 4+ (g) 1 5+ (h) 3+ 4+ 5+ 4+ 4+ 7+ 3+ (i) 4+ 6+ (j) 5+ 5+ 5+ 7+ 3+ 1 NSSAL 108 Draft

KenKen Puzzles (B) Insert the numbers 1, 2, and 3 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation. In these questions, we have limited ourselves to the operations of addition and multiplication. (a) 2 5+ (b) 9 3+ 4+ 6 3+ 6 (c) 4+ 6 (d) 12 3 18 4+ 3+ (e) 4+ 6 (f) 6 3+ 3+ 5+ 2 3 3 NSSAL 109 Draft

KenKen Puzzles (C) Normally with 3 by 3 KenKen Puzzles, we only use the numbers 1, 2, and 3 in the grid. We are going to change this. For the puzzles below, we are going to use the numbers 3, 4, and 5. New Instructions: Insert the numbers 3, 4, and 5 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation. In these questions, we have limited ourselves to the operations of addition and multiplication. (a) 12 8+ (b) 15 20 4 9+ 12 15 5 7+ (c) 15 4 (d) 8+ 12+ 7+ 8+ 12 20 9+ (e) 12+ 11+ (f) 12 8+ 15 14+ 12 5 NSSAL 110 Draft

KenKen Puzzles (D) Normally with 3 by 3 KenKen Puzzles, we only use the numbers 1, 2, and 3 in the grid. We are going to change this. For the puzzles below, we are going to use the numbers 5, 6, and 7. New Instructions: Insert the numbers 5, 6, and 7 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation. (a) 35 13+ (b) 42 11+ 5 11+ 12+ 42 30 7 (c) 30 19+ (d) 17+ 35 11+ 18+ 13+ 7 (e) 42 5 (f) 17+ 42 11+ 13+ 13+ 35 30 NSSAL 111 Draft

KenKen Puzzles (E) Insert the numbers 1, 2, 3, and 4 into the grid such that: no number is repeated in the same row or column, and the numbers in the cages produce the target number using the indicated operation. In these questions, we have limited ourselves to the operations of addition and multiplication. (a) 8 4+ 12 (b) 3 2 4 1 6+ 6+ 7+ 6+ 6 4+ 4 6 1 8 (c) 6 12 (d) 6+ 3 4 12 1 7+ 3+ 9+ 3 24 1 2 8+ 2 NSSAL 112 Draft

Find the Two Numbers Example: Find the two numbers that multiply to give 12, and add to give 7. Answer: The numbers are 3 and 4 because 3 4 12 and 3 4 7. Questions: Find two numbers that: (a) multiply to give 15, and add to give 8. Answer: & (d) multiply to give 12, and add to give 13. Answer: & (g) multiply to give 16, and add to give 8. Answer: & (j) multiply to give 12, and add to give 8. Answer: & (m) multiply to give 22, and add to give 13. Answer: & (p) multiply to give 40, and add to give 14. Answer: & (s) multiply to give 35, and add to give 12. (v) Answer: & multiply to give 8, and add to give 9. Answer: & (b) multiply to give 20, and add to give 12. Answer: & (e) multiply to give 18, and add to give 9. Answer: & (h) multiply to give 30, and add to give 17. Answer: & (k) multiply to give 10, and add to give 11. Answer: & (n) multiply to give 42, and add to give 13. Answer: & (q) multiply to give 63, and add to give 16. Answer: & (t) multiply to give 50, and add to give 27. Answer: & (w) multiply to give 60, and add to give 23. Answer: & (c) multiply to give 28, and add to give 11. Answer: & (f) multiply to give 40, and add to give 13. Answer: & (i) multiply to give 36, and add to give 13. Answer: & (l) multiply to give 25, and add to give 10. Answer: & (o) multiply to give 24, and add to give 14. Answer: & (r) multiply to give 32, and add to give 12. Answer: & (u) multiply to give 24, and add to give 10. Answer: & (x) multiply to give 100, and add to give 20. Answer: & NSSAL 113 Draft

Which Combination of Numbers Works? In each case you have been given three numbers and an incomplete calculation. Insert the numbers in the appropriate positions to make the calculation complete. (a) 1 4 5 - = 19 (b) 2 5 7 + = 17 (c) 3 6 8 + - = 5 (d) 4 5 6 + = 34 (e) 3 6 7 - = 15 (f) 4 5 20 + = 10 (g) 3 7 9 + - = 13 (h) 5 7 8 - = 27 (i) 4 8 12 + = 14 (j) 2 5 20 - = 2 (k) 6 7 10 + - = 9 (l) 3 6 7 + = 45 (m) 3 5 15 + = 6 (n) 8 16 24 + = 26 (o) 5 6 9 - = 49 NSSAL 114 Draft

Magic Squares In a magic square, the numbers in each column, row, and diagonal all add up to the same number. For example, with the magic square on the right, the numbers in each column, row, and diagonal all add up to 30. 7 14 9 12 10 8 11 6 13 Complete each of the magic squares below. (a) 6 (b) 3 (c) 7 3 5 7 2 6 4 7 5 5 (d) 4 (e) 4 (f) 10 3 8 8 7 6 1 8 5 12 (g) 5 (h) 4 (i) 12 7 9 9 2 7 10 3 8 6 NSSAL 115 Draft

Addition Pyramids With addition pyramids, the two numbers in adjoining boxes add to give the number in the box immediately above. 8 18 34 3 5 7 11 14 20 5 2 9 5 9 11 Insert the missing numbers in each of the following addition pyramids. 4 1 8 3 1. 2. 9 3. 13 4 6 5 10 3. 4. 14 6. 9 8 2 9 8 7. 8. 9. 9 9 7 2 10 3 6 2 4 10. 18 11. 12. 19 11 3 8 10 1 7 6 13. 14. 21 15. 7 12 9 14 3 2 4 8 NSSAL 116 Draft

16. 17. 18. 30 16 10 7 7 6 0 5 8 2 1 5 19. 20. 21. 13 12 7 12 8 3 9 2 7 3 2 6 22. 23. 24. 40 17 20 22 10 9 11 12 10 3 6 5 NSSAL 117 Draft

Row Factors and Column Factors In each question you have been provided with a chart that is missing four numbers. These numbers are the factors of the numbers found to the right of each row, and factors of the numbers found at the bottom of each column. Find the missing numbers. Example: Answer: 15 5 3 15 28 7 4 28 35 12 35 12 Questions: (a) 10 (b) 18 (c) 20 12 2 12 8 15 6 6 8 30 (d) 27 (e) 60 (f) 28 7 8 3 21 9 24 20 4 21 (g) 18 (h) 18 (i) 40 20 45 7 36 10 15 54 8 35 (j) 24 (k) 20 (l) 14 18 42 32 27 16 30 28 28 16 (m) 54 (n) 56 (o) 35 40 6 27 72 30 21 16 15 63 NSSAL 118 Draft

Letter and Number Sentences 1. A B 9 2. C D 5 (a) If A is 5, how much is B? (a) If C is 12, how much is D? (b) If B is 7, how much is A? (b) If D is 4, how much is C? (c) If A is 3, how much is B? (c) If C is 20, how much is D? (d) If B is 1, how much is A? (d) If D is 8, how much is C? 3. E F 24 4. G H 6 (a) If E is 6, how much is F? (a) If G is 30, how much is H? (b) If F is 3, how much is E? (b) If H is 3, how much is G? (c) If E is 12, how much is F? (c) If G is 42, how much is H? (d) If F is 1, how much is E? (d) If H is 10, how much is G? 5. I J 7 6. K L 30 (a) If I is 16, how much is J? (a) If K is 10, how much is L? (b) If J is 5, how much is I? (b) If L is 5, how much is K? (c) If I is 11, how much is J? (c) If K is 2, how much is L? (d) If J is 10, how much is I? (d) If L is 30, how much is K? 7. M N 4 8. P Q 13 (a) If M is 36, how much is N? (a) If P is 9, how much is Q? (b) If N is 3, how much is M? (b) If Q is 2, how much is P? (c) If M is 28, how much is N? (c) If P is 6, how much is Q? (d) If N is 5, how much is M? (d) If Q is 8, how much is P? NSSAL 119 Draft

Math Logic Puzzles For each, find the numbers represented by the symbols,, and. Hint: For each of the puzzles, one of the equations, not necessarily the first equation, allows you to solve for a symbol very quickly. Puzzle 1: - = 2 + 1 = 6 + = 8 Puzzle 2: + = 8 + = 6 + = 7 Puzzle 3: + = 8 3 = 6 + = 10 Puzzle 4: - = 3 + + = 10 4 = 8 Puzzle 5: - 2 = 7 + + = 17 = 18 Puzzle 6: - = 5 + + = 9 + = Puzzle 7: - 3 = + = 2 14 = 2 Puzzle 8: + + 2 = 3 = 4 - = 6 Puzzle 9: 24 = + + 1 = 9 + = 3 Answers (in no particular order) = 4, = 6, = 2 = 6, = 4, = 12 = 6, = 2, = 9 = 14, = 6, = 4 = 11, = 3, = 8 = 7, = 5, = 1 = 2, = 5, = 3 = 4, = 2, = 5 = 1, = 7, = 4 NSSAL 120 Draft

Number Sentences (A) In each case create four number sentences using the three numbers provided. Example 1: Example 2: 2 18 9 8 5 13 Answer: Answer: 2 9 18 18 9 2 8 5 13 13 5 8 9 2 18 18 2 9 5 8 13 13 8 5 Questions: 1. 12 4 8 2. 10 15 5 3. 8 16 2 4. 4 5 9 5. 28 7 4 6. 9 45 5 7. 12 3 9 8. 3 15 5 9. 20 10 30 10. 30 180 6 NSSAL 121 Draft

Number Sentences (B) Create as many number sentences as possible using three numbers from the chart at a time and limiting yourself to the operations of addition, subtraction, multiplication, and division. Example: 2 28 3 4 6 7 You can create 16 number sentences using these numbers. Answer: 2 3 6 6 2 3 2 4 6 6 2 4 3 2 6 6 3 2 4 2 6 6 4 2 4 7 28 28 4 7 3 4 7 7 3 4 7 4 28 28 7 4 4 3 7 7 4 3 1. You can create 12 number sentences using these numbers. 4 27 20 5 3 9 2. You can create 20 number sentences using these numbers. 2 12 24 3 4 8 3. You can create 24 number sentences using these numbers. 3 9 6 12 18 2 NSSAL 122 Draft

Order of Operations (A) Below, the same question was done by four different learners. The problem was that everyone ended up with different answers. Dave's Answer: Nashi's Answer Rana's Answer Montez's Answer 3 8 4 2 24 4 2 20 2 10 Dave worked from left to right. He did the multiplication first, followed by the subtraction, and then did the division. 3 8 4 2 3 4 2 12 2 6 Nashi started with the subtraction, followed by multiplication, and then did the division. 3 8 4 2 24 4 2 24 2 22 Rana started with the multiplication, followed by the division, and then did the subtraction. 3 8 4 2 3 8 2 3 6 18 Montez worked from right to left. He started with the division, followed by the subtraction, and then did the multiplication. All of these learners started with the same question, but ended up with very different answers based on the order they chose to do the operations. Only one of the learners is correct. Do you know which one? The correct answer is 22. Rana did the question correctly because she knew the order of operations, the rules used to clarify which mathematical operations are done first in a mathematical expression. Most people remember the proper order by using the acronym BEDMAS. B - brackets first E - then exponents (e.g. squaring, cubing) DM - followed by division and multiplication in the order they appear (i.e. from left to right) AS - followed by addition and subtraction in the order they appear (i.e. from left to right) For this activity sheet we are only going to look at questions involving division, multiplication, addition, and subtraction (i.e. only the "DMAS" portion of "BEDMAS") Example 1 Evaluate each of the following. (a) 5 7 3 (b) 15 3 2 (c) 10 3 8 4 (d) 5 4 6 3 Answers: (a) The mathematical expression 5 7 3 only involves the operations of addition and multiplication. According to BEDMAS, we do multiplication before addition. 5 7 3 5 21 26 NSSAL 123 Draft

(b) The mathematical expression 15 3 2 only involves the operations of division and subtraction. According to BEDMAS, we do division before subtraction. 15 3 2 5 2 3 (c) The mathematical expression 10 3 8 4 involves the operations of subtraction, addition and multiplication. According to BEDMAS, multiplication is done before subtraction or addition. Once this is done we have to decide between the subtraction and addition. When these operations occur in the same question, we always work from left to right. That means we will do the subtraction before the addition. 10 3 8 4 10 3 2 7 2 9 (d) The mathematical expression 5 4 6 3 involves the operations of multiplication, addition, and division. According to BEDMAS we do division and multiplication before addition. However, do we do the division before the multiplication, or vice versa? When these two operations occur in the same question, we always work from left to right. 5 4 6 3 20 6 3 20 2 22 Questions Evaluate each of the mathematical expressions. Show your work and do not use a calculator. (a) 6 2 1 (b) 10 3 2 (c) 18 10 2 (d) 25 10 5 (e) 5 8 2 (f) 9 2 3 NSSAL 124 Draft

(g) 12 6 5 (h) 18 2 3 (i) 18 2 4 (j) 6 5 4 (k) 3 2 6 1 (l) 10 3 3 1 (m) 8 12 4 3 (n) 4 2 3 5 (o) 3 6 2 5 (p) 12 4 3 9 (q) 28 4 2 3 (r) 10 6 3 5 (s) 10 15 5 2 (t) 12 5 4 10 (u) 7 3 16 2 (v) 45 5 6 4 (w) 3 4 5 7 2 (x) 6 16 4 3 8 NSSAL 125 Draft

Order of Operations (B) Below, the same question was done by four different learners. The problem was that everyone ended up with different answers. Kendrick's Answer: Helen's Answer Jun's Answer Nasrin's Answer 2 6 4 2 2 10 2 100 2 50 2 6 4 2 6 2 6 4 10 2 2 6 4 2 6 16 2 22 2 11 2 6 4 2 6 16 2 6 8 14 Kendrick worked from left to right. He did the addition first, followed by the squaring, and then did the division. Helen started with the division, followed by the squaring, and then did the addition. Jun started with the squaring, followed by the addition, and then did the division. Nasrin started with the squaring, followed by the division, and then did the addition. All of these learners started with the same question, but ended up with very different answers based on the order they chose to do the operations. Only one of the learners is correct. Do you know which one? The correct answer is 14. Nasrin did the question correctly because he knew the order of operations, the rules used to clarify which mathematical operations are done first in a mathematical expression. The proper order can be remembered using the acronym BEDMAS. B - brackets first E - then exponents (e.g. squaring, cubing) DM - followed by division and multiplication in the order they appear (i.e. from left to right) AS - followed by addition and subtraction in the order they appear (i.e. from left to right) For this activity sheet we are only going to look at questions involving exponents, division, multiplication, addition, and subtraction (i.e. only the "EDMAS" portion of "BEDMAS") Example 1 Evaluate each of the following. 2 3 (a) 5 3 2 (b) 4 5 2 (c) 2 6 9 2 5 NSSAL 126 Draft (d) 3 29 3 24 6 Answers: 2 (a) The mathematical expression 5 3 2 involves the operations of addition, squaring, and multiplication. According to BEDMAS, we would do the squaring (i.e. exponents) first, followed by multiplication, and finally the addition. 2 5 3 2 2 5 9 2 Remember: 3 means 3 3 5 18 23

3 (b) The mathematical expression 4 5 2 involves the operations of multiplication, subtraction, and cubing. According to BEDMAS, we would do the cubing (i.e. exponents) first, followed by multiplication, and finally the subtraction. 3 4 5 2 3 4 5 8 Remember: 2 means 2 2 2 20 8 12 2 (c) The mathematical expression 6 9 2 5 involves the operations of squaring, division, addition, and multiplication. According to BEDMAS, we would do the squaring (i.e. exponents) first. Next we have to decide between the division and multiplication. When these operations occur in the same question, we always work from left to right. That means we will do the division before the multiplication. The last operation we will complete is the addition. 2 6 9 2 5 36 9 2 5 4 2 5 4 10 14 3 (d) The mathematical expression 29 3 24 6 involves the operations of subtraction, cubing, addition, and division. According to BEDMAS, we would do the cubing (i.e. exponents) first. Next we would do the division. Once this is done we have to decide between the subtraction and addition. When these operations occur in the same question, we always work from left to right. That means we will do the subtraction before the addition. 3 29 3 24 6 29 27 24 6 29 27 4 2 4 6 Questions Evaluate each of the mathematical expressions. Show your work and do not use a calculator. (a) 2 24 4 8 (b) 2 3 5 6 (c) 3 30 2 3 NSSAL 127 Draft

(d) 2 4 3 5 (e) 3 6 5 3 (f) 2 4 2 3 (g) 2 5 3 2 (h) 2 20 4 2 (i) 3 18 2 6 (j) 2 2 3 5 2 (k) 3 2 5 30 6 (l) 2 30 2 6 1 2 (m) 10 4 3 2 (n) 2 9 4 2 1 (o) 2 3 5 3 2 (p) 2 2 4 3 2 (q) 3 2 5 2 4 3 (r) 2 2 6 4 2 5 NSSAL 128 Draft

Order of Operations (C) Below, the same question was done by four different learners. The problem was that everyone ended up with different answers. Kimi's Answer: Ryan's Answer Paulette's Answer Ajay's Answer 2 4 5 2 20 2 20 4 16 2 2 4 5 2 4 3 2 4 9 36 2 4 5 2 4 5 4 4 1 4 2 2 4 5 2 4 3 12 144 2 Kimi started with the multiplication, followed by the squaring, and then did the subtraction. Ryan started with the operation in the brackets, followed by the squaring, and then did the multiplication. Paulette started with the squaring, followed by the subtraction, and then did the multiplication. Ajay started with the operation in the brackets, followed by the multiplication, and then did the squaring. All of these learners started with the same question, but ended up with very different answers based on the order they chose to do the operations. Only one of the learners is correct. Do you know which one? The correct answer is 36. Ryan did the question correctly because he knew the order of operations, the rules used to clarify which mathematical operations are done first in a mathematical expression. The proper order can be remembered using the acronym BEDMAS. B - brackets first E - then exponents (e.g. squaring, cubing) DM - followed by division and multiplication in the order they appear (i.e. from left to right) AS - followed by addition and subtraction in the order they appear (i.e. from left to right) Example 1 Evaluate each of the following. (a) 3 6 1 2 (b) 7 5 3 3 7 (c) 2 3 9 20 1 1 3 Answers: (a) With the mathematical expression 3 6 1 2 we have multiplication, subtraction embedded within a set of brackets, and squaring. According to BEDMAS, we start with the operations in the brackets, followed by the squaring (i.e. exponents), and then finish off with the multiplication. 2 3 6 1 3 5 2 2 3 25 Remember: 5 means 5 5 75 NSSAL 129 Draft

(b) With the mathematical expression 7 5 3 3 7 we have subtraction embedded within a set of brackets, cubing, addition, and multiplication. According to BEDMAS, we start with the operations in the brackets. This will be followed by the cubing (i.e. exponents). We will then do the multiplication, and then finish up with the addition. 3 7 5 3 7 3 2 3 7 3 8 3 7 Remember: 2 means 2 2 2 8 21 29 (c) With the mathematical expression 2 3 9 20 1 1 3 we will start with the addition that is embedded within a set of brackets. Next we will work with the exponents (i.e. the squaring and the cubing). Following this we do the multiplication. That leaves us with the addition and multiplication. When these operations occur in the same question, we always work from left to right. That means we will do the addition before the subtraction. 2 3 9 20 1 1 3 9 20 2 3 2 3 9 20 4 27 9 80 27 89 27 62 Questions Evaluate each of the mathematical expressions. Show your work and do not use a calculator. (a) 10 5 1 2 (b) 8 6 3 4 (c) 36 1 2 2 2 3 (d) 7 4 6 (e) 3 6 2 (f) 2 8 3 2 NSSAL 130 Draft

(g) 3 7 6 2 (h) 10 25 7 2 (i) 3 4 6 4 2 2 (j) 3 11 2 (k) 7 20 3 (l) 32 5 3 3 2 (m) 4 1 7 3 (n) 3 7 5 2 5 (o) 2 4 2 3 6 (p) 1 1 8 5 2 6 (q) 5 7 4 1 1 3 (r) 4 5 2 3 7 2 NSSAL 131 Draft

Patterns NSSAL 132 Draft

What's the Pattern? (A) Look for a pattern and then fill in the three missing symbols. (a),,,,,,,,,,,,,,,, (b),,,,,,,,,,,,,,,, (c),,,,,,,,,,,,,,,,, (d),,,,,,,,,,,,, (e),,,,,,,,,,,, (f) A,, B,, C,, D,, E,, F,,,, (g),,,,,,,,,,,,, (h),,,,,,,,,,,,,,, (i),,,,,,,,,,,,, (j), R,, P,, R,, P,, R,, P,, R,,,, (k),,,,,,,,,,,,,,,,,, (l),,,,,,,,,,,,,,,,, (m),,,,,,,,,,,,,,,, (n) Z, z, Y, y, X, x, W, w, V, v, U, u,,, (o),,,,,,,,,,,,,,,,,, (p),,,,,,,,,,,,,,,,,, NSSAL 133 Draft

What's the Pattern? (B) Look for a pattern and then fill in the three missing symbols. Hint: Sometimes more than one trait is changing. e.g. Every figure is rotated slightly counter clockwise (45 o ) and every fifth figure is not bolded.,,,,,,,,,,,,,, (a),,,,,,,,,,,,,,,, (b),,,,,,,,,,,,,,,, (c),,,,,,,,,,,,, (d),,,,,,,,,,,,,,,, (e),,,,,,,,,,,,,,,, (f),,,,,,,,,,,, (g),,,,,,,,,,, (h),,,,,,,,,,,,,,,, (i),,,,,,,,,,,,,,, (j),,,,,,,,,,,,,,,, (k),,,,,,,,,,,,,,,,, (l),,,,,,,,,,,,,,,, (m),, A,,, B,,, C,,, D,,,, (n),,,,,,,,,,,,,,,,,, (o),,,,,,,,,,,,,,, NSSAL 134 Draft

Toothpick Patterns You have been supplied with a sequence of shapes where each shape is created using toothpicks. For example a triangle is made up of 3 toothpicks. In these questions, you are going to be looking for a pattern in terms of the number of toothpicks as you move from one figure to the next. There are three specific parts to each question. (a) Draw the next figure in the sequence. (b) Describe the sequence in terms of numbers (i.e. numbers of toothpicks in each figure). (c) In words, describe what is happening to the numbers as you move from figure to figure in the sequence. Example: Answer: (a) Next Figure: (b) Sequence Using Numbers: 4, 7, 10, 13, 16 (c) Describe Sequence Using Works: Start at 4 and keep adding 3. 1. 2. 3. NSSAL 135 Draft

4. 5. 6. 7. 8. NSSAL 136 Draft

Create the Pattern (A) Using the instructions, create the first five numbers in the sequence. e.g. Start at 7 and go up by 3 each time. Answer: 7, 10, 13, 16, 19 (a) Start at 9 and go up by 2 each time. (b) Start at 24 and go down by 1 each time. (c) Start at 8 and go up by 3 each time. (d) Start at 4 and go up by 5 each time. (e) Start at 33 and go down by 3 each time. (f) Start at 29 and go down by 2 each time. (g) Start at 11 and go up by 4 each time. (h) Start at 30 and go down by 2 each time. (i) Start at 3 and go up by 6 each time. (j) Start at 2 and go up by 4 each time. (k) Start at 11 and go up by 5 each time. (l) Start at 38 and go down by 3 each time. (m) Start at 36 and go down by 4 each time. (n) Start at 23 and go up by 6 each time. (o) Start at 40 and go down by 5 each time. (p) Start at 13 and go up by 10 each time. (q) Start at 72 and go down by 2 each time. (r) Start at 99 and go down by 10 each time. (s) Start at 41 and go up by 4 each time.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, NSSAL 137 Draft

Create the Pattern (B) Using the instructions, create the first four numbers in the sequence. e.g. Start at 125 and go up by 6 each time. Answer: 125, 131, 137, 143 (a) Start at 63 and go up by 7 each time. (b) Start at 234 and go down by 2 each time. (c) Start at 81 and go up by 3 each time. (d) Start at 79 and go down by 3 each time. (e) Start at 126 and go up by 5 each time. (f) Start at 540 and go down by 10 each time. (g) Start at 352 and go up by 20 each time. (h) Start at 47 and go up by 4 each time. (i) Start at 68 and go down by 4 each time. (j) Start at 275 and go up by 25 each time. (k) Start at 134 and go up by 6 each time. (l) Start at 456 and go down by 100 each time. (m) Start at 99 and go down by 11 each time. (n) Start at 347 and go up by 3 each time. (o) Start at 605 and go down by 5 each time. (p) Start at 710 and go up by 30 each time. (q) Start at 670 and go down by 20 each time. (r) Start at 412 and go up by 6 each time. (s) Start at 364 and go down by 3 each time.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, NSSAL 138 Draft

Number Patterns (A) Look at the pattern and fill in the missing numbers. (a) 6, 8, 10, 12, 14, 16,,, (b) 23, 22, 21, 20, 19, 18, 17, 16, 15,,, (c) 5, 7, 9, 11, 13, 15, 17, 19, 21,,,? (d) 30, 28, 26, 24, 22, 20, 18,,, (e) 0, 3, 6, 9, 12, 15,,, (f) 10, 15, 20, 25, 30, 35,,, (g) 40, 36, 32, 28, 24, 20,,, (h) 31, 28, 25, 22, 19, 16, 13,,, (i) 7, 12, 17, 22, 27, 32, 37, 42,,, (j) 45, 47, 49, 51, 53, 55, 57,,, (k) 19, 22, 25, 28, 31, 34, 37,,, (l) 51, 47, 43, 39, 35, 31, 27, 23,,, (m) 67, 62, 57, 52, 47, 42, 37,,, (n) 44, 43,, 41,, 39, 38,, 36 (o) 23,, 27, 29, 31,,, 37, 39 (p) 30,,, 21, 18, 15, 12,, 6 (q) 17, 21,,, 33,, 41, 45, 49, 53 (r), 14, 19, 24,,, 39, 44, 49 (s), 33,, 39, 42,, 48, 51, 54, 57 (t),, 41, 36, 31,, 21, 16, 11, 6 (u) 91,, 93,, 95,, 97 NSSAL 139 Draft

Number Patterns (B) Look at the pattern and fill in the missing numbers. (a) 2, 4, 6, 8, 10, 12,,, (b) 4, 7, 10, 13, 16,,, (c) 29, 27, 25, 23, 21,,,? (d) 55, 50, 45, 40, 35,,, (e) 3, 10, 17, 24, 31, 38,,, (f) 64, 56, 48, 40, 32, 24,,, (g) 0, 6, 12, 18, 24, 30, 36,,, (h) 1, 12, 23, 34, 45, 56,,, (i) 44, 40, 36, 32, 28, 24, 20,,, (j) 100, 104, 108, 112, 116, 120,,, (k) 675, 680, 685, 690, 695, 700, 705, 710,,, (l) 190, 210, 230, 250, 270, 290, 310, 330,,, (m) 326, 324, 322, 320, 318, 316,,, (n) 6, 10, 14,, 22, 26,,, 38 (o) 40,, 34, 31,, 25, 22,, 16 (p) 56, 61,, 71, 76, 81,,, 96, 101, 106 (q), 25, 29,, 37, 41, 45,, 53, 57 (r), 245,, 233, 227, 221, 215,, 203 (s) 16,,, 40, 48,, 64, 72, 80 (t),, 292,, 284, 280, 276, 272, 268 (u) 420,, 460,, 500,, 540 NSSAL 140 Draft

Row, Column, and Diagonal Patterns Describe the pattern between numbers found in columns, rows and diagonals. (Note: Rows go from left to right. Columns go from top to bottom. Diagonals go from the upper left to the lower right.) e.g. 4 6 8 4 6 8 4 6 8 4 6 8 10 12 14 10 12 14 10 12 14 10 12 14 16 18 20 16 18 20 16 18 20 16 18 20 Row Pattern: Column Pattern: Diagonal Pattern: Add 2 Add 6 Add 8 1. 5 8 11 2. 25 23 21 3. 1 11 21 14 17 20 19 17 15 31 41 51 23 26 29 13 11 9 61 71 81 Row Pattern: Row Pattern: Row Pattern: Column Pattern: Column Pattern: Column Pattern: Diagonal Pattern: Diagonal Pattern: Diagonal Pattern: 4. 42 38 34 5. 29 31 33 6. 17 12 7 30 26 22 23 25 27 32 27 22 18 14 10 17 19 21 47 42 37 Row Pattern: Row Pattern: Row Pattern: Column Pattern: Column Pattern: Column Pattern: Diagonal Pattern: Diagonal Pattern: Diagonal Pattern: NSSAL 141 Draft

What's the Relationship? A chart containing numbers between and equal to 1 and 50 is provided. Some of the numbers are enlarged and bolded. What is the relationship amongst those enlarged and bolded numbers? Write the answer in as many ways as you can think of. Example 1: Example 2 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 Answers: Multiples of 6 Divisible by 6 Divisible by both 2 and 3 Start at 6 and keep adding 6 Start at 48 and keep subtracting 6 Answers: All are prime numbers Only divisible by 1 and themself (a) (b) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 (c) (d) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 NSSAL 142 Draft

(e) (f) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 (g) (h) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 (i) (j) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 (k) (l) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 46 47 48 49 50 NSSAL 143 Draft

Input Output (A) A number is put in (the input number) and a different number is spit out (the output number). In each case, determine the mathematical rule that changes the input number to the output number. Three examples have been provided to help you understand what needs to be done. Example I: Input Output 2 6 5 15 10 30 Example II: Input Output 10 4 7 1 21 15 Example III: Input Output 16 8 20 10 6 3 (a) Rule: Input 3 = Output Input Output 7 11 Rule: 5 9 2 6 (b) Rule: Input - 6 = Output Input Output 3 6 Rule: 7 14 4 8 (c) Rule: Input 2 = Output Input Output 27 9 Rule: 12 4 18 6 (d) Input Output 14 9 16 11 5 0 Rule: (e) Input Output 6 30 2 10 9 45 Rule: (f) Input Output 18 15 9 6 7 4 Rule: (g) Input Output 20 5 32 8 8 2 Rule: (h) Input Output 4 10 9 15 2 8 Rule: (i) Input Output 9 36 3 12 4 16 Rule: NSSAL 144 Draft

Input Output (B) A number is put in (the input number) and a different number is spit out (the output number). In each case, determine the mathematical rule that changes the input number to the output number. Three examples have been provided to help you understand what needs to be done. Example I: Input Output 4 28 7 49 6 42 Example II: Input Output 15 4 20 11 10 1 Example III: Input Output 60 10 18 3 36 6 (a) Rule: Input 7 = Output Input Output 4 36 Rule: 9 81 7 63 (b) Rule: Input - 9 = Output Input Output 13 6 Rule: 19 12 11 4 (c) Rule: Input 6 = Output Input Output 4 13 Rule: 15 24 9 18 (d) Input Output 35 5 21 3 56 8 Rule: (e) Input Output 7 42 4 24 9 54 Rule: (f) Input Output 48 6 8 1 32 4 Rule: (g) Input Output 16 23 9 16 12 19 Rule: (h) Input Output 25 15 36 26 19 9 Rule: (i) Input Output 3 24 5 40 9 72 Rule: NSSAL 145 Draft

Input Output (C) A number is put in (the input number) and a different number is spit out (the output number). In each case, determine the mathematical rule that changes the input number to the output number. Three examples have been provided to help you understand what needs to be done. Example I: Input Output 900 54000 30 1800 7 420 Example II: Input Output 150 130 70 50 210 190 Example III: Input Output 120 40 600 200 3000 1000 (a) Rule: Input 60 = Output Input Output 17 47 Rule: 120 150 73 103 (b) Rule: Input - 20 = Output Input Output 7 350 Rule: 20 1000 9 450 (c) Rule: Input 3 = Output Input Output 190 130 Rule: 72 12 350 290 (d) Input Output 160 40 2800 700 36 9 Rule: (e) Input Output 500 300 986 786 1700 1500 Rule: (f) Input Output 60 24000 3 1200 90 36000 Rule: (g) Input Output 150 80 1000 930 97 27 Rule: (h) Input Output 2670 2970 800 1100 156 456 Rule: (i) Input Output 1600 800 60000 30000 480 240 Rule: NSSAL 146 Draft

Input Output (D) In each case, determine the mathematical rule that changes the input number to the output number. For these questions, the input number is multiplied by 2, 3, 4, or 5 and then has a number added to or subtracted from it. Example I: Input Output 4 7 2 3 9 17 Example II: Input Output 1 7 6 27 3 15 Example III: Input Output 8 36 10 46 3 11 (a) Rule: (Input 2 ) - 1 = Output Input Output 6 17 8 21 3 11 Rule: (b) Rule: (Input 4 ) + 3 = Output Input Output 10 31 1 4 7 22 Rule: (c) Rule: (Input 5 ) - 4 = Output Input Output 2 1 8 13 9 15 Rule: (d) Input Output 4 14 2 6 7 26 Rule: (e) Input Output 3 14 0 5 6 23 Rule: (f) Input Output 7 36 4 21 1 6 Rule: (g) Input Output 9 37 4 17 2 9 Rule: (h) Input Output 3 13 8 38 1 3 Rule: (i) Input Output 6 16 2 4 5 13 Rule: NSSAL 147 Draft

Filling or Draining A large container, which can hold 20 litres of water when filled to the brim, is either being filled or drained at a constant rate. You will be able to tell based on the sequence of diagrams of the container that have been supplied. Your mission is to complete the next diagram in the sequence, then describe each situation using words, using a table, and using an equation, and finally predict when the container will be full or empty. e.g. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Answer: In the last diagram, we should show the water level at the 8 L mark. Written Description: Table of Values: Time Litres 0 14 1 12 2 10 3 8 The container initially had 14 L of water in it and it is being drained at a rate of 2 litres per minute. 10 L Equation: Litres = 14-2 Time or L = 14-2T If the container initially held 14 L of water and it's losing 2 L per minute, then in 7 minutes the container will be empty (i.e. hold 0 L of water) NSSAL 148 Draft

1. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Empty: 2. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Full: NSSAL 149 Draft

3. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Full: 4. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Empty: NSSAL 150 Draft

5. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Empty: 6. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Full: NSSAL 151 Draft

7. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Empty: 8. 10 L 10 L 10 L 10 L time = 0 minutes time = 1 minute time = 2 minutes time = 3 minutes Written Description: Table of Values: Time Litres Equation: Full: NSSAL 152 Draft

Travelling Towards or Away From Home Montez is either travelling towards or away from his home at a constant speed. You will be able to tell by looking at the sequence of diagrams that have been provided. Your mission is to describe each situation using words, using a table of values (where the times go from 0 seconds to 4 seconds) and using an equation, and finally predict how far Montez is from home at t = 7 seconds. e.g. t = 0 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Answer: Written Description: Montez is initially 7 metres from home and runs away from the home at a rate of 4 metres per second. Table of Values: Time Distance from Home 0 7 1 11 2 15 3 19 4 23 Equation: distance = 7 + 4 time or d = 7 + 4t At t = 7 seconds, Montez will be 35 metres from home. The easiest way to figure this out is to substitute 7 in for t in the equation d = 7 + 4t, and then solve for d. You could also take the table of values and expand it until you reach a time of 7 seconds or jump along the number line on the diagram four spaces for every second until you reach the desired time. NSSAL 153 Draft

1. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Table of Values: Time Distance from Home Equation: At t = 7 seconds 2. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m NSSAL 154 Draft

Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds 3. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds NSSAL 155 Draft

4. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds 5. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m NSSAL 156 Draft

Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds 6. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds NSSAL 157 Draft

7. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds 8. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m NSSAL 158 Draft

Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds 9. t = 0 seconds t = 1 second 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m t = 2 seconds 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m 0 m 5 m 10 m 15 m 20 m 25 m 30 m 35 m Written Description: Table of Values: Time Distance from Home Equation: At t = 7 seconds NSSAL 159 Draft

Weight of the Water A spring balance is used to measure the weight of an object that is suspended below it. That weight will be measured in newtons (N). In this situation we have a container suspended below our spring balance that is either being filled or drained of water at a constant rate. Your mission is to describe each situation using words, using a table of values (where the times go from 0 seconds to 4 seconds) and using an equation, and finally predict the weight of the water at t = 6 seconds. The scale was adjusted so that the weight of the empty container is not included. e.g. time = 0 seconds time = 1 second time = 2 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 Answer: Written Description: The container initially contained water weighting 5 newtons and then water was added such that the weight increased by 2 newtons per second. Table of Values: Time Weight 0 5 1 7 2 9 3 11 4 13 Equation: weight = 5 + 2 time or w = 5 + 2t At t = 6 seconds, the weight of the container and its contents should be 17 newtons. NSSAL 160 Draft

1. time = 0 seconds time = 1 second time = 2 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 Written Description: Table of Values: Time Weight Equation: At t = 6 seconds 2. time = 0 seconds time = 1 second time = 2 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 NSSAL 161 Draft

Written Description: Table of Values: Time Weight Equation: At t = 6 seconds 3. time = 0 seconds time = 1 second time = 2 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 Written Description: Table of Values: Time Weight Equation: At t = 6 seconds NSSAL 162 Draft

4. time = 0 seconds time = 1 second time = 2 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 Written Description: Table of Values: Time Weight Equation: At t = 6 seconds 5. time = 0 seconds time = 2 seconds time = 4 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 NSSAL 163 Draft

Written Description: Table of Values: Time Weight Equation: At t = 6 seconds 6. time = 0 seconds time = 2 seconds time = 4 seconds Newtons 0 Newtons 0 Newtons 0 5 5 5 10 10 10 15 15 15 20 20 20 25 25 25 30 30 30 Written Description: Table of Values: Time Weight Equation: At t = 6 seconds NSSAL 164 Draft

Word Problems NSSAL 165 Draft

Describing the Relationships with Words Example: Given the diagram on the right, describe as many mathematical relationships using the different shapes. Answer: There are 3 arrows. There are 5 lightning bolts. There are 6 hearts. There are a total of 14 shapes. There is 1 more heart than lightning bolts. There is 1 less lightning bolt than hearts. There are 2 more lightning bolts than arrows. There are 2 less arrows than lightning bolts. There are 3 more hearts than arrows. There are 3 less arrows than hearts. There are twice as many hearts as arrows. There are half as many arrows as hearts. Now do the same with this diagram that has moons, suns and hearts. NSSAL 166 Draft

List the Numbers Based on the Written Description 1. List all the whole numbers between 8 and 15. 2. List all the even numbers between and equal to 10 and 22. 3. List all the multiples of 10 between and equal to 1 and 100. 4. List all the numbers that are divisible by 5 between 13 and 41. 5. List all the two digit numbers whose tens digit and one digit are the same. 6. List all the numbers that are divisible by 3 between 16 and 32. 7. List all prime numbers between and equal to 5 and 18. 8. List all the odd numbers that are divisible by 3 between 2 and 26. 9. List all the even numbers that are divisible by 5 between 3 and 47. 10. List all the two digit numbers whose digits add to 7. 11. List all the two digit numbers greater than 30 that are multiples of 9. 12. List all the numbers less than 35 that are divisible by 8. 13. List all composite numbers (i.e. not prime) between and equal to 9 and 21. 14. List all the numbers that are divisible by 2 and 3 between 5 and 35. 15. List all the odd numbers that are divisible by 5 between 7 and 56. NSSAL 167 Draft

Addition and Subtraction Crossword Complete the following crossword using words to express your answer (e.g. seven). Do not use a calculator. 1. 3. 4. 2. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. Across: 1. nine subtract seven 2. four plus eight 3. forty plus ten 5. eight subtract four 6. three add four 8. six increased by seven 10. nineteen decreased by three 13. five plus six 15. eleven minus two Down: 1. six plus four 2. five minus two 3. sixty subtract twenty 4. six add six 5. decrease sixteen by one 7. increase nine by two 9. seventeen subtract eight 10. thirty plus thirty 11. six add two NSSAL 168 Draft

Across: 17. twenty subtract eighteen 19. sixteen decreased by fifteen 21. subtract seventy from eighty 23. two increased by ten 25. fourteen subtract eleven 27. one plus seven 29. add eight to twelve 31. sixty decreased by fifty 33. eighteen minus twelve 34. decrease thirteen by eight 35. seventeen subtract ten 36. increase ten by thirty 37. thirteen minus four Down: 12. seventy decreased by seventy 14. add five to five 16. seventeen minus nine 18. decrease twenty by nineteen 20. increase four by seven 22. fifteen subtract seven 24. zero plus five 26. subtract ten from twenty-one 28. fifty subtract twenty 30. increase eight by three 31. fifteen decreased by twelve 32. add zero to nine NSSAL 169 Draft

Multiplication and Division Crossword Complete the following crossword using words to express your answer (e.g. twenty-seven). Include hyphens (-) where appropriate. Do not use a calculator. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. Across 2. four multiplied by twenty 5. five times six Down 1. eight times four 3. four multiplied by four NSSAL 170 Draft

Across 7. eighteen divided by nine 8. nine times four 9. eight multiplied by three 12. seven times five 15. twenty-seven divided by three 17. three multiplied by ten 19. three times five 20. six multiplied by seven 23. twenty-five divided by five 24. twenty-four divided by two 25. seven divided by seven 26. sixty divided by six 28. thirty-five divided by five 32. three times three 33. two multiplied by eight 34. eighty divided by eight 36. forty-eight divided by six 37. fifteen divided by three 38. seven times ten 40. six divided by one 41. sixty divided by thirty 42. seven multiplied by two 44. one hundred divided by ten 45. six times nine Down 4. four times seven 5. two times six 6. forty divided by ten 10. forty divided by eight 11. eighteen divided by three 13. nine times nine 14. ten multiplied by five 16. four times five 18. twenty-one divided by seven 21. fifty-six divided by eight 22. eleven times one 27. ten times nine 29. sixty-three divided by seven 30. eight times seven 31. eight multiplied by eight 34. two times six 35. thirty divided by six 37. twenty-four divided by six 38. fifty-four divided by nine 39. twelve divided by three 40. forty-nine divided by seven 41. sixty divided by twenty 43. one hundred divided by fifty NSSAL 171 Draft

Operations Crossword Complete the following crossword using words to express your answers (e.g. thirty-five). Include hyphens (-) where appropriate. Do not use a calculator. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. Across 2. nine times six 4. seven multiplied by three 7. thirty-two divided by eight Down 1. sixteen minus six 2. thirty-five divided by seven 3. forty-three plus three NSSAL 172 Draft

Across 9. one hundred subtract ten 11. twelve minus nine 12. forty-five divided by nine 14. seven increased by three 15. nine times nine 16. fifty-six divided by eight 18. twenty-one decreased by two 21. subtract thirty from thirty 22. seven multiplied by six 23. ten times seven 26. seventeen decreased by six 29. forty-nine divided by seven 31. eight divided by eight 36. six multiplied by six 38. three times four 41. one hundred subtract ninety-nine 42. eighty divided by forty 43. fourteen decreased by five 44. twenty multiplied by three 45. forty-four divided by four Down 4. eighteen subtract five 5. sixteen divided by eight 6. four add five 8. five multiplied by two 10. three times eight 13. eight multiplied by nine 17. nine increased by four 19. twenty-seven divided by nine 20. subtract fifteen from nineteen 23. eighteen divided by three 24. sixty-three divided by seven 25. twelve times zero 27. nine multiplied by nine 28. eighty minus seventy 30. two times forty 32. thirty divided by two 33. subtract six from eleven 34. thirty divided by five 35. four multiplied by two 36. one hundred divided by five 37. zero multiplied by six 39. seventeen minus eight 40. sixty divided by ten NSSAL 173 Draft

Word Sentence to Number Sentence to Answer (A) In each case take the word sentence, make a number sentence out of it, and then provide the answer. A few examples have been provided. Word Sentence Number Sentence Answer e.g. What is the product of seven and three? 7 3 21 e.g. What is five increased by six? 5 6 11 e.g. What is a third of twelve? 12 3 4 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) What is the sum of three and eight? What is six multiplied by five? What do you get when you double three? What is nine decreased by four? What is half of ten? Given seven and five, what is their total? What is eight times three? What is twelve divided by two? What is seven increased by six? What do you get when you triple six? What do you get when eight is taken away from ten? What is seven less four? (m) What is three plus eleven? (n) (o) (p) (q) (r) (s) (t) (u) (v) What do we get when ten is broken into five equal parts? How much more is nine compared to two? What is a quarter of eight? What is the product of eight and two? What is six combined with eight? What is six taken from thirteen? What is ten increased by six? How many threes fit into fifteen? What do you get when nine is removed from ten? NSSAL 174 Draft

Word Sentence to Number Sentence to Answer (B) In each case take the word sentence, make a number sentence out of it, and then provide the answer. A few examples have been provided. Word Sentence Number Sentence Answer e.g. The sum of seven and nine 7 9 16 e.g. What is twenty-two decreased by nine 22 9 13 e.g. What is a quarter of twenty 20 4 5 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) What do you get when you double eleven? What is thirty-five divided by seven? What is seven times six? What is seventeen increased by eight? What do you get when nine is taken away from fifteen? What is the sum of twelve and seven? What do we get when ten is broken into two equal parts? What is sixteen plus ten? What is the product of nine and seven? What is half of twenty-four? What is thirty-seven less five? What is six multiplied by eight? (m) What is three taken from forty-nine? (n) (o) (p) (q) (r) (s) (t) (u) (v) What is twenty-six increased by eleven? What do you get when six is removed from twenty-three? How many nines fit into eighty-one? What is forty-five decreased by six? What is eighteen combined with nine? What do you get when you triple twelve? Given seven and seventeen, what is their total? How much more is thirty-six compared to three? What is a third of twenty-seven? NSSAL 175 Draft

Word Sentence to Number Sentence to Answer (C) In each case take the word sentence, make a number sentence out of it, and then provide the answer. A few examples have been provided. Word Sentence Number Sentence Answer e.g. What is the product of nine hundred and eight 900 8 7200 e.g. How many eights are in three hundred twenty? 320 8 40 e.g. What do we get when sixty is increased by seventy 60 70 130 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Given five hundred and two hundred, what is their total? What is fifty multiplied by three? What is three hundred increased by four hundred twenty? What is forty removed from one hundred? What is a third of nine thousand? How many sevens fit into three hundred fifty? What is seventy times eighty? What is the sum of eleven and eighty? How much more is ninety compared to thirty? What is five thousand plus eight thousand? What is two hundred sixty decreased by twenty? What do you get when you double four thousand? (m) What is six hundred increased by two hundred thirty? (n) (o) (p) (q) (r) (s) (t) (u) (v) What do you get when you triple forty? What is one thousand nine hundred less eight hundred? What is half of sixteen thousand? What is two hundred eighty divided by seven? What do you get when ten is taken away from ninety? What is sixty combined with eighty? What do we get when six is broken into six equal parts? What is seventy taken from ninety-six? What is the product of six and seven thousand? NSSAL 176 Draft

What are the Possibilities? (A) The following questions have more than one answer. Find all the possible answers in each case. Example 1 The product of two whole numbers is greater than 8 and less than 13. What are the possibilities for the two numbers? Answer: The word "product" means that we are dealing with the operation of multiplication. We need to find all the pairs of whole numbers (e.g. 0, 1, 2, 3, ) that multiply to give us 9, 10, 11, or 12 (i.e. greater than 8 and less than 13). 1 9 9 3 3 9 1 10 10 2 5 10 1 11 11 1 12 12 2 6 12 3 4 12 Therefore the possibilities are: 1 and 9 3 and 3 1 and 10 2 and 5 1 and 11 1 and 12 2 and 6 3 and 4 Example 2 The difference of two single digit numbers is 3. What are the possibilities for the two numbers? Answer: The word "difference" means that we are dealing with the operation of subtraction. Notice that we are told to consider only single digit numbers (i.e. number 1 through 9), rather than multi-digit numbers (e.g. 13, 25, 159). 3 0 3 4 1 3 5 2 3 6 3 3 7 4 3 8 5 3 9 6 3 Therefore the possibilities are: 3 and 0 4 and 1 5 and 2 6 and 3 7 and 4 8 and 5 9 and 6 Example 3 The sum of two even numbers is 8. What are the possibilities for the two numbers? Answer: The word "sum" means that we are dealing with the operation of addition. We are told to work only with even numbers (e.g. 2, 4, 6, 8, 10, ) whose sum is 8. 8 0 8 2 6 8 4 4 8 Therefore the possibilities are: 8 and 0 2 and 6 4 and 4 NSSAL 177 Draft

Questions 1. The sum of two single digit numbers is 5. What are the possibilities for the two numbers? 2. The product of two whole numbers is 18 or 20. What are the possibilities for the two numbers? 3. When dividing two single digit numbers, the quotient is 2. What are the possibilities for the two numbers? 4. The difference of two single digit numbers is 5. What are the possibilities for the two numbers? 5. The product of two whole numbers is a whole number that is between, or equal to, 4 and 6. What are the possibilities for the two numbers? 6. The sum of two single digit numbers is greater than 14 and less than 19. What are the possibilities for the two numbers? 7. When dividing a two digit number that is 24 or less by a single digit number, the quotient is 4. What are the possibilities for the two numbers? NSSAL 178 Draft

8. The difference of two whole numbers, which are both less than or equal to 6, is 2 or 3. What are the possibilities for the two numbers? 9. The product of an even and odd number is equal a whole number that is 10 or less. What are the possibilities for the two numbers? 10. The sum of two odd numbers is 8 or 10. What are the possibilities for the two numbers? 11. When dividing a two digit number by a single digit odd number, the quotient is 2. What are the possibilities for the two numbers? 12. The difference of two even numbers, which are both less than or equal to 10, is 4. What are the possibilities for the two numbers? NSSAL 179 Draft

What are the Possibilities? (B) The following questions have more than one answer. Find all the possible answers in each case. e.g. The product of two single digit odd numbers is greater than 8 and less than 40. What are the possibilities for the two numbers? Answer: Start by listing all single digit odd numbers. 1, 3, 5, 7, 9 The word product tells us that we are multiplying. We need to look at all the possible ways of multiplying two of those odd numbers. These are listed below. 1 1 1 1 3 3 1 5 5 1 7 7 1 9 9 3 3 9 3 5 15 3 7 21 3 9 27 5 5 25 5 7 35 5 9 45 7 7 49 7 9 63 9 9 81 Now we only want those numbers whose products are greater than 8 and less than 40. That means we are limited to the following. 1 9 9 3 3 9 3 5 15 3 7 21 3 9 27 5 5 25 5 7 35 So there are seven combinations of numbers that work. 1 and 9 3 and 3 3 and 5 3 and 7 3 and 9 5 and 5 5 and 7 1. The product of two single digit even numbers is 16 or greater. What are the possibilities for the two numbers? 2. The product of two different single digit odd numbers is less than 30. What are the possibilities for the two numbers? NSSAL 180 Draft

3. The sum of two odd numbers is 14, and their product is greater than 20. What are the possibilities for the two numbers? 4. Two single digit numbers differ by 3, and their product is less than 45 and greater than 5. What are the possibilities for the two numbers? 5. The product of two whole numbers is 24, and their sum is 14 or less. What are the possibilities for the two numbers? 6. The product of two even numbers is 24 or less, and their sum is greater than 8. What are the possibilities for the two numbers? NSSAL 181 Draft

Does It Make Sense? A statement has been supplied. You decide whether the statement makes sense. If not, explain why. 1. Jim purchased a song from itunes for $9. Before the purchase he had $20 in his itunes account; after the purchase, he had $11 in the account. 2. Janice purchased 2 litres of homogenized milk, 4 litres of skim milk, and 1 litre of chocolate milk. In total she purchased 8 litres of milk. 3. Tanya and her two sisters decided to equally share the $210 bill for their parents' anniversary gift. That meant that each girl had to pay $70. 4. Kiana ran 6 kilometres per day over 7 days. In that period of time she ran 36 kilometres. 5. Yisha had 3 quarters, 1 dime, and 1 nickel. That means that he was 10 cents short of one dollar. 6. The roommates in an apartment decided to purchase a $600 flat screen television and share in the expense equally. If there were 100 roommates, then that meant that each had to pay $6. 7. Sapphire bought 6 sweaters, each costing $15 before taxes. Her total bill for the sweaters before taxes would be $90. 8. There were 26 students in the class at the beginning of the year. Over the course of the year, 4 transferred out and 1 transferred in. That means that by the end of the year, there were 21 students in the class. NSSAL 182 Draft

9. Faris only works Monday through Wednesday. Each day he works 8 hours. Over 2 weeks, he works a total of 48 hours. 10. There were initial 20 people signed up for the workshop. Over the next week that number doubled. At the last minute, 6 people said that they would be unable to attend. In the end, 34 people attended the workshop. 11. Jacob bought 3 bags of potatoes and 2 bags of carrots. The each bag of potatoes had a mass of 5 kg, and a bag of carrots had a mass of 1 kg. The total mass of carrots and potatoes that were purchased by Jacob was 30 kg. 12. Each day, Anne drove at 100 km/h for 6 hours. If she maintains this, then she will travel 18 000 km over 3 days. 13. The brand new 50 inch flat screen television cost $100 but the taxes came to $15, meaning that the total bill was $115. 14. The time it takes Arthur to get ready for work is 1 hour and 15 minutes. His shower takes 20 minutes. Breakfast and watching the morning news takes 25 minutes. The remaining 30 minutes is spent doing things like brushing his teeth, making his bed, getting dressed, and using the washroom. 15. There were 12 apples and 18 oranges. If they were shared equally among 3 people, then each person would get 4 oranges and 6 apples. 16. Helen was selling beverages at the fair for $2. Half of the money on each beverage was profit. If she sold 230 beverages, then her profit was $460. NSSAL 183 Draft

Insert Your Own Numbers and Words Below you have been given a written statement that is missing numbers (smaller blanks) and words (larger blanks). Your job is to add your own numbers and words so that the written statement makes sense. Reasonable numbers and words must be used. Naturally there are an infinite numbers of acceptable answers. e.g. Kimi purchased, each costing. These items came to a total of. Learner #1's Acceptable Answer: Kimi purchased 7 pairs of socks, each costing $3. These items came to a total of $21. Learner #2's Acceptable Answer: Kimi purchased 2 jars of peanut butter, each costing $4.50. These items came to a total of $9. 1. Tammy and Peter have and. That means that they have a total of. 2. The bag of had a mass of kg. If kg is removed, then that means kg remains. 3. Nita split the evenly amongst her friends. That meant that each friend got. 4. The children each had. That means that altogether they had. 5. The temperature of the was initially degrees Celsius. Over time, the temperature dropped by o C, so that it ended up being o C. 6. At the beginning of the day Jorell had litres of. He used litres and a friend later returned litres she had taken a few weeks ago. Jorell now had litres. NSSAL 184 Draft

Put the Numbers in Where It Makes Sense (A) With each question, you have been given a brief statement and you must fit the numbers (supplied in the boxes to the right) into the appropriate blanks so that it all makes sense. A number can only be used once. 1. Lei and Jun are siblings. Lei is years younger than Jun. If Jun is years old, then Lei is years old. 27 4 31 2. Marcus has dime and nickels in his pocket. If he has nickels and dimes, then he has a total of cents. 55 7 2 3. Very few men attended the show. If there were men and women, then there times as many women as men. 8 3 24 4. Normally people attend the neighborhood watch meeting. That number increased slightly by such that people attended. 15 12 3 5. Anne had dollars but spent most of her money on a dollar top (after taxes). She now has dollars left in her purse. 35 5 40 6. Bashir had candies to split evenly between his children. Each child got candies; enough to ruin their supper. 12 36 3 7. If there are minutes in an hour, then we know that there are minutes in hours. 60 180 3 8. Ryan, who prefers running, ran for minutes and biked for minutes. That means he trained for a total of minutes. 15 25 40 9. The mechanic ordered containers of engine oil at a cost of dollars per container. The total cost was dollars. 120 40 3 10. room mates got together to purchase an dollar couch. If they all paid the same amount, then each pays dollars. 800 4 200 NSSAL 185 Draft

Put the Numbers in Where It Makes Sense (B) With each question, you have been given a brief statement and you must fit the numbers (supplied in the boxes to the right) into the appropriate blanks so that it all makes sense. A number can only be used once. 1. Tanya has dimes and quarters in her purse. That means she has cents of change in her purse. 2 80 3 2. Bill and Ajay are friends. Bill is years older than Ajay. If Bill is years old, then Ajay is years old. 50 3 47 3. Kim bought apples and 4 oranges. Therefore she bought times as many apples as oranges, or more apples than oranges. 12 8 3 4. Three friends equally share the cost of a dollar pizza that was divided into 6 pieces. Each pays dollars and gets pieces. 7 2 21 5. Ryan had dollars but spent most of his money on a dollar DVD (after taxes). He now has dollars left. 11 19 30 6. If there are hours in one day, then there are hours in days. 48 24 2 7. The room temperature was degrees Celsius. If it is turned up slightly by degrees, then the new temperature is degrees. 3 18 21 8. There were millilitres of water in a container. If only millilitres is poured out, then the container still has millilitres. 250 50 300 9. There are 8 SUVs and cars in the lot. Therefore there are times as many cars as SUVs, or more cars than SUVs. 4 24 32 10. The store owner ordered packages of printer paper at a cost of dollars per package. His bill (before taxes) was dollars. 50 2 25 NSSAL 186 Draft

Put the Numbers in Where It Makes Sense (C) With each question, you have been given a brief statement and you must fit the numbers (supplied in the boxes to the right) into the appropriate blanks so that it all makes sense. A number can only be used once and there is one extra number provided in the boxes that should not be used. 1. The cereal, the more expensive item, cost dollars, and the dish soap cost dollars. The total cost was dollars. 3 5 2 8 2. The jar contained candies. If you ate, which is most of the candy, then that would leave in the jar. 30 60 40 10 3. kg of flour must be divided evenly amongst families. Each family was pleased to get kg. 10 20 60 3 4. The DVD cost dollars. The socks cost dollars. The DVD was dollars more expensive than the socks. 10 8 18 12 5. The corner store owner sold bottles of pop. If each sold for dollars, then his total pop sales were dollars. 30 40 90 3 6. Tom drove for more hours than Ed. Tom drove hours, and Ed drove for hours. 8 7 2 9 7. Kim worked hours on Monday and less on Tuesday. If she got hours on Tuesday, then her total was hours. 8 15 6 7 8. Hinto had nickels and quarters. He had a total of cents in nickels and quarters. 3 65 2 90 9. The friends on his Facebook account increased by, going from to 94 70 24 54 10. There times as many children at the movie compared to adults. There were adults and children. 15 4 80 20 NSSAL 187 Draft

Put the Numbers in Where It Makes Sense (D) With each question, you have been given a brief story and you must fit the numbers (supplied in the box below) into the appropriate blanks in the story so that it all makes sense. A number can only be used once. 1. A cinema in a movie theatre can hold people. Unfortunately that day, only half of the cinema was full meaning only people are viewing the movie. The theatre charges dollars for child tickets and dollars for adult tickets. The total earnings for that showing in that cinema were dollars. 6 120 456 10 60 2. Attendance for the annual blues concert is normally people. This year, the number attending grew by, meaning that a total of people attended. If individual tickets sold for, the promoters expected to bring in dollars more than last year just in ticket sales. 925 75 3000 850 40 3. Taylor works at a hardware store where he makes dollars per hour. Typically he works hours per week, just shy of full time hours, and brings in dollars (before deductions). If he works an additional hours a week, he will make dollars more (before deductions). 38 75 5 570 15 4. Tanya has teenage children. Montez, the oldest, is years old. Tylena, the youngest, is years old. Kiana, the middle child, is years older than Tylena, making her years old. Tanya, the mother, is years old. 13 2 43 18 3 15 NSSAL 188 Draft

5. A group of seniors wants to charter buses to go on a trip. They check with the local charter company and learn that each bus can take people and that the company charges dollars a day for the bus and driver. Since seniors wish to take the trip, then that means that they will need to charter buses. Unfortunately that means that seats on the buses will be unused. If the seniors are planning on taking a two day trip, the total cost for chartering the buses is dollars (before taxes). 10 50 4800 800 3 140 6. A tank initially held litres of water. A pump that removes water from the tank at a rate of litres per minute is switched on ten minutes. That means that litres have been removed, leaving litres in the tank. If someone comes after the pump was switched off and pours litres of water into the tank, the tank will now hold litres of water. 20 400 450 200 50 600 7. Two brothers, Brian and Dave, work for the same company. Brian makes dollars more per hour than Dave. Since Brian makes dollars per hour, that means that Dave makes dollars per hour. That means that in a hour work week, Brian will make dollars before deductions, and David will make dollars before deductions. 640 16 3 40 19 760 8. There were times as many people at the Rolling Bones concert than at the Tragically Flipped concert. If people were at the Flip concert, then that means that people were at the Bones concert. The Bones charged dollars per ticket, while the Flip only charged dollars per ticket. That means that the Bone brought in dollars more in ticket sales for their concert. 7000 40 9 6 020 000 63 000 100 NSSAL 189 Draft

Not Enough Information is Provided In each situation below, you are asked to solve a problem but not quite enough information is provided. Explain what is needed to complete the question. e.g. For a Christmas bonus, the owner of a company is going to rent a bus to take his 110 employees to a concert. How much is it going to cost to rent the buses? Answer: We need to know if the buses are the same size, how many passengers each bus holds, and how much the bus company charges for each bus for this particular round trip. 1. The jar of marbles has a mass of 40 grams. What is the mass of each marble? 2. Manish bought six cans of apple juice. How much did he pay? 3. Marcus has a $600 to pay his friends for helping him shingle his cottage roof. How much should each get? 4. If a large container of water has water being removed from it at a constant rate of 2 litres per minute, then how much water will be left in the container? 5. If at the fire hall fund raiser, volunteers are selling hotdogs for $1, chips for $1.25, and pop for $0.75, then how much money would they make by the end of the day? 6. Jun's children would like to spend a few days at an overnight outdoor adventure camp this summer. The camp charges $40 per day per child. This includes meals. How much will Jun have to pay? NSSAL 190 Draft

Word Problems with Too Much Information With each word problem, identify the extra information (i.e. number) that is not needed to solve the problem, and then identify the correct solution from the multiple choice selections. e.g. There are 3 children in Tammy's family and she needs to purchase 2 litres of orange juice, 5 litres of milk, and 4 litres of apple juice each week for them. How many litres in total of fluids does she purchase each week for her children? (a) 3 2 5 10 (b) 5 4 3 3 (c) 5 4 2 7 (d) 2 5 4 11 Answer: Extra Information: There are 3 children in Tammy's family Correct Solution: (d) 2 5 4 11 e.g. There are 18 kg of potatoes and 12 kg of turnip. If these vegetables are to be shared equally by 3 families, how many kilograms of turnip does each family get? (a) 18 12 30 (b) 12 3 4 (c) 18 3 6 (d) 3 12 36 Answer: Extra Information: 18 kg of potatoes Correct Solution: (b) 12 3 4 1. A stapler costs $5, a notebook costs $3, and a calendar costs $10. How much more is the calendar compared to the stapler? (a) 10 5 5 (b) 10 3 7 (c) 10 5 15 (d) 5 3 15 Extra Information: 2. A bottle of pop costs $2 and a bag of potato chips costs $3. How much does it cost to purchase 8 bottles of pop? (a) 3 8 11 (b) 2 3 5 (c) 8 2 16 (d) 8 2 4 Extra Information: 3. Tyrus is taking a flight. His carry-on bag weighs 10 kg, and his two check-in bags weigh 16 kg and 24 kg. How much do his check-in bags weigh in total? (a) 24 16 8 (b) 24 16 40 (c) 16 10 6 (d) 16 10 26 Extra Information: NSSAL 191 Draft

4. Kiana has 4 children, 6 nieces, and 8 nephews. What is the difference between the number of nieces and the number of nephews Kiana has? (a) 6 4 2 (b) 8 4 2 (c) 6 4 24 (d) 8 6 2 Extra Information: 5. There are 20 pens and 10 pencils to be shared equally among 5 employees. How many pens does each employee get? (a) 20 10 10 (b) 10 5 2 (c) 20 5 4 (d) 20 10 200 Extra Information: 6. There are 7 men and 8 women in a running club. If each woman ran 6 kilometres that day, how far did the women travel in total? (a) 7 6 42 (b) 8 6 14 (c) 7 8 15 (d) 6 8 48 Extra Information: 7. After 3 hours, Ryan completed 2 pages of math homework and 6 pages of English homework. How many pages of homework did he complete within that period of time? (a) 6 3 2 (b) 2 6 8 (c) 3 5 15 (d) 6 3 9 Extra Information: 8. Dave has $30 to spend at the flea market. No sales tax is charged at the flea market. He is trying to decide if he should buy a $12 DVD or a $23 sweatshirt. If he purchases the DVD, how much change will he have? (a) 30 12 18 (b) 12 23 35 (c) 30 12 42 (d) 23 12 11 Extra Information: 9. In 3 hours, Anne could read 90 pages of a novel or run 15 km. How many pages of a novel can Anne read in an hour? (a) 3 15 45 (b) 90 3 30 (c) 3 90 93 (d) 90 15 75 Extra Information: 10. When Lei jogs, she travels at 6 kilometres per hour. When she cycles, she travels at 20 kilometres per hour. How far can she jog in 4 hours? (a) 4 6 10 (b) 20 6 14 (c) 20 4 5 (d) 6 4 24 Extra Information: NSSAL 192 Draft

Create Your Own Math Statement In each case you are provided with a mathematical operation and its corresponding solution. Your mission is to create your own real world statement that corresponds to that operation. Use complete sentences. Try to be creative. Do not use the same type of application more than once (e.g. don't create two math statements involving how much money is left after making a purchase). Naturally there will be a wide range of acceptable answers. e.g. 16-5 = 11 Possible Answer: There were 16 people attending Jeff's party. Five people had to leave at 10:00 p.m., leaving 11 people still at the party. (a) 7 + 9 = 16 (b) 24-9 = 15 (c) 3 6 = 18 (d) 35 5 = 7 NSSAL 193 Draft

(e) 30-12 = 18 (f) 6 7 = 42 (g) 18 6 = 3 (h) 4 + 5 = 9 (i) 7 + 5-2 = 10 (j) 6 4 + 3 = 27 NSSAL 194 Draft

Word Problems (A) Answer the following questions. Show your work (i.e. Show the operation you used). e.g. Marcy went to the flea market and bought each of her 3 nephews the same toy truck. Each toy cost $8. How much did she spend on toys? Answer: 3 8 = 24 She spent $24 on toys for her nephews. 1. Last week Micheline trained 5 hours for the iron man competition, and this week she trained for 6 hours. How many hours in total did she train over this two week period? 2. Nita purchased a small bottle of over-the-counter medication. The bottle initially contained 20 tablets. A few weeks later, there were only 6 tablets left in the bottle. How many tablets had she used? 3. Rhonda ran 5 kilometres each day for 7 days. How far did she run during that week? 4. Four friends have $28 to split evenly between them. How much does each person get? 5. Ajay had $35 cash but then spent $13 on a paperback novel and coffee. How much cash did he have left? 6. A building is 27 metres high. If each story is 3 metres high, how many stories does the building have? 7. Thomas grew tomato plants in his backyard. Two months later, he picked 8 tomatoes from one of the plants and 7 tomatoes from another. How many tomatoes did he pick altogether on that day? 8. A vendor is charging $3 for a hot dog and pop. If 40 customers purchased this combination, how much money did he bring in from the sales of the hot dog and pop combo. 9. Two departments in a company were combined to create one new department. If there were 10 people in the first department, and 9 people in the second department, how many are now in the new department. Assume that no one was fired or laid off. NSSAL 195 Draft

10. Three room mates pooled their money to buy a $900 flat screen television. How much did each pay, assuming they all paid the same amount? 11. Two neighbors live along the same lake. Kiana has 15 metres of beachfront, while Lei has 28 metres of beachfront. How much more beachfront does Lei have compared to Kiana? 12. Two people are cycling. One cyclist is travelling at a speed of 12 km/h, and the other at 19 km/h. How much faster is the second cyclist? 13. There are 5 construction sites, and each site requires 9 workers. How many workers are needed in total? 14. A century is 100 years. A decade is 10 years. How many decades are in a century? 15. Anne has $60. Dave has $39 more than Anne. How much money does Dave have? 16. The owner of a bookstore ordered 60 copies of a new hardcover book. If each book costs her $9, how much will she have to pay for all the books? 17. On Thursday, the low temperature of the day was 4 o C, while the high temperature was 17 o C. What is the difference between the high and low temperature for that day? 18. Manish went for a hike with his friend. Both carried a pack; Manish's pack weighed 12 kg, and his friend's weighed 14 kg. Part way through the hike, the friend injured his ankle, so Manish had to carry out both packs. How much did Manish have to carry out on the return trip? 19. A local rock band was organizing its own concert. They were hoping to raise $480. If the tickets to the show cost $6, how many tickets need to be sold? 20. The doctor instructed the patient to take 4 pills per day for 10 days. How many pills did the doctor prescribe to this patient? NSSAL 196 Draft

Word Problems (B) Answer the following questions. Show all your work in the space provided. 1. A skydiver jumps from the aircraft at an altitude of 3640 metres. At an altitude of 1780 metres, she deploys the parachute. How far did she fall before deploying the chute? 2. Sapphire had 237 books in her collection. She went to a used bookstore and bought 19 more. How many books does she now have? 3. Six campaign workers have to hand out information booklets to the 498 households in a neighborhood. If each worker must distribute the same number of booklets, how many booklets should each worker distribute? 4. Each container of drywall compound weights 27 kilograms. If a contractor needs to purchase 15 containers, what will the total weight be? 5. Jeff's band knows 24 rock songs, 19 blues songs, and 5 country songs. How many songs do they know in total? NSSAL 197 Draft

6. Ryan's take-home pay this month was $1920. If his rent was $650, how much is left over for other expenses? 7. A vehicle travelled 207 kilometres on 9 litres of gasoline. How far could the vehicle travel on one litre of gasoline? 8. The local professional hockey team drew 8454 people to their first game, and 7461 people to their second game. How many people in total attended the first two games? 9. Sixteen people decided to go to an outdoor concert. If each ticket cost $85, how much was spent in total by the sixteen people on tickets? 10. Three friends are driving to a vacation spot in the same car. If they have to travel 1365 kilometres and decide to share the driving equally, how far does each have to drive? NSSAL 198 Draft

11. Jacob has 89 DVD movies. If Sasha has 47 more DVD movies, how many does she have? 12. There are 257 employees at the company. If 118 of them are women, how many are men? 13. Originally there was 196 litres of liquid in the barrel. If 68 litres is removed, how much remains in the barrel? 14. A local charity wants to raise $1260 by selling $9 tickets to the dance at the fire hall. How many tickets need to be sold so that the charity reaches its desired goal? 15. A doggie daycare company has 31 sites across the country. If each site can serve 25 dogs on any one day, what is the maximum number of dogs that can be served by the company on one day? NSSAL 199 Draft

Same Numbers, Similar Context, Different Math (A) Word problems that use similar numbers in similar contexts have been grouped together. The mathematics to solve these grouped word problems, however, is quite different. Your mission is to solve each of these problems, showing the number sentence (e.g. 5 + 16 = 21) that was used solve the question. If there are any word problems involving the purchasing of product, do not worry about the taxes associated with those purchases. 1. (a) Five women went out for lunch and each spent $20. How much was spent in total? (b) Five women wished to purchase a $20 cheese plate for their afternoon party. If they shared in the cost of the cheese plate equally, how much did each woman have to pay? (c) Twenty women were supposed to attend the lunch but five cancelled out at the last moment. How many women attended the lunch? (d) Restaurant reservations were made for twenty women but five women turned up unexpectedly. How many women attended the lunch? 2. (a) Marcus has two dogs; one weighs 40 kg and the other weighs 8 kg. How many times heavier is the large dog compared to the small dog? (b) Jacob's overweight dog originally weighed 40 kg, but after being put on a new diet and exercise program, the dog's weight dropped by 8 kg. How much does the dog weigh? (c) Hanna runs a large kennel and presently owns 40 dogs. If each dog eats 8 kg of dry dog food per month, how many kilograms of dog food does she need each month? (d) At one year, Manish's dog weighed 40 kg. Over the next year the dog gained another 8 kg. How much does the dog weigh? NSSAL 200 Draft

3. (a) Before starting his exercise program, Jim estimated that he only did physical activity for 5 hours per month. After starting his exercise program, he estimates that he is doing 30 hours per month. How many additional hours of exercise are being received under this new program compared to when Jim had no program? (b) Rana was exercising for approximately 30 hours per month, and then decided to increase that by an additional 5 hours per month. How many hours per month of exercise is she now receiving? (c) Each month Grace exercises for 30 hours. Each month Tanya only exercises for 5 hours. How many times larger is Grace's exercise program compared to Tanya's? (d) Each month Bashir exercises for 30 hours. How many hours of exercise would he get over 5 months? 4. (a) Caledonia Elementary School was taking 50 children on a field trip. School board policy requires 10 chaperones. How many people in total should be attending the trip? (b) A college was organizing a ski day for its learners. They decided that they would need 10 buses to transport learners. If each bus can take 50 learners, how many learners in total can the college take to the ski hill? (c) Parker Middle School was going to take 50 students on a field trip, but 10 were unable to attend due to illness. How many students were able to make the trip? (d) Sampson High School was initially planning on using a bus to transport 50 students to the science fair. A bus was unavailable so they decided to rent vans. If each van can transport 10 students, how many vans would be needed? NSSAL 201 Draft

Similar Numbers, Similar Context, Different Math (B) Word problems that use similar numbers in similar contexts have been grouped together. The mathematics to solve these grouped word problems, however, is quite different. Your mission is to solve each of these problems, showing the number sentence (e.g. 5 + 16 = 21) that was used solve the question. If there are any word problems involving the purchasing of product, do not worry about the taxes associated with those purchases. 1. (a) Janice bought a $40 item at the store. If she received $10 change, how much money did she initially pass to the cashier? (b) Janice was hosting a celebration for her family and needed to purchase several $40 items. If she purchased 10 of these items, how much did she pay? (c) Janice wanted to purchase a $40 item but only had $10 on her. Her sister lent her the rest of the money to buy the item. How much money did her sister lend her? (d) Janice received a $40 gift from her 10 friends. If the friends equally shared in the cost of the gift, how much did each person pay? (e) If Janice bought two $40 items and three $10 items, what was the total bill? (f) In January Janice still owed $40 on the purchase of an item. Since that time she has made two monthly payments, each of $10. How much does she still owe? (g) Janice wanted to buy three $40 items but only had nine $10 bills in her purse. How much more money does she need to make the purchase? 2. (a) If Samir has to take 2 pills per day for 20 days, then how many pills did he ultimately have to take? (b) Samir's pill bottle contained 20 pills. If he was instructed to take 2 pills per day, how long would his supply of pills last? (c) Samir's pill bottle contained 20 pills. If he took 2 pills on the first day, how many pills are left for the remaining days? NSSAL 202 Draft

(d) Samir's new pill bottle contains 20 pills and his old pill bottle only contains 2 pills. How many pills does he have in total? (e) Samir has initially had 20 pills. If he takes 2 pills per day for three days, how many pills will be left? (f) Samir had three bottles, each containing 20 pills. He also had four sample packages, each containing 2 pills. How many pills does he have in total? (g) Samir has 20 pills and must take 2 pills twice a day. How long will his supply of pills last? 3. (a) If a business has 5 employees in one department and 30 employees in another department, then how many people do they have in the two departments? (b) If a business has 5 departments, each with 30 employees, then how many employees do they have in total? (c) A business had 30 employees but unfortunately had to lay off 5 people. How many employees do they now have? (d) A business has 30 employees that are shared equally amongst the 5 departments. How many employees does each department have? (e) A business runs three shifts each day. Each shift is made up of 5 managers and 30 assembly line workers. How many employees does this business need each day? (f) The 5 managers each make twenty dollars per hour. The 30 assembly line workers each make ten dollars per hour. Assuming that all employees are at work during the day, how much does the business pay out per hour for employee wages? (g) A business originally had 30 employees but proceeded to hire four teams, each made up of 5 employees. How many employees does the company now have? NSSAL 203 Draft

More than One Question Example Frank collected famous autographs. He had 5 autographs from baseball players, 8 from football players, and 10 from hockey players. (a) How many more autographs does he have football players compared to baseball players? (b) How many autographs does he have in total? (c) If Frank had not collected football player autographs, how many autographs would he have in total? (d) Suppose Frank also wanted to collect autographs of basketball players and set a goal of having 3 times as many of autographs of basketball players as compared to hockey players. If he reached this goal, how many basketball player autographs would he have? Answers: (a) 8 5 3 autographs (b) 5 8 10 23 autographs (c) 5 10 15 autographs (d) 3 10 30 autographs Questions 1. The large container initial held 12 litres of water. Meera first removed 5 litres of water, then removed 3 litres of water. (a) How much water did Meera remove in total? (b) How much more water did Meera first remove compared to the amount she removed the second time? (c) In the end, how much water remained in the large container? (d) If Meera had not removed water for the second time, how much would have remained in the large container. NSSAL 204 Draft

2. Harris retired and purchased a hobby farm. On this farm he several types of animals which included 2 cows and 14 chickens. He also had sheep and pigs. The number of sheep was 3 times the number of cows. He had half as many pigs as chickens. (a) How many sheep did Harris have? (b) How many more chickens did he have compared to cows? (c) How many pigs did Harris have? (d) How many animals did he have in total? (e) If he sold all his pigs, how many animals would he have? 3. Candice restores antique automobiles and motorcycles. She presently has 3 automobiles, and 4 times as many motorcycles. (a) How many motorcycles does she have? (b) How many antique vehicles does she have in total? (c) Assuming that each car has a spare tire, how many tires does she have for her antique automobiles? (d) How many more antique motorcycles does she have compared to antique automobiles? (e) If she purchased another automobile, but the number of motorcycles remained the same, how many times more motorcycles would she have compared to automobiles? NSSAL 205 Draft

Food Chart (A) The following chart shows the amounts of protein, fat and carbohydrates in different servings of foods. Food and Serving Protein (grams) Fat (grams) Carbohydrates (grams) Watermelon (1 slice) 3 2 35 Apple Pie (1 slice) 3 18 60 White Bread (1 slice) 2 1 12 Tomato Juice (1 cup) 2 0 10 Peanut Butter (1 tablespoon) 5 8 3 Canned Tuna in Oil (3 ounces) 24 7 0 Beef and Vegetable Stew (1 cup) 16 11 15 Poached Egg (1 egg) 6 5 1 Blueberries (1 cup) 1 1 20 Corn Chips (1 ounce) 2 9 16 Answer each of the following using the information supplied in the above chart. Include the number sentence (e.g. 10-6 = 4) that you used to find your answer. 1. If you were to have one slice of watermelon and one slice of white bread, then how many grams of protein would you have ingested (i.e. eaten)? 2. What's the difference in the number of grams of fat between one tablespoon of peanut butter and one poached egg? 3. If you ate two cups of blueberries, then how many grams of carbohydrates would you have ingested? 4. How many times larger is the number of grams of protein in one cup of beef and vegetable stew compared to one cup of tomato juice? 5. If you ate a poached egg, a slice of white bread, and one cup of tomato juice, then how many grams of carbohydrates would you have ingested? 6. How many times larger is the number of grams of fat in two slices of apple pie compared to one ounce of corn chips? 7. What is the difference in the number of grams of protein between one 3 ounce can of tuna (in oil) and five slices of watermelon? NSSAL 206 Draft

Food Chart (B) The following chart shows the amounts of protein, fat and carbohydrates in different servings of foods. Food and Serving Food Energy (kilocalories) Sodium (milligrams) Carbohydrates (grams) Watermelon (1 slice) 155 10 35 Apple Pie (1 slice) 405 476 60 White Bread (1 slice) 65 129 12 Tomato Juice (1 cup) 40 881 10 Peanut Butter (1 tablespoon) 95 75 3 Canned Tuna in Oil (3 ounces) 165 303 0 Beef and Vegetable Stew (1 cup) 220 292 15 Poached Egg (1 egg) 75 140 1 Blueberries (1 cup) 80 9 20 Corn Chips (1 ounce) 155 233 16 Answer each of the following using the information supplied in the above chart. Show your work. 1. If you drank a cup of tomato juice and ate one poached egg, how many kilocalories of food energy would you have ingested? 2. How many times larger is the number of grams of carbohydrates in two cups of beef and vegetable stew compared to one cup of tomato juice? 3. What is the difference in the number of milligrams of sodium in one slice of apple pie and one poached egg? 4. How many milligrams of sodium are there in four slices of white bread? NSSAL 207 Draft

5. If you ate one slice of watermelon, one tablespoon of peanut butter, and one ounce of corn chips, how many kilocalories would be ingested? 6. What is the difference in the number of milligrams of sodium in three ounces of corn chips and two tablespoons of peanut butter? 7. How many grams of carbohydrates would be ingested if you ate two slices of pie, three slices of watermelon, and one cup of blueberries? 8. How many times larger is the amount of sodium in two poached eggs compared to four slices of watermelon? 9. What is the difference in the number of kilocalories of a meal comprised of one cup of beef and vegetable stew and one cup of tomato juice, and a meal comprised of a three ounce can of tuna and a slice of white bread. 10. How many times larger is the amount of carbohydrates in a meal comprised of one slice of apple pie and two cups of blueberries, compared to a meal comprised of one cup of beef and vegetable stew and one slice of watermelon? NSSAL 208 Draft

Keeping Track of New Stock (A) The store just started selling five new products. A large order of each item was made at the beginning of week one and all of these items were placed on their shelves. The spreadsheet below shows how many units of each product are present on the shelves at the beginning of each week. Assume that the shelves were not restocked with the new items. Delicate Deluxe Dog Extra Soft Greek Olives Ceramic Pots Chocolates Food Toilet Tissue Week 1 30 40 20 20 10 Week 2 24 34 13 18 4 Week 3 10 22 4 15 0 Use the information in the spreadsheet to answer the following questions. Show the number sentence (e.g. 19-8 = 11) that you used to solve the question. 1. How many times larger was the number of units of deluxe dog food compared to the number of units of ceramic pots at the beginning of week one? 2. How many more units of delicate chocolates were there on the shelves at the beginning of week one compared to units of extra soft toilet tissue? 3. In total, how many units of Greek olives and ceramic pots were on the shelves at the beginning of week two? 4. If they had tripled their order of extra soft toilet paper at the beginning of week one, how many units would they have ordered? 5. How many units of delicate chocolates were sold between the beginning of week one and the beginning of week three? 6. How many times larger is the number of units of extra soft toilet paper on week one compared to week three? 7. In total, how many units of delicate chocolates, extra soft toilet paper and Greek olives were on the shelves at the beginning of week three? 8. If five customers wanted to buy all the units of Greek olives that were present at the beginning of week three and each would purchase the same amount, how many units would each customer get? NSSAL 209 Draft

Keeping Track of New Stock (B) The store just started selling five new products. A large order of each item was made at the beginning of week one and all of these items were placed on their shelves. The spreadsheet below shows how many units of each product are present on the shelves at the beginning of each week. Assume that the shelves were not restocked with the new items. Delicate Deluxe Dog Extra Soft Greek Olives Ceramic Pots Chocolates Food Toilet Tissue Week 1 30 40 20 20 10 Week 2 24 34 13 18 4 Week 3 10 22 4 15 0 Use the information in the spreadsheet to answer the following questions. Show the number sentence (e.g. (45-33) + (30-25) = 17) that you used to solve the question. 1. If the store doubled the number of units of deluxe dog food and ceramic pots they ordered on week one, how many units of these two items would they have in total at that time? 2. How many units of deluxe dog food and Greek olives were sold in total between the beginning of week two and the beginning of week three? 3. How many more units of deluxe dog food were sold between weeks one and two compared to units of Greek olives sold in the same time period? 4. How many more units of delicate chocolates were sold between weeks two and three compared to units of extra soft toilet tissue sold in the same time period? 5. How many more combined units of deluxe dog food and extra soft toilet tissues are on the shelves at the beginning of week two compared to the number of units of delicate chocolates at that same time? 6. If the units sold of delicate chocolates tripled between the beginning of week one and the beginning of week two, then how many units would have been sold at that time? 7. How many times larger was the number of units sold of ceramic pots between the beginning of week one and the beginning of week three compared to units sold of Greek olives over the same period? 8. How many times larger was the number of units sold of deluxe dog food between the beginning of week two and the beginning of week three compared to units sold of the same product between the beginning of week one and the beginning of week two? NSSAL 210 Draft

Consumer Math NSSAL 211 Draft

How Much Do They Have? (A) Determine the amount of money each person has. Kate s Money: Paula s Money: Meera s Money: Ryan s Money: Yoshi s Money: Your Answers: Kate s Money: Paula s Money: Meera s Money: Ryan s Money: Yoshi s Money: NSSAL 212 Draft

How Much Do They Have? (B) Determine the amount of money each person has. Dave s Money: Shelly s Money: Maurita s Money: Jun s Money: Lei s Money: Your Answers: Dave s Money: Shelly s Money: Maurita s Money: Jun s Money: Lei s Money: NSSAL 213 Draft

How Much Do They Have? (C) Determine the amount of money each person has. Andrew s Cash: Mary s Cash: Kara s Cash: Montez s Cash: Shima s Cash: Your Answers: Andrew s Cash: Mary s Cash: Kara s Cash: Montez s Cash: Shima s Cash: NSSAL 214 Draft

How Much Do They Have? (D) Determine the amount of money each person has. Hamid s Cash: Tanya s Cash: Samir s Cash: Mark s Cash: Hatsu s Cash: Your Answers: Hamid s Cash: Tanya s Cash: Samir s Cash: Mark s Cash: Hatsu s Cash: NSSAL 215 Draft

How Much Do They Have? (E) Determine the amount of money each person has. We apologize that the bills are not the appropriate size compared to the coins. Sasha s Money: Hinto s Money: Lisa s Money: Tiva s Money: Meera s Money: Your Answers: Sasha s Money: Hinto s Money: Lisa s Money: Tiva s Money: Meera s Money: NSSAL 216 Draft

Emptying the Junk Drawer You were emptying your junk drawer and scattered the money across the top of your table (See below.). You have few bills and lots of change. How much money do you have from that drawer? Use the chart on the next to organize the information and complete your calculations. NSSAL 217 Draft

Bills or Change Number of Each Value in Dollars $20 bills $10 Bills $5 Bills Toonies ($2 coins) Loonies ($1 coins) Quarters (25 coins) Dimes (10 coins) Nickels (5 coins) Total: If you found three more nickels, five more quarters, and four more loonies, how much would you have in total? NSSAL 218 Draft

Connect Four Money Game Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place a paper clip on each of the strips below (i.e. Nickel and Dime Strip, and Quarter and Loonie Strip). Once they have chosen the coinage, they can capture one square with the appropriate total (e.g. 3 nickels plus 1 loonie is equal to $1.15). They either mark the square with an X or place a colored counter on the square. There may be other squares with that same total but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that total using an O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: $0.35 $1.05 $1.10 $0.45 $0.35 $0.95 $0.45 $0.85 $0.60 $1.15 $0.65 $1.10 $1.10 $0.95 $1.20 $0.30 $0.90 $0.85 $0.65 $0.55 $0.70 $1.10 $1.20 $0.35 $0.30 $0.90 $0.35 $0.60 $0.80 $0.40 $0.60 $1.05 $0.70 $0.85 $1.15 $0.55 Nickel and Dime Strip: Quarter and Loonie Strip: 1 nickel 2 nickels 3 nickels 1 dime 2 dimes 1 quarter 2 quarters 3 quarters 1 loonie NSSAL 219 Draft

Find the Price Using the internet, flyers, and/or catalogues, find the price of each of the items. Assume that we are purchasing new items. If the price is a sale price, check off the appropriate box. Also identify the name of the business in which you can purchase the item at that price. Answers are going to vary because learners are likely to be using different websites, flyers, and catalogues. Milk (2 litres) Tube of Toothpaste Hamburger Meat (1 kg) Price: Sale Price: Sale Price: Sale Business: Business: Business: Cooked Chicken Head of Lettuce 20 inch Delivery Pizza Price: Sale Price: Sale Price: Sale Business: Business: Business: Woman's Winter Boots Pair of Men's Jeans Leather Gloves Price: Sale Price: Sale Price: Sale Business: Business: Business: Mountain Bike (Adult) Table Lamp Toaster Oven Price: Sale Price: Sale Price: Sale Business: Business: Business: Queen Size Mattress Gas Barbeque Portable Music Player Price: Sale Price: Sale Price: Sale Business: Business: Business: 40 inch Flatscreen TV Leather Sofa Compact Car (e.g. Corolla) Price: Sale Price: Sale Price: Sale Business: Business: Business: NSSAL 220 Draft

Name a Product near that Price In this activity you are to name a product near the indicated price. Naturally every learner will have different answers. You can use flyers or catalogues to assist with this activity. e.g. Name a product that worth approximately $2. Some Possible Answers: Can of Soup, Pen, Comb, Small Package of Screws Price Your Product Price Your Product 1. $1 2. $5 Price Your Product Price Your Product 3. $10 4. $20 Price Your Product Price Your Product 5. $40 6. $70 Price Your Product Price Your Product 7. $100 8. $150 Price Your Product Price Your Product 9. $250 10. $400 Price Your Product Price Your Product 11. $700 12. $1000 Price Your Product Price Your Product 13. $1500 14. $2000 Price Your Product Price Your Product 15. $4000 16. $8000 NSSAL 221 Draft

Least to Most Expensive In each case you are supplied with four common items that one might purchase. Your mission is to number the items 1 through 4 in the space below, where 1 is the least expensive, and 4 is the most expensive. 1. Two Slice Toaster Litre of Milk Refrigerator Electric Fry Pan 2. Silver Earrings Leather Jacket Pair of Socks Pencil 3. Power Drill Winter Gloves Fingernail Clippers Mattress (Queen) 4. Hardcover Book Birthday Card Prescription Glasses Pair of Winter Boots 5. Coffee Table Kitchen Stove Can Opener Electric Kettle 6. Four Winter Tires 20 inch Television DVD Player Four Litres of Oil 7. Small Flashlight Delivery Pizza Reclining Chair Table Lamp 8. Hair Dryer Coffee Mug Chocolate Bar Toaster Oven 9. Paperback Novel Big Concert Ticket Spring Jacket Bus Toll 10. Love Seat Dish Soap 10 kg Turkey Four Litres of Milk NSSAL 222 Draft

What Are the Three Items Worth? In each case, you are given three items and four prices. Match the best price to the item. Item: Price Item: Price 1. Hammer 2. Box of Cereal Florescent Light Bulb Can of Pop A Pair of Jeans T-shirt Price Choices: $1, $3, $10, $50 Price Choices: $2, $6, $12, $50 Item: Price Item: Price 3. Sofa 4. Fast-food Hamburger A Pair of Sunglasses A Pair of Work Boots Microwave Oven Knapsack for School Price Choices: $2, $20, $150, $600 Price Choices: $3, $40, $90, $400 Item: Price Item: Price 5. A Man's Haircut 6. Tube of Toothpaste Loaf of Bread An Adult Bicycle Small Waste Paper Basket Winter Coat Price Choices: $2, $25, $80, $250 Price Choices: $3, $15, $35, $120 NSSAL 223 Draft

What Is It Worth? (A) You have been given a list of items and been asked to select a price that best matches that item. The prices have been supplied below. Only use each price once. You will also be asked to write out the value using words (e.g. $1249 is one thousand two hundred forty-nine dollars). (a) Item Ride-on Lawn Mower Approximate Price (Number) Approximate Price (Words) (b) DVD/Blu-ray Player (c) Toaster (d) HD Video Camera (e) Compact Car (f) 42 inch Flat Screen TV (g) Tank of Gas (Compact Car) Prices to Choose From: $17 $14 900 $50 $2149 $549 $329 $38 900 $99 NSSAL 224 Draft

What Is It Worth? (B) You have been given a list of items and been asked to select a price that best matches that item. The prices have been supplied below. Only use each price once. You will also be asked to write out the value using words (e.g. $1249 is one thousand two hundred forty-nine dollars). (a) Item Washing Machine Approximate Price (Number) Approximate Price (Words) (b) Hair Dryer (c) Minivan (d) Fast Food Meal for One (e) Gasoline Push Mower (f) Child's Bicycle (g) Four Person Hot Tub Prices to Choose From: $239 $8 $3599 $21 $12 900 $469 $22 900 $69 NSSAL 225 Draft

Purchasing Groceries On this page and the next, you have been provided with a list of common items that can be found at a grocery store. Your job is to indicate which products you would purchase for each of the four scenarios. Scenario #1: You are single and have a limited budget of $150. Scenario #2: You are single and have a limited budget of $230. Scenario #3: You are a parent with two children (ages 7 and 10), and have a limited budget of $250. Scenario #4: You are a parent with two children (ages 7 and 10), and have a limited budget of $350. Be prepared to discuss your selections with your instructor and/or classmates. Please note that items whose weight is marked with an asterisk (*), do not have to purchase at that weight. For example, one pound (lb.) of tomatoes can be purchased for $2, but half a pound of tomatoes can be purchased for $1. You decide how much you need. In these cases just indicate the amount to be purchased using the appropriate dollar value. Item Price Scenario #1 Single, $150 budget Potatoes (10 lb. bag) $4 Potato Salad (454 g) $3 Green Peppers (four pack) $6 Tomatoes (1 lb.*) $2 Baby Carrots (340 g) $2 Cucumber $2 Cauliflower (1 lb.*) $4 Apples (5 lbs.) $5 Oranges (4 lbs.) $4 Pears (1 lb.*) $2 Peaches (1 lb.*) $3 Seedless Red Grapes (1 lb.*) $4 Bananas (1 lb.*) $2 Strawberries (1 lb.) $3 Kiwi (4) $2 Whole Pineapple $5 Loaf of Bread (675 g) $2 Crackers (450 g) $2 Cereal (445 g) $4 Milk (2 l) $4 Cheese (500 g block) $6 Cheese Slices (500 g) $6 Parmesan Cheese (250 g) $6 Margarine (454 g) $3 Scenario #2 Single, $220 budget Scenario #3 Family of 3, $250 budget Scenario #4 Family of 3, $350 budget NSSAL 226 Draft

Item Price Scenario #1 Single, $150 budget Dozen Small Eggs $2 Stew Beef (1 lb.) $6 Ground Beef (1 lb.*) $6 Port Tenderloin (1 lb.*) $5 Bacon (500 g) $6 Roasting Chicken (5 lb.) $14 Trout Fillets (1 lb.*) $8 Haddock Fillets (1 lb.*) $6 Salmon Portion (140 g) $5 Canned Tuna (170 g) $2 Canned Cooked Ham (454 g) $7 Chicken Noodle Soup (540 ml) $2 Canned Chili (425 g) $3 Frozen Pizza (400 g) $6 Frozen Lasagna (1 kg) $9 Frozen Meatballs (680 g) $10 Frozen French Fries (454 g) $4 Frozen Corn (750 g) $3 Frozen Mixed Vegetables (1 kg) $3 Frozen Lemonade (295 ml) $1 Peanut Butter (500 g) $4 Roasted Cashews (100 g) $2 Macaroni and Cheese (200 g) $1 Ketchup (1 L) $3 Sunflower Oil (1 L) $6 Tea (240 bags) $11 Coffee (300 g) $8 Cranberry Cocktail (1.89 L) $3 Pop (2 L) $2 Potato Chips (235 g) $4 Chocolate Bars (four pack) $4 Ice Cream (1.5 L) $4 Deodorant (150 g) $4 Toothpaste (130 ml) $3 Bathroom Tissue (8 rolls) $5 Paper Towels (2 rolls) $3 Dishwashing Liquid (950 ml) $2 Bathroom Cleaner (500 ml) $2 Total: Scenario #2 Single, $220 budget Scenario #3 Family of 3, $250 budget Scenario #4 Family of 3, $350 budget NSSAL 227 Draft

Measurement NSSAL 228 Draft

Which Measurement Is Reasonable? In each case, you have been given a situation or object in which you must consider which supplied measurement is most appropriate. 1. The length of an adult's arm (a) 65 centimetres (c) 45 kilometres 2. The length of three city blocks (a) 9 metres (c) 3 centimetres (b) 30 metres (d) 110 centimetres (b) 20 kilometres (d) 1 kilometre 3. The amount of lemonade that could be held in a pitcher (a) 30 millilitres (b) 8 litres (c) 2 litres (d) 50 millilitres 4. The weight of a ten year old boy (a) 75 grams (c) 100 kilograms 5. The amount of water in a drinking glass (a) 3 litres (c) 350 millilitres (b) 34 kilograms (d) 450 grams (b) 300 litres (d) 40 millilitres 6. The height of a three-story apartment building (a) 12 metres (b) 100 cm (c) 1 kilometre (d) 30 metres 7. The weight of a compact car (a) 900 grams (c) 300 kilograms (b) 1800 kilograms (d) 7000 grams 8. The length of a man's fingernail on his pinkie finger (a) 4 centimetres (b) 7 metres (c) 2 metres (d) 1 centimetre 9. The distance from Halifax, Nova Scotia to Truro, Nova Scotia (a) 15 kilometres (b) 4000 metres (c) 125 centimetres (d) 100 kilometres 10. The amount of gasoline that can be held in a compact car's gas tank (a) 50 millilitres (b) 8 litres (c) 40 litres (d) 130 millilitres NSSAL 229 Draft

Telling Time (A) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 230 Draft

Telling Time (B) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 231 Draft

Telling Time (C) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 232 Draft

Telling Time (D) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 233 Draft

Telling Time (E) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 234 Draft

Telling Time (F) (a) (b) (c) (d) (e) (f) (g) (h) (i) All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 235 Draft

Connect Four Time Ahead Game (A) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place paper clips on the strips below; one on the Start Time Strip and one on the Minutes Ahead Strip. If the player chose 3:30 (start time) and 45 (minutes ahead), then they could capture a square labelled 4:15. They either mark the square with an X or place a colored counter on the square. There may be other squares with this same time but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that time using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 5:00 4:30 6:00 4:15 3:30 5:45 3:45 5:15 4:00 4:45 3:45 4:30 4:45 5:45 3:15 5:00 4:00 5:15 3:15 4:00 5:30 4:15 6:00 3:45 4:15 5:00 4:45 5:15 3:15 5:30 5:30 3:30 4:30 3:45 5:00 4:15 Start Time Strip Minutes Ahead Strip 3:00 3:30 4:00 4:30 5:00 15 30 45 60 NSSAL 236 Draft

Connect Four Time Ahead Game (B) Number of Players: Two Objective: The winner is the first player to connect four of his/her pieces horizontally, vertically or diagonally. Instructions: 1. Roll a die to see which player will go first. 2. The first player looks at the board and decides which square he/she wishes to capture. They place paper clips on the strips below; one on the Start Time Strip and one on the Minutes Ahead Strip. If the player chose 2:45 (start time) and 30 (minutes ahead), then they could capture a square labelled 3:15. They either mark the square with an X or place a colored counter on the square. There may be other squares with this same time but only one square can be captured at a time. 3. Now the second player is ready to capture a square but he/she can only move one of the paperclips. They then mark the square with that time using a O or a different colored marker. If a player cannot move a single paperclip to capture a square, a paperclip must still be moved in order to ensure that the game can continue. 4. Play alternates until one player connects four squares. Remember that only one player clip is moved at a time. If none of the players is able to connect four, then the winner is the individual who has captured the most squares. Game Board: 3:45 3:00 4:15 3:15 4:00 3:30 3:15 4:30 2:30 3:30 2:45 3:45 2:45 4:00 3:15 3:45 3:30 4:15 3:45 3:30 4:15 3:00 4:00 3:15 4:30 3:00 3:45 3:15 2:30 3:30 3:15 2:45 3:30 4:00 3:45 3:00 Start Time Strip Minutes Ahead Strip 2:15 2:30 2:45 3:00 3:15 3:30 15 30 45 60 NSSAL 237 Draft

How Much Time Has Passed? (A) With each question you have been given a start time and a finish time. Your job is to determine how much time has passed between those two times. (a) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (b) Start Time: Finish Time: Time Passed: hour(s), minutes (c) Start Time: Finish Time: Time Passed: hour(s), minutes (d) Start Time: Finish Time: Time Passed: hour(s), minutes NSSAL 238 Draft

(e) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (f) Start Time: Finish Time: Time Passed: hour(s), minutes (g) Start Time: Finish Time: Time Passed: hour(s), minutes (h) Start Time: Finish Time: Time Passed: hour(s), minutes All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 239 Draft

How Much Time Has Passed? (B) With each question you have been given a start time and a finish time. Your job is to determine how much time has passed between those two times. (a) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (b) Start Time: Finish Time: Time Passed: hour(s), minutes (c) Start Time: Finish Time: Time Passed: hour(s), minutes (d) Start Time: Finish Time: Time Passed: hour(s), minutes NSSAL 240 Draft

(e) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (f) Start Time: Finish Time: Time Passed: hour(s), minutes (g) Start Time: Finish Time: Time Passed: hour(s), minutes (h) Start Time: Finish Time: Time Passed: hour(s), minutes All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 241 Draft

How Much Time Has Passed? (C) With each question you have been given a start time and a finish time. Your job is to determine how much time has passed between those two times. (a) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (b) Start Time: Finish Time: Time Passed: hour(s), minutes (c) Start Time: Finish Time: Time Passed: hour(s), minutes (d) Start Time: Finish Time: Time Passed: hour(s), minutes NSSAL 242 Draft

(e) Start Time Finish Time Your Answers: Start Time: Finish Time: Time Passed: hour(s), minutes (f) Start Time: Finish Time: Time Passed: hour(s), minutes (g) Start Time: Finish Time: Time Passed: hour(s), minutes (h) Start Time: Finish Time: Time Passed: hour(s), minutes All images generated using the online applet found at: http://www.wmnet.org.uk/wmnet/custom/files_uploaded/uploaded_resources/503/clock.swf NSSAL 243 Draft

Geometry (From 3D to 2D) NSSAL 244 Draft

Isoball As an introduction to 3D geometry, we are going to be playing an online game in which you use a limited number of geometric pieces and directional arrows to move a ball from a raised position to a hole located at a specific point on the floor. This game is available at: http://www.coolmath-games.com/0-isoball-3/index.html (or Google Search: Coolmath Games Isoball) Below we have shown the "before" and "after" images for one particular round of this game Before We were given 2 direction arrows, 4 wedges and 9 cubes that must be placed so that the ball can move from the upper left to the hole on the floor. All the objects must be used. After The objects have been correctly place. The objects can be rotated by repeatedly clicking on the item in the lower menu before placing it in position. Making sure that you have at least 45 minutes to work on this game, see how many rounds you can complete successfully within that time. Periodically call your instructor over so that he/she can see the progress you are making. NSSAL 245 Draft

Orthographic Projections (A) An orthographic projection is a method of representing a three-dimensional object in two dimensions. One creates six basic views (top, bottom, right, left, front, and back views) that together describe the original three-dimensional object. Example 1 Suppose we took four hex-a-links (i.e. cubic building blocks) and attached them together to form the letter L as shown in the accompanying diagram. We want to create the orthographic projection for this L-shaped object. Answer: Front View Back View Right View Left View Top View Bottom View Example 2 Suppose we took six hex-a-links and attached them together to form the following figure. Create the orthographic projection (i.e. six views) for this object. Answer: Front View Back View Right View Left View Top View Bottom View Notice that some of the views have vertical and horizontal lines drawn across them. That is there to indicate the certain faces/surfaces of the figure are closer or further away from you from that NSSAL 246 Draft

viewing position. If all of the faces/surfaces are the same distance away from your viewing position, then there are no horizontal or vertical lines across the 2D drawing. Questions For each of the figures, draw the six views in the space provided. Feel free to use hex-a-links to create a model of the figure. 1. This figure is comprised of four cubes. Front View Back View Right View Left View Top View Bottom View 2. This figure is comprised of five cubes. Front View Back View Right View Left View Top View Bottom View NSSAL 247 Draft

3. This figure is comprised of four cubes. Front View Back View Right View Left View Top View Bottom View 4. This figure is comprised of five cubes. Front View Back View Right View Left View Top View Bottom View NSSAL 248 Draft

5. This figure is comprised of five cubes. Front View Back View Right View Left View Top View Bottom View 6. This figure is comprised of six cubes. Front View Back View Right View Left View Top View Bottom View NSSAL 249 Draft

Orthographic Projections (B) For each of the figures, draw the six views in the space provided. Feel free to use hex-a-links to create a model of the figure. 1. This figure is comprised of five cubes. Front View Back View Right View Left View Top View Bottom View 2. This figure is comprised of five cubes. Front View Back View Right View Left View Top View Bottom View NSSAL 250 Draft

3. This figure is comprised of six cubes. Front View Back View Right View Left View Top View Bottom View 4. This figure is comprised of six cubes. Front View Back View Right View Left View Top View Bottom View NSSAL 251 Draft

Transfer Image to Dot Paper In each case, transfer the image of the three dimensional figure to the dot paper. Two sample questions are done for you so that you can see how the edges of the figure are formed by connecting two points. e.g. Image Dot Paper Image Dot Paper e.g. 1. 2. 3. 4. 5. 6. The images drawn on the dot paper are actually isometric projections. We will talk about these in our next lesson and learn how to change an orthographic projection to an isometric projection, and vice versa. NSSAL 252 Draft

Isometric Projections In the previous section we learned about orthographic projections; a series of drawing that showed the six perspectives of a three dimensional object. There are other types of projections called isometric projections or drawings. In these projections the image of an object is presented from a skewed direction such that more than one side of the object is viewed in the same picture. Specifically the object's vertical lines are drawn vertically, and the horizontal lines in the width and depth planes are shown at 30 degrees to the horizontal. Rather than using traditional drafting techniques (i.e. a 30 o -60 o -90 o triangle and T-square), we will be using isometric dot paper to accomplish the same task. Isometric dot paper is comprised of a series of diagonal dots, that when joined can form isometric drawings. Blank Isometric Dot Paper Cube Drawn on Isometric Dot Paper 30 o 30 o f t s Notice that the front (f), side (s), and top (t) faces have been labeled on the cube above. With the questions in the last section, you were supplied with isometric drawings of a figure and then been asked to create the corresponding orthographic projections. In this section, we will be supplied with the orthographic projections and asked to draw the corresponding isometric diagram on the isometric dot paper. For these particular questions, we will be dealing with simple figures where only three perspectives (front, right side, and top views) will be supplied. Example Front View Right Side Top View Isometric Drawing NSSAL 253 Draft

Questions 1. Front View Right Side Top View Isometric Drawing 2. Front View Right Side Top View Isometric Drawing 3. Front View Right Side Top View Isometric Drawing NSSAL 254 Draft

4. Front View Right Side Top View Isometric Drawing 5. Front View Right Side Top View Isometric Drawing 6. Front View Right Side Top View Isometric Drawing NSSAL 255 Draft

7. Front View Right Side Top View Isometric Drawing 8. Front View Right Side Top View Isometric Drawing 9. Front View Right Side Top View Isometric Drawing NSSAL 256 Draft

Orthographic Isometric Challenge You need at least two learners to complete this activity and 26 cube-a-links (i.e. interlocking cubes). Each person/team will create two challenging cube-a-links models, pass these models to the opposing person/team, and then both people/teams will complete the isometric diagram and orthographic projections for the models handed to them by the competition. The first model must be comprised of only six cube-a-links, and the second of only seven cube-a-links. Challenge #1 Isometric Diagrams for First Model Comprised of Six Cube-a-Links Orthographic Projection for First Model Comprised of Six Cube-a-Links Front View Back View Right View Left View Top View Bottom View NSSAL 257 Draft

Challenge #2 Isometric Diagrams for First Model Comprised of Seven Cube-a-Links Orthographic Projection for Second Model Comprised of Seven Cube-a-Links Front View Back View Right View Left View Top View Bottom View NSSAL 258 Draft

Edges, Faces and Vertices (A) Faces: any flat surface Edges: where two faces meet Vertex: where edges meet Example: This figure has: 6 faces 12 edges 8 vertices Questions: Determine the number of faces, edges and vertices for each of these figures. Drawing on the diagrams with colored pencils can be useful when trying to count edges and vertices (so that you don't count the same vertex or edge more than once). 1. 2. 3. Number of Faces: Number of Faces: Number of Faces: Number of Edges: Number of Edges: Number of Edges: Number of Vertices: Number of Vertices: Number of Vertices: 4. 5. 6. Number of Faces: Number of Faces: Number of Faces: Number of Edges: Number of Edges: Number of Edges: Number of Vertices: Number of Vertices: Number of Vertices: 7. 8. 9. Number of Faces: Number of Edges: Number of Vertices: Number of Faces: Number of Edges: Number of Vertices: Number of Faces: Number of Edges: Number of Vertices: NSSAL 259 Draft

Edges, Faces and Vertices (B) Faces: any flat surface Edges: where two faces meet Vertex: where edges meet Example: Questions: This figure has: 8 faces 18 edges 12 vertices Determine the number of faces, edges and vertices for each of these figures. 1. 2. 3. Number of Faces: Number of Faces: Number of Faces: Number of Edges: Number of Edges: Number of Edges: Number of Vertices: Number of Vertices: Number of Vertices: 4. 5. 6. Number of Faces: Number of Faces: Number of Faces: Number of Edges: Number of Edges: Number of Edges: Number of Vertices: Number of Vertices: Number of Vertices: 7. 8. 9. Number of Faces: Number of Edges: Number of Vertices: Number of Faces: Number of Edges: Number of Vertices: Number of Faces: Number of Edges: Number of Vertices: NSSAL 260 Draft

Construct the Geometric Figure Learners can cut each of the following out, fold on the dotted lines, and using tape and/or glue create the desired geometric figure. (Tabs have been included for pasting purposes.) NSSAL 261 Draft

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Nets The net of a solid is created by making cuts along some edges of a solid and opening it up to form a plane figure. Based on this definition, a net can be folded up to create the original 3D solid. On this activity sheet we want you to match the original object to its corresponding net. Original Object Matches With 1. A Net 2. B 3. C 4. D 5. E 6. F NSSAL 266 Draft

Draw the nets associated with each of these figures NSSAL 267 Draft

Describe the Faces The faces of a three dimension object can be described using terms like triangles, quadrilaterals, etc. Triangles - three sided figures Equilateral Triangles - all sides are of the same length Isosceles Triangles - two sides are of the same length Scalene Triangles - none of the sides are of the same length Right Triangles - one of the interior angles is right-angled (i.e. a 90 o angle) Quadrilaterals - four sided figures Trapezoid - one pair of parallel sides Parallelogram - two pair of parallel sides Rhombus - two pair of parallel sides and all sides are of equal length Rectangle - two pair of parallel sides and four right angles Square - two pair of parallel sides, four right angles, and all sides of equal length Other Polygons - multi-sided figures Pentagon - five sided figure Hexagon - six sided figure Octagon - eight sided figure NSSAL 268 Draft

Questions: 1. Nets have been drawn for a variety of three dimensional objects. Indicate how many faces we are dealing with, describe the faces of those objects using the appropriate terminology (e.g. equilateral triangle, square, pentagon, ), and indicate whether some of the faces have the same dimensions. If sides appear to be the same length, if sides appear parallel, or if angles appear to be right angled, assume that this is the case. e.g. Answer: There are a total of five faces. Two of the faces are identical isosceles triangles Two of the faces are identical rectangles. The last face is a rectangle. (a) (b) (c) (d) NSSAL 269 Draft

2. Isometric diagrams have been provided. You must identify how many faces you are dealing with, describe those faces using the appropriate terminology, and indicate how many faces have the same dimensions. (a) (b) (c) (d) NSSAL 270 Draft

(e) (f) (g) (h) NSSAL 271 Draft

3. You will be given a figure and asked to state the number of faces, draw the individual faces separately, include the dimensions of the faces, indicate the number of faces that have the same dimensions, and describe those faces using the appropriate terminology term (e.g. equilateral triangle, square, pentagon, ). Please note, if something looks like a right angle in the diagram, just assume that it is. Similarly, if things look parallel, assume that they are. e.g. 11 cm 11 cm 8 cm 20 cm Answer: Total Number of Faces: 5 Two Isosceles Triangle Faces Two Rectangle Faces 11 cm 11 cm 11 cm 8 cm 20 cm One Rectangle Face 8 cm 20 cm (a) Assume that all four interior angles on the base are right angled. 6 cm 6 cm 14 cm NSSAL 272 Draft

(b) Assume that all four interior angles on the base are right angled. 6 cm 10 cm 8 cm 10 cm (c) Assume that all four interior angles on the base are right angled. 24 mm 24 mm 15 mm 15 mm (d) Assume that all four interior angles on the base are right angled. 4 m 16 m 9 m NSSAL 273 Draft

(e) 11 cm 11 cm 7 cm 7 cm 7 cm (f) Assume that all four interior angles on the base are right angled. 6 m 4 m 5 m 9 m 9 m (g) Assume that all four interior angles on the base are right angled. 8 cm 30 cm 8 cm NSSAL 274 Draft

(h). Assume that all four interior angles on the base are right angled 13 cm 13 cm 4 cm 4 cm 10 cm 10 cm (i) Assume that all four interior angles on the base are right angled 5 m 5 m 5 m 2 m (j) 10 cm 10 cm 6 cm 6 cm 8 cm 8 cm NSSAL 275 Draft

(k) Assume that all four interior angles on the base are right angled. Also note that all edges on this figure measure 2 metres. 2 m (l) Notice that the back face and front face are not the same size. 10 cm 4 cm 2 cm 4 cm 8 cm 10 cm NSSAL 276 Draft

Geometry Terminology Crossword 1. 2. 3. 4. 5. 6. 7. 8. 9 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Across 1. a point where edges meet 4. a four sided figure 8. a type of projection used to represent a three dimensional object which shows six basic views (top, bottom, right, left, front, and back) of the object 10. a triangle with a 90 o angle 11. a triangle where two sides are of the same length 15. a triangle where the three sides are of different lengths 16. any flat surface on a three dimensional solid. 17. an eight sided figure 18. a six sided figure NSSAL 277 Draft

19. created when two faces meet Down 2. a triangle where all sides are of the same length 3. a representation of a three dimensional solid created by cutting along the edges of the solid and opening it up to form a plane figure 5. a type of projection used to represent a three dimensional object which shows the object from a skewed direction such that more than one face is visible in the picture 6. a five sided figure 7. a four sided figure with two pair of parallel sides 9. a four sided figure with two pair of parallel sides and four sides of equal length 12. a four sided figure with only one pair of parallel sides 13. a four sided figure with two pair of parallel sides, sides of equal length, and four right angles 14. a four sided figure with two pair of parallel sides and four right angles NSSAL 278 Draft

Reflections (A) Draw the reflected image on the isometric dot paper. NSSAL 279 Draft

Reflections (B) Draw the reflected image on the isometric dot paper. NSSAL 280 Draft

Reflections (C) Draw the reflected image on the isometric dot paper. NSSAL 281 Draft

Base Ten Blocks NSSAL 282 Draft

What's the Number? What number is represented by each of these sets of base ten blocks? (a) (b) Number: (c) Number: (d) Number: Number: NSSAL 283 Draft

(e) Number: (f) Number: (g) Number: (h) Number: Scrambled Answer Key (In no particular order) 2308 3132 3406 2247 3080 524 1420 1358 4019 NSSAL 284 Draft

Express the Number Different Ways In each case, determine the number represented by the base ten blocks. Then write the number in its expanded form and write the number out using words. An example has been provided. e.g. (a) Number: 3257 Expanded Form: 3000 + 200 + 50 + 7 Using Words: Three thousand, two hundred fifty-seven Number: Expanded Form: Using Words: (b) Number: Expanded Form: Using Words: (c) Number: Expanded Form: Using Words: NSSAL 285 Draft

(d) Number: Expanded Form: Using Words: (e) Number: Expanded Form: Using Words: (f) Number: Expanded Form: Using Words: (g) Number: Expanded Form: Using Words: NSSAL 286 Draft

Express with the Fewest Number of Manipulatives Example 1 In the example below, we have used 38 manipulatives (base ten blocks) to represent a number. This same number can be expressed using a fewer number of manipulatives. We can use a fewer number of manipulatives by recognizing that 10 ones tiles (unit tiles) are equal to 1 tens tile (rod), that 10 tens tiles are equal to 1 hundreds tile (flat), and that 10 hundreds tiles are equal to 1 thousands tile (block). We have to do some regrouping. Above, we have regrouped things so that we have a set of 10 rods (equivalent to 1 flat) and two groups of 10 unit tiles (each group being equivalent to a rod). Below we have replaced the 10 rods with a flat, and the 20 unit tiles with 2 rods. The two tables below show how the number of manipulatives (base ten blocks) changed between our original representation and our final one. We went from using 38 manipulatives (1 +13 + 24) to 11 manipulatives (2 + 5 + 4) by regrouping. Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 1 13 24 2 5 4 Both of these base ten block representations represent the same number, 254. Questions 1. For each base ten block representation, regroup the tiles to create a new, yet equivalent, representation that uses the fewest number of manipulatives. Draw or use Base Ten Stamps (available from your instructor) to create this new representation. Once this is done, complete the two tables showing how the manipulative count changed from the original NSSAL 287 Draft

representation to the new representation. Also identify what number is represented by the base ten blocks. (a) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: (b) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: NSSAL 288 Draft

(c) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: (d) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: NSSAL 289 Draft

(e) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: (f) Original Representation: New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: NSSAL 290 Draft

Example 2 In example 1, we used regrouping and base ten blocks to create our new representation and we ended up creating the following two tables showing how the number of manipulatives changed from one representation to another. Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 1 13 24 2 5 4 Let's consider the following question. Could we have gone directly from the first table to the second table without ever drawing or physically handling the base ten blocks? The answer is yes. We do it by regrouping within the first table. Below we have created the table for original representation again but now we have also expressed the number of rods as 10 + 3, and the number of unit tiles as 20 + 4. The 10 rods can be exchanged for 1 flat, and the 20 unit tiles for 2 rods (see arrows below). Flats (Hundreds) 1 Original Representation Rods (Tens) 13 (10 + 3) Unit Tiles (Ones) 24 (20 + 4) Moves over as 1 flat Moves over as 2 rods Once this exchange (i.e. regrouping) is complete, we get the new representation. Flats (Hundreds) (1+1) 2 New Representation Rods (Tens) (2+3) 5 Unit Tiles (Ones) 4 So the number that was originally represented by 1 flat, 13 rods, and 24 unit tiles is more efficiently represented by 2 flats (2 hundreds), 5 rods (5 tens), and 4 unit tiles (ones). The number represented is two hundred fifty-four (254). NSSAL 291 Draft

Questions 2. Look at the original representation then complete the two tables of values where the second table would correspond to the representation that uses the fewest number of manipulatives. Also identify the number we are working with. Please note that you do not need to draw or use base ten blocks to complete this question. (a) Original Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: (b) Original Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: (c) Original Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) Number: NSSAL 292 Draft

3. This question is very similar to question 2 but we have not provided a diagram of the original representation. For this reason, we have had to complete the table for the original representation. Your mission is to complete the second table that corresponds to the representation that uses the fewest number of manipulatives. Also identify the number we are working with. (a) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 5 14 17 Number: (b) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 4 23 19 Number: (c) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 6 31 13 Number: (d) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 3 16 27 Number: NSSAL 293 Draft

(e) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 4 15 38 Number: (f) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 5 24 25 Number: (g) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 6 22 34 Number: (h) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 4 32 27 Number: (i) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 3 33 18 Number: NSSAL 294 Draft

Adding 1. Write out the addition problem and its answer based on the base ten blocks that have been provided. Example 1 Example 2 Tens Ones Tens Ones Answer: Answer: 3 2 5 3 2 5 1 1 5 7 6 4 (a) (b) Tens Ones Tens Ones Answer: Answer: (c) (d) Tens Ones Tens Ones Answer: Answer: NSSAL 295 Draft

(e) (f) Tens Ones Tens Ones Answer: Answer: (g) Hundreds Tens Ones Answer: (h) Hundreds Tens Ones Answer: Look back at your answers. Do you see a pattern? Hopefully you recognize that you align the numbers so that you can add the ones, the tens, and the hundreds. By doing so, you end up with the answer. Please note that we only presented addition problems that do not require regrouping; that is, that the totals for the ones, tens, or hundreds digits was never greater than 9. We will learn how to handle questions that involve regrouping in the next section. NSSAL 296 Draft

2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial representation of these addition problems. Also complete the addition problem. (a) 3 1 Tens Ones 5 4 (b) 2 5 Tens Ones 4 3 (c) 1 2 Tens Ones 6 6 NSSAL 297 Draft

NSSAL 298 Draft Hundreds Tens Ones (d) 3 3 1 6 2 1 3. Complete the following addition problems. You do not have to use the base ten blocks. (a) 2 7 3 1 (b) 6 3 2 4 (c) 1 2 7 2 (d) 5 4 3 4 (e) 3 3 6 5 (f) 0 2 9 2 (g) 2 5 1 4 3 1 (h) 2 4 1 6 1 2 (i) 1 7 3 8 2 1 (j) 3 0 5 1 8 2 (k) 3 4 2 0 4 7 (l) 5 2 3 1 2 4 (m) 5 6 4 1 1 2 3 1 (n) 8 6 0 2 1 3 4 1 (o) 4 1 0 2 4 5 1 3

Adding with Regrouping On the previous activity sheet, we learned how to add multi-digit numbers with and without base ten blocks. All of the questions in the previously activity were special in that none of them required one to do regrouping. Regrouping occurs when totals for a place value (ones, tens, or hundreds digits) is greater than 9. Example 1: Original Question: 3 5 2 7 The problem is that when we look at the base ten blocks we have 12 ones Next Step: Break the 12 ones into two groups. One group will be made up of 10 ones, and the other will be made up of 2 ones. Final Step: Exchange the 10 ones for a rod (which is equal to 10 ones) 6 2 Tens Ones Tens Ones Tens Ones 1 3 2 5 7 Questions 1. Provide a written description for each step providing the original question and the final answer for each three step process involving the base ten blocks. (a) Next Step: Final Step: Tens Ones Tens Ones Tens Ones NSSAL 299 Draft

Step 1 (Original Question) Step 2 (Next Step) Step 3 (Final Step) (b) Next Step: Final Step: Tens Ones Tens Ones Tens Ones Step 1 (Original Question) Step 2 (Next Step) Step 3 (Final Step) NSSAL 300 Draft

(c) Next Step: Final Step: Tens Ones Tens Ones Tens Ones Step 1 (Original Question) Step 2 (Next Step) Step 3 (Final Step) 2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial representation of these addition problems. Please combine steps one and two (i.e. Original Question and Next Step which involves grouping). Also complete the addition problem. (a) 3 2 6 9 Steps 1 and 2 Step 3 Tens Ones Tens Ones NSSAL 301 Draft

(b) 2 1 5 8 Steps 1 and 2 Step 3 Tens Ones Tens Ones (c) 3 4 9 7 Steps 1 and 2 Step 3 Tens Ones Tens Ones Example 2: Now let's drop the base ten blocks, and see if we can come up with a rule for adding two digit numbers where regrouping is required. We go back to our original example 35 + 27. We start by stacking the numbers such that the ones digits line up and the tens digits line up. 3 5 2 7 Now we only look at the ones digits, the 5 and 7. We know that when these digits are added, we get 12, where the tens digit is 1, and the ones digit is 2. That tens digit (1) will be added to the tens digits in our original question (We are regrouping here.), and the ones digit (2) will be go in the ones spot. All we left to do is add the tens. Our final answer is 62. 1 2 5 7 1 3 2 6 5 7 2 NSSAL 302 Draft

In the last, we showed the ones digits being added separately and then fitted back into the original question. Typically this addition with the ones digits is done in your head. Example 3: Work out 65 + 25 Answer: 1 6 5 2 5 9 0 In your head you add the 5 and 5. This gives you 10. The tens digit of 1 is regrouped so that it goes with the other tens digits (6 and 2). The ones digit of 0 stays in the ones spot. All we have left to do is add the tens. Our final answer is 90. Example 4: Work out 39 + 48 Answer: 1 3 9 4 8 8 7 In your head you add the 9 and 8. This gives you 17. The tens digit of 1 is regrouped so that it goes with the other tens digits (3 and 4). The ones digit of 7 stays in the ones spot. All we have left to do is add the tens. Our final answer is 87. Example 5: Work out 73 + 52 Answer: 1 5 7 1 2 5 2 3 In your head you add the 3 and 2. This gives you 5, therefore no regrouping needs to be done here. The tens digit of 5 is then added to the tens digit of 7. This gives us 12. The 1 will become a hundreds digit (regrouping) and the 2 will remain a tens digit. Our final answer is 125. If you were to think of this in terms of base ten blocks, it would look like this. Steps 1 and 2 Step 3 Tens Ones Hundreds Tens Ones NSSAL 303 Draft

Questions: 3. Add the following. All of these require some regrouping. (a) (b) (c) 4 6 3 7 4 9 1 5 2 3 4 7 (d) (e) (f) 5 6 2 8 6 2 2 8 2 5 7 5 (g) (h) (i) 7 7 3 6 9 5 1 5 4 4 3 1 4. Add the following. Not all of these require regrouping. (a) (b) (c) 6 2 7 7 3 2 8 3 1 9 2 4 (d) (e) (f) 1 5 3 5 4 6 3 6 5 5 2 7 (g) (h) (i) 6 3 3 4 7 8 4 5 6 1 8 5 NSSAL 304 Draft

Subtracting 1. Write out the subtraction problem and its answer based on the base ten blocks that have been provided. Example: Tens Ones Answer: 6 4 2 1 4 3 (a) Tens Ones Answer: (b) Tens Ones Answer: NSSAL 305 Draft

(c) Tens Ones Answer: (d) Tens Ones Answer: (e) Tens Ones Answer: NSSAL 306 Draft

(f) Hundreds Tens Ones Answer: (g) Hundreds Tens Ones Answer: 2. Draw or use the Base Ten Stamps (available from your instructor), to draw the pictorial representation of these addition problems. Also complete the addition problem. (a) 7 4 Tens Ones 5 2 NSSAL 307 Draft

(b) 8 6 Tens Ones 3 6 (c) 2 7 9 Hundreds Tens Ones 1 2 6 (d) 2 5 8 Hundreds Tens Ones 4 3 Look back at your answers to questions 1 and 2. Do you see a pattern? Hopefully you recognize that you align the numbers so that you can subtract the ones, the tens, and the hundreds separately. By doing so, you end up with the answer. Please note that we only presented NSSAL 308 Draft

NSSAL 309 Draft subtraction problems that do not require regrouping; that is, that the digit that that is taken away from the corresponding digit is always smaller or equal to the corresponding digit. We will learn how to handle questions that involve regrouping in the next section. 3. Complete the following subtraction problems. You do not have to use the base ten blocks. (a) 3 2 6 7 (b) 1 8 3 9 (c) 2 3 8 5 (d) 6 3 6 8 (e) 7 2 8 9 (f) 0 5 9 7 (g) 5 1 7 6 (h) 4 2 6 2 (i) 7 3 7 4 (j) 2 1 1 4 5 2 (k) 1 4 3 6 7 5 (l) 1 2 5 8 7 6 (m) 1 0 5 3 8 9 (n) 0 4 2 3 4 7 (o) 2 3 8 4 9 8 (p) 0 6 4 1 5 7 8 3 (q) 6 1 0 2 8 4 4 7 (r) 0 2 8 4 0 9 8 6 (s) 5 6 3 5 8 9 7 (t) 6 0 6 7 9 4 6 8 (u) 0 2 4 1 8 7 5

Subtracting with Regrouping Sometimes when we are doing a subtraction question using base ten blocks, we are unable to take away the necessary blocks. Such is the case with the question below, 65-39. The problem is that we have to take away 9 one blocks, but there are only 5 one blocks present. Tens Ones 6 5 3 9 We get around this is by regrouping. In this case we exchange 1 ten block for 10 one blocks. Tens Ones 5 15 6 5 3 9 Now the subtraction can be completed. (See below.) The final answer is 26. Tens Ones 5 15 6 5 3 9 2 6 NSSAL 310 Draft

Let's try another question where regrouping is required. Such is the case with 218-147. We don't have enough ten blocks. We only have 1 ten block but we need to remove 4 ten blocks. Hundreds Tens Ones 2 1 8 1 4 7 We will regroup. In this case we exchange 1 hundred block for 10 ten blocks. Hundreds Tens Ones 1 11 2 1 8 1 4 7 Now the subtraction can be done. (See below.) The final answer is 71. Hundreds Tens Ones 1 11 2 1 8 1 4 7 7 1 NSSAL 311 Draft

Questions 1. With each of the following questions, regrouping will have to be done. A second chart has been provided where you can draw in the blocks after the regrouping has taken place, and then complete the subtraction by crossing out the appropriate blocks. (Do not spend a lot of time drawing the blocks; very rough sketches will do.) Make sure that you also supply the final answer. (a) Tens Ones 8 6 3 8 Tens Ones 8 6 3 8 (b) Tens Ones 7 4 5 7 NSSAL 312 Draft

Tens Ones 7 4 5 7 (c) Tens Ones 9 2 6 8 Tens Ones 9 2 6 8 NSSAL 313 Draft

(d) Hundreds Tens Ones 2 3 6 1 5 2 Hundreds Tens Ones 2 3 6 1 5 2 (e). Hundreds Tens Ones 2 4 7 8 1 NSSAL 314 Draft

Hundreds Tens Ones 2 4 7 8 1 (f). Hundreds Tens Ones 2 8 4 2 3 5 Hundreds Tens Ones 2 8 4 2 3 5 NSSAL 315 Draft

2. The following questions are partially completed. Although we are not using base ten blocks, we can see that the regrouping was required. Complete each of the questions. (a) 7 14 8 4 2 9 (b) 8 11 9 1 7 6 (c) 5 13 6 3 3 8 7 12 3 15 8 16 (d) 8 2 6 2 5 3 (e) 4 5 6 2 6 6 (f) 7 9 6 5 6 9 3. Complete the following questions. Please note that some questions involve regrouping, while others do not. (a) 6 6 1 8 (b) 5 1 3 7 (c) 7 8 4 3 (d) 9 4 6 8 (e) 6 7 2 3 (f) 7 2 9 3 6 1 (g) 5 6 9 3 9 0 (h) 4 9 6 2 6 5 (i) 6 8 3 6 5 8 NSSAL 316 Draft

Answers Expanded Form (A) (page 2) 1. (a) 40 + 2 (b) 600 + 90 + 4 (c) 3000 + 900 + 80 + 5 (d) 500 + 60 + 9 (e) 70 + 8 (f) 4000 + 200 + 80 + 1 (g) 800 + 60 + 7 (h) 30 + 1 (i) 6000 + 400 + 90 + 7 (j) 500 + 20 + 8 (k) 800 + 20 + 6 (l) 5000 + 900 + 20 + 3 (m) 50 + 9 (n) 3000 + 40 + 5 (o) 4000 + 800 + 8 (p) 700 + 3 (q) 6000 + 400 + 20 (r) 5000 + 90 + 9 (s) 800 + 10 (t) 9000 + 600 + 3 2. (a) 58 (b) 629 (c) 5874 (d) 286 (e) 8387 (f) 35 (g) 493 (h) 721 (i) 619 (j) 7082 (k) 850 (l) 503 (m) 1708 (n) 6089 (o) 5340 (p) 8657 (q) 58 (r) 352 (s) 1259 (t) 649 (u) 8367 (v) 7580 (w) 6084 (x) 8035 Expanded Form (B) (page 3) 1. (a) 50 000 + 4000 + 900 + 80 + 2 (b) 5000 + 600 + 80 + 5 (c) 700 000 + 40 000 + 6000 +100 + 70 +3 (d) 20 000 + 7000 + 900 + 50 + 9 (e) 300 000 + 6000 + 700 + 80 + 1 (f) 40 000 + 3000 + 900 + 8 (g) 300 000 + 70 000 + 2000 + 80 (h) 50 000 + 700 + 30 + 6 (i) 200 000 + 70 000 + 400 + 80 (j) 900 000 + 8000 + 700 + 4 2. (a) 67 591 (b) 562 713 (c) 41 278 (d) 850 374 (e) 602 892 (f) 95 043 (g) 530 905 (h) 684 710 (i) 29 756 (j) 735 269 (k) 290 468 (l) 907 135 NSSAL 317 Draft

Write the Number (A) (page 4) 1. (a) 82 (b) 49 (c) 16 (d) 10 (e) 46 (f) 27 (g) 74 (h) 13 (i) 56 (j) 11 (k) 38 (l) 23 (m) 8 (n) 99 (o) 17 (p) 83 (q) 12 (r) 52 (s) 90 (t) 31 (u) 7 (v) 63 (w) 15 (x) 68 2. (a) fifty-nine (b) forty-two (c) eighteen (d) thirty-seven (e) sixty-one (f) ninety-five (g) twenty-one Write the Number (B) (page 5) 1. (a) 932 (b) 246 (c) 712 (d) 360 (e) 79 (f) 621 (g) 107 (h) 589 (i) 490 (j) 42 (k) 811 (l) 276 (m) 702 (n) 319 (o) 12 (p) 531 (q) 670 (r) 9 (s) 186 (t) 900 (u) 216 (v) 65 (w) 720 (x) 462 2. (a) five hundred seventy-eight (b) three hundred fifty-two (c) seventy-nine (d) two hundred seventeen (e) nine hundred six (f) seven hundred forty (g) five hundred forty-one NSSAL 318 Draft

Write the Number (C) (pages 6 and 7) 1. (a) 8 321 (b) 4 683 (c) 7 513 (d) 411 (e) 9 512 (f) 3 429 (g) 2 950 (h) 1 078 (i) 207 (j) 5 983 (k) 6 807 (l) 9 046 (m) 597 (n) 8 274 (o) 15 (p) 4 928 (q) 1 318 (r) 38 (s) 3 076 (t) 6 900 (u) 7 308 (v) 760 (w) 9570 2. (a) four thousand, five hundred sixty-seven (b) two thousand, three hundred fifty-one (c) five hundred forty-seven (d) nine thousand, one hundred eighty-nine (e) six thousand, nine hundred eleven (f) sixty-three (g) eight thousand, sixty-three (h) one thousand, nine hundred four (i) seven hundred eight (j) seven thousand, eight hundred fifty Write the Number (D) (pages 8 and 9) 1. (a) 56 746 (b) 239 115 (c) 40 371 (d) 3 605 (e) 523 090 (f) 60 208 (g) 93 (h) 305 068 (i) 901 (j) 13 715 (k) 536 000 (l) 407 052 (m) 9 460 (n) 50 609 (o) 713 391 (p) 12 096 (q) 630 (r) 200 516 (s) 80 570 (t) 10 400 (u) 306 111 (v) 915 (w) 807 002 2. (a) thirty-four thousand, seven hundred eighty-one (b) two hundred forty-five thousand, three hundred fifty-nine (c) seven hundred eighty (d) twelve thousand, six hundred ninety-two (e) three hundred four thousand, five hundred sixty-two NSSAL 319 Draft

(f) seven thousand, twenty-three (g) seventy thousand, six hundred fifty (h) six hundred thirty-four thousand, nine hundred four (i) fifty-three thousand, eleven (j) nine hundred forty thousand, sixty Write the Number (E) (pages 10 and 11) 1. (a) 10 906 802 (b) 1 205 016 (c) 734 000 000 (d) 80 529 070 (e) 412 670 000 (f) 85 015 900 (g) 97 812 (h) 627 000 750 (i) 40 065 090 (j) 506 070 900 (k) 302 028 (l) 11 003047 (m) 90 313 004 (n) 520 000 672 2. (a) seven million, three hundred five thousand, four hundred eleven. (b) twenty-three million, seventy-eight thousand, six hundred (c) three hundred twenty-eight million, one hundred nine thousand (d) thirteen million, four hundred thirty-six thousand, five hundred (e) six million, nine thousand, seven hundred forty (f) four hundred ninety-eight thousand, three hundred fifteen (g) five hundred forty million, six hundred seventy-nine thousand, twenty (h) ninety-five million, eight hundred eleven thousand, two Place Value (page 12) 1. (a) 4 2. (a) 6 (b) 2 (b) 7 (c) 5 (c) 5 3. (a) 0 4. (a) 1 (b) 7 (b) 4 (c) 8 (c) 5 NSSAL 320 Draft

5. (a) 2 6. (a) 9 (b) 4 (b) 0 (c) 9 (c) 1 7. (a) 5 8. (a) 3 (b) 8 (b) 0 (c) 0 (c) 8 9. (a) 6 10. (a) 2 (b) 1 (b) 7 (c) 8 (c) 1 11. (a) 5 12. (a) 5 (b) 2 (b) 2 (c) 3 (c) 1 NSSAL 321 Draft

Before, After, or Between (A) (page 13) Number Word Description 1. What number is after 6? 7 seven 2. What number is before 11? 10 ten 3. What number is between 18 and 20? 19 nineteen 4. What number is after 15? 16 sixteen 5. What number is between 23 and 25? 24 twenty-four 6. What number is before 27? 26 twenty-six 7. What number is between 28 and 30? 29 twenty-nine 8. What number is after 34? 35 thirty-five 9. What number is before 37? 36 thirty-six 10. What number is after 11? 12 twelve 11. What number is between 46 and 48? 47 forty-seven 12. What number is after 59? 60 sixty 13. What number is before 70? 69 sixty-nine 14. What number is between 81 and 83? 82 eighty-two 15. What number is after 42? 43 forty-three 16. What number is between 90 and 92? 91 ninety-one 17. What number is before 77? 76 seventy-six 18. What number is after 99? 100 one hundred 19. What number is between 52 and 54? 53 fifty-three 20. What number is before 80? 79 seventy-nine NSSAL 322 Draft

Before, After, or Between (B) (page 14) Number Word Description 1. What number is after 325? 326 three hundred twenty-six 2. What number is before 421? 420 four hundred twenty 3. What number is between 188 and 190? 189 one hundred eighty-nine 4. What number is after 239? 240 two hundred forty 5. What number is between 356 and 358? 327 three hundred fifty-seven 6. What number is before 650? 649 six hundred forty-nine 7. What number is between 286 and 288? 287 two hundred eighty-seven 8. What number is before 700? 699 six hundred ninety-nine 9. What number is before 998? 997 nine hundred ninety-seven 10. What number is after 437? 436 four hundred thirty-six 11. What number is between 638 and 640? 639 six hundred thirty-nine 12. What number is after 399? 400 four hundred 13. What number is before 900? 899 eight hundred ninety-nine 14. What number is between 513 and 515? 514 five hundred fourteen 15. What number is after 661? 662 six hundred sixty-two 16. What number is before 712? 711 seven hundred eleven 17. What number is between 600 and 602? 601 six hundred one 18. What number is after 807? 808 eight hundred eight 19. What number is after 999? 1000 one thousand 20. What number is between 499 and 501? 500 five hundred NSSAL 323 Draft

Closer to, and Odd or Even (A) (page 15) Word Description Number Closer to 0 or 100 Odd or Even (a) eighteen 18 0 even (b) seventy-six 76 100 even (c) eighty-three 83 100 odd (d) forty 40 0 even (e) twenty-four 24 0 even (f) thirty-nine 39 0 odd (g) ninety-three 93 100 odd (h) sixty-five 65 100 odd (i) forty-six 46 0 even (j) seventy-one 71 100 odd (k) eleven 11 0 odd (l) thirty-eight 38 0 even (m) forty-nine 49 0 odd (n) seventy-two 72 100 even (o) ninety-six 96 100 even (p) twenty-seven 27 0 odd (q) sixteen 16 0 even (r) twelve 12 0 even (s) forty-four 44 0 even (t) eighty-five 85 100 odd (u) fifty-eight 58 100 even (v) thirty-seven 37 0 odd NSSAL 324 Draft

Closer to, and Odd or Even (B) (page 16) Word Description Number Closer to 0 or 1000 Odd or Even (a) two hundred forty-nine 249 0 odd (b) six hundred twenty-three 623 1000 odd (c) seven hundred ninety-four 794 1000 even (d) one hundred eighty-six 186 0 even (e) five hundred twelve 512 1000 even (f) three hundred seven 307 0 odd (g) four hundred sixty 460 0 even (h) ninety-nine 99 0 odd (i) two hundred seventy-six 276 0 even (j) five hundred forty-seven 547 1000 odd (k) one hundred eighty-four 184 0 even (l) nine hundred eight 908 1000 even (m) fifty-three 53 0 odd (n) three hundred fifty 350 0 even (o) nine hundred ninety-six 996 1000 even (p) six hundred forty-five 645 1000 odd (q) one thousand, thirty-one 1031 1000 odd (r) two hundred seventy-seven 277 0 odd (s) three thousand, ten 3010 1000 even (t) seven hundred sixty-nine 769 1000 odd (u) two thousand, three hundred 2300 1000 even (v) eight hundred fifteen 815 1000 odd NSSAL 325 Draft

Give an Example (page 19) Answers will vary. We have supplied possible answers. 1. 10 years in a decade, 10 millimetres in a centimetre, a dime is worth 10 cents 2. 12 inches in a foot, 12 eggs in a carton of a dozen eggs, 12 beers in a case 3. age legally recognized as an adult, 18 holes of golf 4. 24 hours in a day, 24 inches in 2 feet, 2-4 of beer 5. a quarter is worth 25 cents, quarter of a century, silver wedding anniversary 6. 30 days in September, April, June and November 7. 50 years in half a century, golden wedding anniversary 8. 60 seconds in a minute, 60 minutes in an hour 9. 100 years in a century, 100 centimetres in one metre 10. 1000 years in a millennium, 1000 metres in a kilometre, 1000 millilitres in a litre NSSAL 326 Draft

Closer To (A) (page 20) 1. Is 6 closer to 5 or 8? 2. Is 3 closer to 1 or 7? 3. Is 4 closer to 0 or 6? 4. Is 7 closer to 4 or 9? 5. Is 5 closer to 1 or 8? 6. Is 8 closer to 4 or 10? 7. Is 6 closer to 3 or 10? 8. Is 2 closer to 0 or 3? 9. Is 9 closer to 7 or 12? 10. Is 8 closer to 3 or 12? 11. Is 6 closer to 0 or 11? 12. Is 7 closer to 5 or 11? 13. Is 9 closer to 6 or 13? 14. Is 10 closer to 7 or 15? 15. Is 11 closer to 10 or 14? 16. Is 10 closer to 6 or 12? 17. Is 15 closer to 13 or 19? 18. Is 13 closer to 10 or 15? 19. Is 16 closer to 14 or 20? 20. Is 12 closer to 8 or 15? 21. Is 19 closer to 15 or 21? 22. Is 18 closer to 16 or 22? 23. Is 24 closer to 20 or 30? 24. Is 27 closer to 20 or 30? 25. Is 39 closer to 30 or 40? 26. Is 46 closer to 40 or 50? 27. Is 73 closer to 70 or 80? 28. Is 94 closer to 90 or 100? 29. Is 28 closer to 20 or 30? 30. Is 60 closer to 0 or 100? 31. Is 40 closer to 0 or 100? 32. Is 70 closer to 0 or 100? 33. Is 30 closer to 20 or 50? 34. Is 70 closer to 50 or 100? NSSAL 327 Draft

Closer To (B) (page 21) 1. Is 36 closer to 30 or 40? 2. Is 44 closer to 40 or 50? 3. Is 67 closer to 60 or 70? 4. Is 50 closer to 20 or 60? 5. Is 60 closer to 10 or 90? 6. Is 80 closer to 70 or 100? 7. Is 100 closer to 80 or 150? 8. Is 150 closer to 130 or 160? 9. Is 270 closer to 250 or 300? 10. Is 420 closer to 400 or 500? 11. Is 200 closer to 0 or 300? 12. Is 500 closer to 400 or 800? 13. Is 700 closer to 600 or 750? 14. Is 600 closer to 550 or 700? 15. Is 640 closer to 600 or 700? 16. Is 870 closer to 800 or 900? 17. Is 81 closer to 20 or 100? 18. Is 67 closer to 30 or 80? 19. Is 58 closer to 0 or 90? 20. Is 37 closer to 0 or 100? 21. Is 99 closer to 0 or 200? 22. Is 230 closer to 100 or 300? 23. Is 341 closer to 300 or 350? 24. Is 789 closer to 750 or 800? 25. Is 699 closer to 600 or 750? 26. Is 219 closer to 100 or 250? 27. Is 224 closer to 200 or 300? 28. Is 547 closer to 500 or 550? 29. Is 839 closer to 800 or 900? 30. Is 658 closer to 650 or 700? 31. Is 2399 closer to 2000 or 3000? 32. Is 1837 closer to 1000 or 2000? 33. Is 5643 closer to 5000 or 6000? 34. Is 2845 closer to 2000 or 4000? NSSAL 328 Draft

Subtraction Search (page 30) 14 20 9 11 12 18 6 6 8 9 5 4 10 8 4 7 8 12 2 9 7 1 6 15 4 11 3 3 7 5 6 1 5 10 16 8 13 10 9 17 15 20 8 7 0 9 20 8 12 2 17 6 9 9 0 Subtraction Facts: 1. 14-6 = 8 2. 20-9 = 11 3. 6-4 = 2 4. 12-5 = 7 5. 9-5 = 4 6. 18-10 = 18 7. 12-4 = 8 8. 9-3 = 6 9. 7-1 = 6 10. 15-4 = 11 11. 6-1 = 5 12. 16-9 = 7 13. 8-5 = 3 14. 13-6 = 7 15. 15-9 = 6 16. 20-10 = 10 17. 20-8 = 12 18. 17-0 = 17 19. 10-8 = 2 20. 9-9 = 0 NSSAL 329 Draft

Random Multiplication Facts Quizzes (pages 44 and 45) Quiz A1 Name: Quiz A2 Name: 2 7 5 8 4 1 2 7 5 8 4 5 10 35 25 40 20 0 0 0 0 0 0 9 18 63 45 72 36 2 4 14 10 16 8 5 2 0 1 9 7 35 14 0 7 63 0 0 0 0 0 0 8 40 16 0 8 72 6 30 12 0 6 54 3 15 6 0 3 27 Quiz A3 Name: Quiz A4 Name: 9 6 3 4 7 9 81 54 27 36 63 2 18 12 6 8 14 1 9 6 3 4 7 5 45 30 15 20 35 0 0 0 0 0 0 1 5 9 2 0 6 6 30 54 12 0 8 8 40 72 16 0 1 1 5 9 2 0 3 3 15 27 6 0 7 7 35 63 14 0 Quiz B1 Name: Quiz B2 Name: 8 3 2 7 6 5 40 15 10 35 30 3 24 9 6 21 18 4 32 12 8 28 24 1 8 3 2 7 6 9 72 27 18 63 54 4 9 0 3 5 8 32 72 0 24 40 2 8 18 0 6 10 4 16 36 0 12 20 7 28 63 0 21 35 6 24 54 0 18 30 NSSAL 330 Draft

Quiz B3 Name: Quiz B4 Name: 8 6 7 1 3 9 72 54 63 9 27 2 16 12 14 2 6 4 32 24 28 4 12 5 40 30 35 5 15 3 24 18 21 3 9 3 5 1 4 9 7 21 35 7 28 63 6 18 30 6 24 54 2 6 10 2 8 18 4 12 20 4 16 36 8 24 40 8 32 72 Quiz C1 Name: Quiz C2 Name: 8 7 5 6 3 6 48 42 30 36 18 4 32 28 20 24 12 8 64 56 40 48 24 2 16 14 10 12 6 7 56 49 35 42 21 6 9 2 8 7 4 24 36 8 32 28 8 48 72 16 64 56 6 36 54 12 48 42 9 54 81 18 72 63 7 42 63 14 56 49 Quiz C3 Name: Quiz C4 Name: 1 6 9 7 3 5 5 30 45 35 15 8 8 48 72 56 24 4 4 24 36 28 12 7 7 42 63 49 21 6 6 36 54 42 18 2 7 6 9 3 3 6 21 18 27 9 7 14 49 42 63 21 4 8 28 24 36 12 8 16 56 48 72 24 9 18 63 54 81 27 NSSAL 331 Draft

Put the Number in the Right Box (page 50) 1. Multiple of 2 Not a Multiple of 2 Multiple of 3 6, 18, 12 15, 9, 21 Not a Multiple of 3 4, 10, 14 11, 19, 7 2. Multiple of 2 Not a Multiple of 2 Multiple of 5 10, 30, 40 15, 25, 45 Not a Multiple of 5 16, 22, 18 19, 9, 21 3. Multiple of 3 Not a Multiple of 3 Multiple of 5 15, 30, 45 20, 25, 40 Not a Multiple of 5 24, 9, 27 8, 28, 26 4 Multiple of 4 Not a Multiple of 4 Multiple of 6 24, 12, 36 30, 18, 6 Not a Multiple of 6 16, 8, 28 21, 9, 15 5. Multiple of 5 Not a Multiple of 5 Multiple of 4 20, 40, 80 12, 32, 28 Not a Multiple of 4 25, 10, 35 27, 12, 19 Multiplying by Multiples of 10, 100, and 1000 (pages 52 and 53) 1. Answer in Written Form (a) 2000 600 1 200 000 One million, two hundred thousand (b) (c) (d) (e) (f) 9 4000 36 000 Thirty-six thousand 300 500 150 000 One hundred fifty thousand 80 400 32 000 Thirty-two thousand 60 60 3 600 Three thousand, six hundred 800 5 4 000 Four thousand 2. (a) 1 400 (b) 540 (c) 12 000 (d) 25 000 (e) 2 400 (f) 400 000 NSSAL 332 Draft

(g) 630 000 (h) 12 000 000 (i) 320 (j) 490 000 (k) 720 (l) 30 000 (m) 270 000 (n) 28 000 (o) 1 800 000 (p) 40 000 (q) 4 800 (r) 1 000 000 (s) 8 000 (t) 8 100 (u) 5 600 000 (v) 64 000 (w) 10 000 000 (x) 720 (y) 90 000 (z) 35 000 Multiplying Two Digit Numbers, Part 1 (Expanded Form) (pages 54 to 58) 1. 60 3 90 5 1 5 3 0 0 2 7 0 5 4 0 0 5 9 8 5 2. 70 4 30 8 3 2 5 6 0 1 2 0 2 1 0 0 2 8 1 2 3. (a) 1118 (b) 1995 (c) 2059 (d) 4399 (e) 2844 (f) 3403 (g) 2928 (h) 5688 NSSAL 333 Draft

4. 400 30 6 70 2 1 2 6 0 8 0 0 4 2 0 2 1 0 0 2 8 0 0 0 3 1 3 9 2 Multiplying Two Digit Numbers, Part 2 (Lattice Method) (pages 59 to 64) 1. (a) 2400 (b) 1476 (c) 7452 (d) 1776 (e) 1206 (f) 2088 2. 2166 3. (a) 1932 (b) 3692 (c) 2808 (d) 3108 Multiplying Multi-Digit Numbers (pages 65 to 68) 1 (a) 28 086 (b) 139 895 (c) 257 948 2. (a) 28 035 (b) 309 628 NSSAL 334 Draft

Division Search (page 70) 48 6 8 18 9 28 15 9 3 9 32 4 8 5 9 2 27 1 7 5 3 10 5 2 24 64 45 42 8 25 16 4 4 6 8 3 5 7 36 20 4 5 5 4 1 6 56 8 7 9 8 6 36 8 18 2 9 Division Facts: 1. 28 4 = 7 2. 27 3 = 9 3. 48 6 = 8 4. 15 5 = 3 5. 18 9 = 2 6. 9 9 = 1 7. 32 4 = 8 8. 45 5 = 9 9. 10 5 = 2 10. 24 8 = 3 11. 64 8 = 8 12. 25 5 = 5 13. 16 4 = 4 14. 42 6 = 7 15. 20 4 = 5 16. 8 8 = 1 17. 36 6 = 6 18. 56 8 = 7 19. 36 9 = 4 20. 18 2 = 9 NSSAL 335 Draft

More Divisibility (A) (page 72) 1. 2 3 5 2 3 5 (a) 64 (b) 35 (c) 81 (d) 90 (e) 40 (f) 42 (g) 105 (h) 307 (i) 208 (j) 635 (k) 915 (l) 410 (m) 720 (n) 816 (o) 1245 (p) 2036 (q) 4109 (r) 7281 (s) 9130 (t) 3075 (u) 8374 (v) 7320 2. Answers will vary. NSSAL 336 Draft

More Divisibility (B) (pages 73 and 74) 1. 2 3 5 6 10 15 (a) 12 (b) 45 (c) 30 (d) 14 (e) 36 (f) 19 (g) 430 (h) 114 (i) 207 (j) 96 (k) 225 (l) 600 (m) 704 (n) 425 (o) 408 (p) 570 (q) 615 (r) 1078 (s) 2310 (t) 7131 (u) 8706 (v) 5603 (w) 4700 (x) 6125 (y) 3210 2. Answers will vary. NSSAL 337 Draft

3. (a) 14 (b) 33 (c) 30 Division with Remainders (pages 76 to 79) 1. (a) 13 5 2, R:3 (b) 7 2 3, R:1 (c) 14 3 4, R:2 (d) 18 3 6 (e) 33 7 4, R:5 (f) 43 8 5, R:3 (g) 25 6 4, R:1 (h) 19 2 9, R:1 (i) 29 3 9, R:2 (j) 40 6 6, R:4 (k) 42 7 6 (l) 22 5 4, R:2 (m) 60 9 6, R:6 (n) 31 8 3, R:7 (o) 13 4 3, R:1 (p) 38 5 7, R:3 (q) 48 9 5, R:3 (r) 32 4 8 (s) 18 4 4, R:2 (t) 19 6 3, R:1 (u) 54 5 10, R:4 (v) 35 8 4, R:3 (w) 50 7 7, R:1 (x) 69 9 7, R:6 2. 20 6 3, R:2 Each person gets 3 apples, and 2 apples are left over. Long Division (Partial Quotient Method) (pages 80 to 87) 1. 637 2. 516 3. 752 4. 254 5. 372 R: 1 6. 928 R: 2 7. 386 R: 5 8. 658 R: 3 9. 583 10. 872 R: 4 11. 958 R: 1 12. 967 R: 2 13. 2741 14. 4217 15. 5736 R: 1 16. 4763 R: 3 17. 3592 18. 6523 R: 5 19. 5217 R: 2 20. 7305 NSSAL 338 Draft

Prime Factorization (pages 88 and 89) 1. (a) 6 2 3 (b) 21 3 7 (c) 10 2 5 (d) 35 5 7 (e) 49 7 7 (f) 26 2 13 (g) 33 3 11 (h) 20 2 2 5 (i) 44 2 2 11 (j) 42 2 3 7 (k) 45 3 3 5 (l) 66 2 3 11 (m) 30 2 3 5 (n) 70 2 5 7 (o) 27 3 3 3 (p) 63 3 3 7 (q) 110 2 5 11 (r) 18 2 3 3 (s) 16 2 2 2 2 (t) 100 2 2 5 5 (u) 36 2 2 3 3 (v) 250 2 5 5 5 (w) 81 3 3 3 3 (x) 24 2 2 2 3 Name the Preceding or Next (page 92) 1. (a) 49 (b) 65 (c) 31 2. (a) 34 (b) 56 (c) 48 3. (a) 30 (b) 15 (c) 50 4. (a) 70 (b) 40 (c) 100 5. (a) 24 (b) 18 (c) 30 6. (a) 32 (b) 24 (c) 12 7. (a) 12 (b) 6 (c) 24 8. (a) 32 (b) 24 (c) 8 9. (a) 30 (b) 48 (c) 24 NSSAL 339 Draft

One of these Things is Not Like the Others (pages 93 and 94) Note: There is often more than one acceptable answer for these questions. 1. The 7 does not belong because it is an odd number and the remaining numbers, 10, 12, and 4, are all even numbers. 2. The 5 does not belong because unlike the remaining numbers, 13, 15, and 9, it is not divisible by 3. 3. The 11 does not belong because it is a prime number and the remaining numbers, 15, 6, and 8, are all composite numbers. 4. The sequence 1, 2, 4, 8, 16 does not belong because you are multiplying a number to one term to get the next term. With the remaining sequences you are adding a number to one term to get the next term. 5. The 6 does not belong because it is not a perfect square while the remaining numbers, 25 (5 2 ), 9 (3 2 ), and 16 (4 2 ), are. 6. The 22 does not belong because unlike the remaining numbers, 15, 40, and 55, it is not divisible by 5. 7. The 9 does not belong because it is a composite number and the remaining numbers, 17, 7, and 19, are all prime numbers. 8. The sequence 66, 63, 60, 57 does not belong because each term is decreasing by 3, while the remaining sequences have terms that are increasing by 3. 9. The 14 does not belong because it is a number other than 12. The words or mathematical expressions are equal to 12. 10. The one hundred five does not belong because it is a three digit number. The remaining numbers are all two digit numbers. 11. The 10-5 does not belong because it is equal to 5, while the rest are equal to 15. 12. The 9 9 does not belong because it is equal to 81, while the rest equal 99. NSSAL 340 Draft

Pathways (page 97) Everything along this pathway equals 8. Everything along this pathway equals 6. 2 4 12 2 9 3 3 2 16 2 6 2 10 4 12 4 6 1 18 3 5 1 4 2 3 5 0 6 32 4 8 1 9 1 15 9 3 3 30 5 8 2 4 2 Everything along this pathway equals 12. Everything along this pathway equals 18. 15 3 9 2 21 3 18 1 6 6 9 9 24 6 12 1 8 4 12 1 2 6 13 5 18 6 3 4 20 8 0 12 6 3 9 3 7 11 18 0 Two of These Boxes Just Don't Belong (A) (page 98) 1. 1 st, 2 nd, and 5 th box equal 5 2. 1 st, 3 rd, and 5 th boxes equal 7 3. 2 nd, 3 rd, and 4 th boxes equal 6 4. 2 nd, 4 th, and 5 th boxes equal 10 5. 2 nd, 3 rd, and 5 th boxes equal 8 NSSAL 341 Draft

6. 1 st, 3 rd, and 4 th boxes equal 11 7. 2 nd, 4 th, and 5 th boxes equal 15 8. 1 st, 3 rd, and 5 th boxes equal 12 9. 2 nd, 3 rd, and 4 th boxes equal 20 10. 1 st, 4 th, and 5 th boxes equal 18 Two of These Boxes Just Don't Belong (B) (page 99) 1. 1 st, 3 rd, and 5 th boxes equal 9 2. 2 nd, 4 th, and 5 th boxes equal 40 3. 1 st, 2 nd, and 4 th boxes equal 16 4. 1 st, 3 rd, and 4 th boxes equal 14 5. 2 nd, 3 rd, and 5 th boxes equal 30 6. 1 st, 4 th, and 5 th boxes equal 50 7. 2 nd, 3 rd, and 4 th boxes equal 60 8. 3 rd, 4 th, and 5 th boxes equal 80 9. 1 st, 2 nd, and 5 th boxes equal 0 10. 3 rd, 4 th, and 5 th boxes equal 90 Equivalent (page 100) Part 1 (a) 8 (b) 5 (c) 4 (d) 6 (e) 7 (f) 2 Part 2 (a) 4 (b) 4 (c) 7 (d) 8 (e) 5 (f) 15 Part 3 (a) 4 (b) 10 (c) 4 (d) 10 (e) 3 (f) 6 Part 4 (a) 2 (b) 12 (c) 4 (d) 30 (e) 5 (f) 40 Part 5 (a) 8 (b) 5 (c) 4 (d) 3 (e) 4 (f) 6 (g) 6 (h) 1 (i) 18 (j) 2 (k) 7 (l) 4 (m) 5 (n) 4 (o) 7 (p) 9 (q) 31 (r) 6 NSSAL 342 Draft

(s) 8 (t) 45 (u) 5 (v) 2 (w) 1 (x) 17 Venn Diagrams and Whole Numbers (pages 101 and 102) 1. 9 14 4 Divisible by 2 Divisible by 5 8 22 10 20 21 15 30 5 25 2. 27 10 6 15 11 25 Divisible by 3 Divisible by 5 9 12 30 20 18 16 3. 4 10 25 9 15 Odd 21 18 3 7 13 23 2 Prime 20 NSSAL 343 Draft

4. 7 3 25 Perfect Square 9 4 16 36 Even 28 18 10 30 15 27 5. 48 18 15 45 55 Multiple of 9 Multiple of 5 90 10 9 30 36 13 7 Whole Number Crossword Puzzle (A) (page 103) 3 8 6 4 2 3 0 7 1 4 2 0 4 2 3 3 7 6 5 0 9 8 3 2 2 7 6 4 2 7 5 6 3 5 8 9 4 6 1 6 1 5 NSSAL 344 Draft

Whole Number Crossword Puzzle (B) (page 104) 4 5 0 8 6 2 3 4 4 8 1 5 4 1 8 3 0 7 3 4 9 4 2 8 2 5 9 3 6 4 1 8 6 3 6 1 4 3 4 7 8 6 Whole Number Crossword Puzzle (C) (page 105) 5 6 0 1 9 9 8 3 7 6 0 0 1 4 0 1 6 3 9 5 2 3 5 4 6 1 2 8 7 4 9 3 8 3 4 2 6 2 3 8 4 8 NSSAL 345 Draft

Whole Number Crossword Puzzle (D) (page 106) 7 7 1 1 8 8 8 7 6 3 0 7 1 3 6 2 6 5 7 4 9 2 7 2 9 8 8 1 8 5 4 2 3 6 1 8 0 8 4 5 7 2 KenKen Puzzles (A) (pages 107 and 108) (a) 2 3 1 (b) 2 3 1 3 1 2 1 2 3 1 2 3 3 1 2 (c) 3 2 1 (d) 1 3 2 1 3 2 3 2 1 2 1 3 2 1 3 NSSAL 346 Draft

(e) 3 2 1 (f) 1 2 3 1 3 2 3 1 2 2 1 3 2 3 1 (g) 1 3 2 (h) 2 1 3 3 2 1 3 2 1 2 1 3 1 3 2 (i) 3 2 1 (j) 2 3 1 1 3 2 3 1 2 2 1 3 1 2 3 NSSAL 347 Draft

KenKen Puzzles (B) (page 109) (a) 2 1 3 (b) 3 1 2 1 3 2 2 3 1 3 2 1 1 2 3 (c) 1 2 3 (d) 2 3 1 3 1 2 1 2 3 2 3 1 3 1 2 (e) 3 1 2 (f) 3 2 1 1 2 3 2 1 3 2 3 1 1 3 2 NSSAL 348 Draft

KenKen (C) (page 110) (a) 4 5 3 (b) 3 5 4 3 4 5 4 3 5 5 3 4 5 4 3 (c) 5 3 4 (d) 3 4 5 4 5 3 5 3 4 3 4 5 4 5 3 (e) 5 4 3 (f) 4 3 5 3 5 4 3 5 4 4 3 5 5 4 3 NSSAL 349 Draft

KenKen Puzzle (D) (page 111) (a) 5 6 7 (b) 7 5 6 7 5 6 6 7 5 6 7 5 5 6 7 (c) 6 5 7 (d) 6 7 5 5 7 6 5 6 7 7 6 5 7 5 6 (e) 7 6 5 (f) 5 7 6 5 7 6 6 5 7 6 5 7 7 6 5 NSSAL 350 Draft

KenKen Puzzles (E) (page 112) (a) 2 3 1 4 (b) 3 1 2 4 4 1 2 3 2 4 3 1 3 2 4 1 4 2 1 3 1 4 3 2 1 3 4 2 (c) 1 2 4 3 (d) 2 1 3 4 3 4 2 1 4 3 1 2 4 1 3 2 3 4 2 1 2 3 1 4 1 2 4 3 Find the Two Numbers (page 113) (a) 3, 5 (b) 10, 2 (c) 4, 7 (d) 12, 1 (e) 3, 6 (f) 8, 5 (g) 4, 4 (h) 2, 15 (i) 4, 9 (j) 6, 2 (k) 1, 10 (l) 5, 5 (m) 2, 11 (n) 6, 7 (o) 2, 12 (p) 4, 10 (q) 7, 9 (r) 8, 4 (s) 7, 5 (t) 2, 25 (u) 4, 6 (v) 1, 8 (w) 20, 3 (x) 10, 10 NSSAL 351 Draft

Which Combination of Numbers Works? (page 114) (a) 4 5-1 = 19 The first two numbers can be interchanged. (b) 2 5 + 7 = 17 The first two numbers can be interchanged. (c) 3 + 8-6 = 5 The first two numbers can be interchanged. (d) 5 6 + 4 = 34 The first two numbers can be interchanged. (e) 3 7-6 = 15 The first two numbers can be interchanged. (f) 20 4 + 5 = 10 (g) 7 + 9-3 = 13 The first two numbers can be interchanged. (h) 5 7-8 = 27 The first two numbers can be interchanged. (i) 8 4 + 12 = 14 (j) 20 5-2 = 2 (k) 6 + 10-7 = 9 The first two numbers can be interchanged. (l) 6 7 + 3 = 45 The first two numbers can be interchanged. (m) 15 5 + 3 = 6 (n) 16 8 + 24 = 26 (o) 6 9-5 = 49 The first two numbers can be interchanged. NSSAL 352 Draft

Magic Squares (page 115) (a) 8 1 6 (b) 3 8 1 (c) 7 2 9 3 5 7 2 4 6 8 6 4 4 9 2 7 0 5 3 10 5 (d) 2 9 4 (e) 9 4 11 (f) 10 3 8 7 5 3 10 8 6 5 7 9 6 1 8 5 12 7 6 11 4 (g) 5 10 3 (h) 6 11 4 (i) 12 5 10 4 6 8 5 7 9 7 9 11 9 2 7 10 3 8 8 13 6 Addition Pyramids (pages 116 and 117) 1. 10 2. 9 3. 13 4 6 5 4 3 10 3. 10 4. 14 6. 9 8 2 5 9 8 1 NSSAL 353 Draft

7. 21 8. 18 9. 16 9 12 9 9 7 9 7 2 10 6 3 6 2 5 4 10. 18 11. 29 12. 19 7 11 18 11 13 6 4 3 8 8 10 1 7 6 0 13. 19 14. 21 15. 24 7 12 9 12 10 14 4 3 9 2 7 5 4 6 8 16. 29 17. 26 18. 30 11 18 10 16 10 20 6 5 13 3 7 9 3 7 13 6 0 5 8 2 1 6 3 1 2 5 8 19. 25 20. 50 21. 28 13 12 27 23 15 13 8 5 7 12 15 8 10 5 8 5 3 2 5 3 9 6 2 7 3 2 6 22. 36 23. 39 24. 40 17 19 19 20 18 22 7 10 9 11 8 12 6 12 10 3 4 6 3 5 6 2 10 1 5 7 3 NSSAL 354 Draft

Factor Rows and Factor Columns (page 118) (a) 2 5 10 (b) 6 3 18 (c) 4 5 20 4 3 12 1 2 2 2 6 12 8 15 6 6 8 30 (d) 3 9 27 (e) 6 10 60 (f) 4 7 28 7 1 7 4 2 8 1 3 3 21 9 24 20 4 21 (g) 9 2 18 (h) 3 6 18 (i) 8 5 40 4 5 20 5 9 45 1 7 7 36 10 15 54 8 35 (j) 3 8 24 (k) 5 4 20 (l) 7 2 14 9 2 18 6 7 42 4 8 32 27 16 30 28 28 16 (m) 9 6 54 (n) 7 8 56 (o) 5 7 35 8 5 40 3 2 6 3 9 27 72 30 21 16 15 63 Letter and Number Sentences (page 119) 1. (a) 4 (b) 2 (c) 6 (d) 8 2. (a) 7 (b) 9 (c) 15 (d) 13 3. (a) 4 (b) 8 (c) 2 (d) 24 4. (a) 5 (b) 18 (c) 7 (d) 60 5. (a) 9 (b) 12 (c) 4 (d) 17 6. (a) 3 (b) 6 (c) 15 (d) 1 7. (a) 9 (b) 12 (c) 7 (d) 20 8. (a) 4 (b) 11 (c) 7 (d) 5 NSSAL 355 Draft

Number Sentences (A) (page 121) 1. 4 8 12 12 8 4 2. 5 10 15 15 5 10 8 4 12 12 4 8 10 5 15 15 10 5 3. 2 8 16 16 2 8 4. 4 5 9 9 5 4 8 2 16 16 8 2 5 4 9 9 4 5 5. 4 7 28 28 7 4 6. 5 9 45 45 9 5 7 4 28 28 4 7 9 5 45 45 5 9 7. 9 3 12 12 3 9 8. 3 5 15 15 3 5 3 9 12 12 9 3 5 3 15 15 5 3 9. 20 10 30 30 10 20 10. 30 6 180 180 6 30 10 20 30 30 20 10 6 30 180 180 30 6 Number Sentences (B) (page 122) 1. 4 5 20 20 4 5 3 9 27 27 3 9 5 4 20 20 5 4 9 3 27 27 9 3 4 5 9 9 4 5 5 4 9 9 5 4 2. 2 4 8 8 2 4 3 8 24 24 3 8 4 2 8 8 4 2 8 3 24 24 8 3 3 4 12 12 4 3 4 8 12 12 4 8 4 3 12 12 3 4 8 4 12 12 8 4 2 12 24 24 2 12 12 2 24 24 12 2 3. 2 9 18 18 2 9 3 6 18 18 6 3 9 2 18 18 9 2 6 3 18 18 3 6 2 6 12 12 2 6 3 9 12 12 3 9 6 2 12 12 6 2 9 3 12 12 9 3 3 6 9 9 3 6 2 3 6 6 3 2 6 3 9 9 6 3 3 2 6 6 2 3 Order of Operations (A) (pages 123 to 125) (a) 11 (b) 4 (c) 23 (d) 23 (e) 42 (f) 15 (g) 11 (h) 27 (i) 13 NSSAL 356 Draft

(j) 26 (k) 14 (l) 2 (m) 8 (n) 23 (o) 8 (p) 30 (q) 1 (r) 19 (s) 16 (t) 10 (u) 13 (v) 7 (w) 45 (x) 34 Order of Operations (B) (pages 126 to 128) (a) 26 (b) 39 (c) 6 (d) 37 (e) 28 (f) 10 (g) 43 (h) 12 (i) 16 (j) 28 (k) 35 (l) 7 (m) 44 (n) 2 (o) 1 (p) 34 (q) 4 (r) 59 Order of Operations (C) (pages 129 to 131) (a) 26 (b) 32 (c) 4 (d) 39 (e) 72 (f) 50 (g) 40 (h) 7 (i) 24 (j) 81 (k) 3 (l) 4 (m) 6 (n) 23 (o) 94 (p) 12 (q) 29 (r) 7 What's the Pattern (A) (page 133) (a),, (b),, (c),, (d),, (e),, (f) G,, H (g),, (h),, (i),, (j) P,, R (k),, (l),, (m),, (n) T, t, R (o),, (p),, NSSAL 357 Draft

What's the Pattern? (B) (page 134) Very Challenging (Only give to your strongest learners) (a),, (b),, (c),, (d),, (e),, (f),, (g),, (h),, (i),, (k),, (m), E, (o),, (j),, (l),, (n),, Toothpick Patterns (pages 135 and 136) Note: The next figures have not been provided in this answer key. 1. (b) 3, 5, 7, 9, 11, 13 (c) Start at 3 and keep adding 2. 2. (b) 8, 12, 16, 20, 24 (c) Start at 8 and keep adding 4. 3. (b) 19, 15, 11, 7, 3 (c) Start at 19 and keep subtracting 4. 4. (b) 8, 15, 22, 29, 36 (c) Start at 8 and keep adding 7. 5. (b) 31, 25, 19, 13, 7 (c) Start at 31 and keep subtracting 6. 6. (b) 10, 16, 22, 28, 34 (c) Start at 10 and keep adding 6. 7. (b) 9, 13, 17, 21, 25 (c) Start at 9 and keep adding 4 NSSAL 358 Draft

8. (b) 4, 14, 24, 34, 44 (c) Start at 4 and keep adding 10. Create the Pattern (A) (page 137) (a) Start at 9 and go up by 2 each time. 9, 11, 13, 15, 17 (b) Start at 24 and go down by 1 each time. 24, 23, 22, 21, 20 (c) Start at 8 and go up by 3 each time. 8, 11, 14, 17, 20 (d) Start at 4 and go up by 5 each time. 4, 9, 14, 19, 24 (e) Start at 33 and go down by 3 each time. 33, 30, 27, 24, 21 (f) Start at 29 and go down by 2 each time. 29, 27, 25, 23, 21 (g) Start at 11 and go up by 4 each time. 11, 15, 19, 23, 27 (h) Start at 30 and go down by 2 each time. 30, 28, 26, 24, 22 (i) Start at 3 and go up by 6 each time. 3, 9, 15, 21, 27 (j) Start at 2 and go up by 4 each time. 2, 6, 10, 14, 18 (k) Start at 11 and go up by 5 each time. 11, 16, 21, 26, 31 (l) Start at 38 and go down by 3 each time. 38, 35, 32, 29, 26 (m) Start at 36 and go down by 4 each time. 36, 32, 28, 24, 20 (n) Start at 23 and go up by 6 each time. 23, 29, 35, 41, 47 (o) Start at 40 and go down by 5 each time. 40, 35, 30, 25, 20 (p) Start at 13 and go up by 10 each time. 13, 23, 33, 43, 53 (q) Start at 72 and go down by 2 each time. 72, 70, 68, 66, 64 (r) Start at 99 and go down by 10 each time. 99, 89, 79, 69, 59 (s) Start at 41 and go up by 4 each time. 41, 45, 49, 53, 57 Create the Pattern (B) (page 138) (a) Start at 63 and go up by 7 each time. 63, 70, 77, 84 (b) Start at 234 and go down by 2 each time. 234, 232, 230, 228 (c) Start at 81 and go up by 3 each time. 81, 84, 87, 90 (d) Start at 79 and go down by 3 each time. 79, 76, 73, 70 (e) Start at 126 and go up by 5 each time. 126, 131, 136, 141 (f) Start at 540 and go down by 10 each time. 540, 530, 520, 510 (g) Start at 352 and go up by 20 each time. 352, 372, 392, 412 (h) Start at 47 and go up by 4 each time. 47, 51, 55, 59 (i) Start at 68 and go down by 4 each time. 68, 64, 60, 56 (j) Start at 275 and go up by 25 each time. 275, 300, 325, 350 (k) Start at 134 and go up by 6 each time. 134, 140, 146, 152 (l) Start at 456 and go down by 100 each time. 456, 356, 256, 156 (m) Start at 99 and go down by 11 each time. 99, 88, 77, 66 (n) Start at 347 and go up by 3 each time. 347, 350, 353, 356 (o) Start at 605 and go down by 5 each time. 605, 600, 595, 590 (p) Start at 710 and go up by 30 each time. 710, 740, 770, 800 (q) Start at 670 and go down by 20 each time. 670, 650, 630, 610 NSSAL 359 Draft

(r) Start at 412 and go up by 6 each time. 412, 418, 424, 430 (s) Start at 364 and go down by 3 each time. 364, 361, 358, 355 Number Patterns (A) (page 139) (a) 6, 8, 10, 12, 14, 16, 18, 20, 22 (b) 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12 (c) 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 (d) 30, 28, 26, 24, 22, 20, 18, 16, 14, 12 (e) 0, 3, 6, 9, 12, 15, 18, 21, 24 (f) 10, 15, 20, 25, 30, 35, 40, 45, 50 (g) 40, 36, 32, 28, 24, 20, 16, 12, 8 (h) 31, 28, 25, 22, 19, 16, 13, 10, 7, 4 (i) 7, 12, 17, 22, 27, 32, 37, 42, 47, 52, 57 (j) 45, 47, 49, 51, 53, 55, 57, 59, 61, 63 (k) 19, 22, 25, 28, 31, 34, 37, 40, 43, 46 (l) 51, 47, 43, 39, 35, 31, 27, 23, 19, 15, 11 (m) 67, 62, 57, 52, 47, 42, 37, 32, 27, 22 (n) 44, 43, 42, 41, 40, 39, 38, 37, 36 (o) 23, 25, 27, 29, 31, 33, 35, 37, 39 (p) 30, 27, 24, 21, 18, 15, 12, 9, 6 (q) 17, 21, 25, 29, 33, 37, 41, 45, 49, 53 (r) 9, 14, 19, 24, 29, 34, 39, 44, 49 (s) 30, 33, 36, 39, 42, 45, 48, 51, 54, 57 (t) 51, 46, 41, 36, 31, 26, 21, 16, 11, 6 (u) 91, 92, 93, 94, 95, 96, 97 Number Patterns (B) (page 140) (a) 2, 4, 6, 8, 10, 12, 14, 16, 18 (b) 4, 7, 10, 13, 16, 19, 22, 25 (c) 29, 27, 25, 23, 21, 19, 17, 15 (d) 55, 50, 45, 40, 35, 30, 25, 20 (e) 3, 10, 17, 24, 31, 38, 45, 52, 59 (f) 64, 56, 48, 40, 32, 24, 16, 8, 0 (g) 0, 6, 12, 18, 24, 30, 36, 42, 48, 54 (h) 1, 12, 23, 34, 45, 56, 67, 78, 89 (i) 44, 40, 36, 32, 28, 24, 20, 16, 12, 8 (j) 100, 104, 108, 112, 116, 120, 124, 128, 132 (k) 675, 680, 685, 690, 695, 700, 705, 710, 715, 720, 725 (l) 190, 210, 230, 250, 270, 290, 310, 330, 350, 370, 390 (m) 326, 324, 322, 320, 318, 316, 314, 312, 310 (n) 6, 10, 14, 18, 22, 26, 30, 34, 38 (o) 40, 37, 34, 31, 28, 25, 22, 19, 16 NSSAL 360 Draft

(p) 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106 (q) 21, 25, 29, 33, 37, 41, 45, 49, 53, 57 (r) 251, 245, 239, 233, 227, 221, 215, 209, 203 (s) 16, 24, 32, 40, 48, 54, 64, 72, 80 (t) 300, 296, 292, 288, 284, 280, 276, 272, 268 (u) 420, 440, 460, 480, 500, 520, 540 Row, Column, and Diagonal Pattern (page 141) Row Pattern Column Pattern Diagonal Pattern 1. Add 3 Add 9 Add 12 2. Subtract 2 Subtract 6 Subtract 8 3. Add 10 Add 30 Add 40 4. Subtract 4 Subtract 8 Subtract 16 5. Add 2 Subtract 6 Subtract 4 6. Subtract 5 Add 15 Add 10 What's the Relationship? (pages 142 and 143) (a) Even Numbers (b) Divisible by 3 Divisible by 2 Multiples of 3 Multiples of 2 Start at 3 and keep adding 3 Start at 2 and keep adding 2 Start at 48 and keep subtracting 3 Start at 50 and keep subtracting 2 (c) Divisible by 5 (d) Start at 1 and keep adding 4 Multiples of 5 Start at 49 and keep subtracting 1 Start at 5 and keep adding 5 Start at 50 and keep subtracting 5 (e) Start at 4 and keep adding 9 Start at 49 and keep subtracting 9 (f) Perfect Squares (g) Start at 1 and keep adding 11 (h) Odd Numbers Start at 45 and keep subtracting 11 Start at 1 and keep adding 2 Start at 49 and keep subtracting 2 (i) Divisible by 4 Multiples of 4 Start at 4 and keep adding 4 Start at 48 and keep subtracting 4 (j) Composite Numbers NSSAL 361 Draft

(k) Start at 2 and keep adding 12 (l) Divisible by 7 Start at 50 and keep subtracting 12 Multiples of 7 Start at 7 and keep adding 7 Start at 49 and keep subtracting 7 Input Output (A) (page 144) (a) add 4 (b) multiply by 2 (c) divide by 3 (d) subtract 5 (e) multiply by 5 (f) subtract 3 (g) divide by 4 (h) add 6 (i) multiply by 4 Input Output (B) (page 145) (a) multiply by 9 (b) subtract 7 (c) add 9 (d) divide by 7 (e) multiply by 6 (f) divide by 8 (g) add 7 (h) subtract 10 (i) multiply by 8 Input Output (C) (page 146) (a) add 30 (b) multiply by 50 (c) subtract 60 (d) divide by 4 (e) subtract 200 (f) multiply by 400 (g) subtract 70 (h) add 300 (i) divide by 2 Input Output (D) (page 147) (a) multiply by 2, then add 5 (b) multiply by 3, then add 1 (c) multiply by 2, then subtract 3 (d) multiply by 4, then subtract 2 (e) multiply by 3, then add 5 (f) multiply by 5, then add 1 (g) multiply by 4, then add 1 (h) multiply by 5, then subtract 2 (i) multiply by 3, then subtract 2 NSSAL 362 Draft

Filling or Draining (pages 148 to 152) 1. Written Description: The container initially had 18 L of water in it and it is being drained at a rate of 3 litres per minute. Table of Values: Time Litres 0 18 1 15 Equation: L = 18-2T 2 12 3 9 Empty: 6 minutes 2. Written Description: The container initially had 6 L of water in it and it is being filled at a rate of 2 litres per minute. Table of Values: Time Litres 0 6 1 8 Equation: L = 6 + 2T 2 10 3 12 Full: 7 minutes 3. Written Description: The container initially had 5 L of water in it and it is being filled at a rate of 3 litres per minute. Table of Values: Time Litres 0 5 1 8 Equation: L = 5 + 3T 2 11 3 14 Full: 5 minutes 4. Written Description: The container initially had 20 L of water in it and it is being drained at a rate of 4 litres per minute. Table of Values: Time Litres 0 20 1 16 Equation: L = 20-4T 2 12 3 8 Empty: 5 minutes NSSAL 363 Draft

5. Written Description: The container initially had 13 L of water in it and it is being drained at a rate of 1 litre per minute. Table of Values: Time Litres 0 13 1 12 Equation: L = 13-1T 2 11 3 10 Empty: 13 minutes 6. Written Description: The container was initially empty and it is being filled at a rate of 5 litres per minute. Table of Values: Time Litres 0 0 1 5 Equation: L = 5T 2 10 3 15 Full: 4 minutes 7. Written Description: The container initially had 10 L of water in it and it is being drained at a rate of 2 litres per minute. Table of Values: Time Litres 0 10 1 8 Equation: L = 10-2T 2 6 3 4 Empty: 5 minutes 8. Written Description: The container initially had 14 L of water in it and it is being filled at a rate of 1 litre per minute. Table of Values: Time Litres 0 14 1 15 Equation: L = 14 + 1T 2 16 3 17 Full: 6 minutes NSSAL 364 Draft

Travelling Towards or Away From Home (pages 153 to 159) 1. Written Description: Montez is initially 9 metres from home and runs away from home at a rate of 2 metres per second. Table of Values: Time Distance from Home 0 9 1 11 Equation: d = 9 + 2t 2 13 3 15 At t = 7 seconds, d = 23 m 4 17 2. Written Description: Montez is initially 4 metres from home and runs away from home at a rate of 3 metres per second. Table of Values: Time Distance from Home 0 4 1 7 Equation: d = 4 + 3t 2 10 3 13 At t = 7 seconds, d = 25 m 4 16 3. Written Description: Montez is initially 30 metres from home and runs towards home at a rate of 4 metres per second. Table of Values: Time Distance from Home 0 30 1 26 Equation: d = 30-4t 2 22 3 18 At t = 7 seconds, d = 2 m 4 14 NSSAL 365 Draft

4. Written Description: Montez is initially 24 metres from home and runs towards home at a rate of 3 metres per second. Table of Values: Time Distance from Home 0 24 1 21 Equation: d = 24-3t 2 18 3 15 At t = 7 seconds, d = 3 m 4 12 5. Written Description: Montez is initially 14 metres from home and runs towards home at a rate of 2 metres per second. Table of Values: Time Distance from Home 0 14 1 12 Equation: d = 14-2t 2 10 3 8 At t = 7 seconds, d = 0 m 4 6 6. Written Description: Montez is initially 20 metres from home and runs away from home at a rate of 1 metre per second. Table of Values: Time Distance from Home 0 20 1 21 Equation: d = 20 + t 2 22 3 23 At t = 7 seconds, d = 27 m 4 24 NSSAL 366 Draft

7. Written Description: Montez is initially 35 metres from home and runs towards home at a rate of 5 metres per second. Table of Values: Time Distance from Home 0 35 1 30 Equation: d = 35-5t 2 25 3 20 At t = 7 seconds, d = 0 m 4 15 8. Written Description: Montez is initially 0 metres from home and runs away from home at a rate of 6 metres per second. Table of Values: Time Distance from Home 0 0 1 6 Equation: d = 6t 2 12 3 18 At t = 7 seconds, d = 42 m 4 24 9. Written Description: Montez is initially 32 metres from home and runs towards home at a rate of 6 metres per second. Table of Values: Time Distance from Home 0 32 1 26 Equation: d = 32-6t 2 20 3 14 At t = 7 seconds, d = 0 m (actually arrived at home 4 8 between t = 5 and t = 6 seconds) NSSAL 367 Draft

Weight of the Water (pages 160 to 164) 1. Written Description: The container initially contained water weighting 2 newtons and then water was added such that the weight increased by 3 newtons per second. Table of Values: Time Weight 0 2 1 5 2 8 Equation: w = 2 + 3t 3 11 4 14 At t = 6 seconds, the weight is 20 N. 2. Written Description: The container initially contained water weighting 1 newton and then water was added such that the weight increased by 4 newtons per second. Table of Values: Time Weight 0 1 1 5 2 9 Equation: w = 1 + 4t 3 13 4 17 At t = 6 seconds, the weight is 25 N. 3. Written Description: The container initially contained water weighting 29 newtons and then water was removed such that the weight decreased by 3 newtons per second. Table of Values: Time Weight 0 29 1 26 2 23 Equation: w = 29-3t 3 20 4 17 At t = 6 seconds, the weight is 11 N. NSSAL 368 Draft

4. Written Description: The container initially contained water weighting 30 newtons and then water was removed such that the weight decreased by 5 newtons per second. Table of Values: Time Weight 0 30 1 25 2 20 Equation: w = 30-5t 3 15 4 10 At t = 6 seconds, the weight is 0 N. 5. Written Description: The container initially contained water weighting 0 newtons (i.e. the container was initially empty) and then water was added such that the weight increased by 4 newtons every 2 seconds, or 2 newtons every second. Table of Values: Time Weight 0 0 1 2 2 4 Equation: w = 2t 3 6 4 8 At t = 6 seconds, the weight is 12 N. 6. Written Description: The container initially contained water weighting 23 newtons and then water was removed such that the weight decreased by 6 newtons every 2 seconds, of 3 newtons every second. Table of Values: Time Weight 0 23 1 20 2 17 Equation: w = 23-3t 3 14 4 11 At t = 6 seconds, the weight is 5 N. NSSAL 369 Draft

Describing the Relationships with Words (page 166) There are 4 moons. There are 5 hearts. There are 8 suns. There is a total of 17 shapes. There is 1 more heart than moons. There is 1 less moon than hearts. There are 4 more suns than moons. There are 4 less moons than suns. There are 3 more suns than hearts. There are 3 less hearts than suns. There are twice as many suns as moons. There are half as many moons as suns. List the Numbers Based on the Written Description (page 167) 1. 9, 10, 11, 12, 13, 14 2. 10, 12, 14, 16, 18, 20, 22 3. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 4. 15, 20, 25, 30, 35, 40 5. 11, 22, 33, 44, 55, 66, 77, 88, 99 6. 15, 18, 21, 24, 27, 30 7. 5, 7, 11, 13, 17 8. 3, 9, 15, 21 9. 10, 20, 30, 40 10. 16, 25, 34, 43, 52, 61, 70 11. 36, 45, 54, 63, 72, 81, 99 12. 8, 16, 24, 32 13. 9, 10, 12, 14, 15, 16, 18, 20, 21 14. 6, 12, 18, 24, 30 15. 15, 25, 35, 45, 55 NSSAL 370 Draft

Addition and Subtraction Crossword (pages 168 and 169) t w o f i f t y e t w e l v e o w n h f o u r s e v e n t h i r t e e n i t l l e i f y v e s i x t e e n n t z e v i i e l e v e n e x g t e r n i n e t w o h e n o n e i y n t e n l g e i e h g t w e l v e t f t h r e e e e i g h t t l t w e n t y v h e l t e n e s i x f i v e e h i r e s e v e n r n f o r t y n e e e y n i n e e NSSAL 371 Draft

Multiplication and Division Crossword (page 170 to 171) t e i g h t y s t i i t h i r t y f t w o t h i r t y - s i x w o e t t w e n t y - f o u r n s y e l i r t h i r t y - f i v e e v f v y x t i n e n i n e - w g f e o h t t h i r t y f i f t e e n f o r t y - t w o y h g y e r h s e - n f i v e t w e l v e l o n e t e n e v s e v e n y i n f e v e s n i i n i n e e s i x t e e n f t e n f x t e i g h t w i t y y f i v e s e v e n t y f s i x - t w o l i e - o e s h u v x f u v i r r e f o u r t e e n x e u w n t e n f i f t y - f o u r o NSSAL 372 Draft

Operations Crossword (pages 172 to 173) t f i f t y - f o u r t w e n t y - o n e i o h n w i v f o u r t i o n i n e t y t h r e e r f i v e w y n t s t e n - e i g h t y - o n e n s e v e n e v t t i n i n e t e e n e y h x h n - i f z e r o t f o r t y - t w o e y o t u s e v e n t y - u e z r i i t r e l e v e n x n w t n i r s e v e n o n e g o f i f n s h e i g i t h i r t y - s i x f h z v w x y g t t w e l v e e - n h e y r s n o i t e o n e i t w o n n n i n e s i x t y e l e v e n NSSAL 373 Draft

Word Sentence to Number Sentence to Answer (A) (page 174) Word Sentence Number Sentence Answer (a) What is the sum of three and eight? 3 8 11 (b) What is six multiplied by five? 6 5 30 (c) What do you get when you double three? 2 3 6 (d) What is nine decreased by four? 9 4 5 (e) What is half of ten? 10 2 5 (f) Given seven and five, what is their total? 7 5 12 (g) What is eight times three? 8 3 24 (h) What is sixteen divided by two? 16 2 8 (i) What is seven increased by six? 7 6 13 (j) What do you get when you triple six? 3 6 18 (k) What do you get when eight is taken away from ten? 10 8 2 (l) What is seven less four? 7 4 3 (m) What is three plus eleven? 3 11 14 (n) What do we get when ten is broken into five equal parts? 10 5 2 (o) How much more is nine compared to two? 9 2 7 (p) What is a quarter of eight? 8 4 2 (q) What is the product of nine and two? 9 2 18 (r) What is six combined with eight? 6 8 14 (s) What is six taken from thirteen? 13 6 7 (t) What is ten increased by six? 10 6 16 (u) How many threes fit into fifteen? 15 3 5 (v) What do you get when nine is removed from ten? 10 9 1 NSSAL 374 Draft

Word Sentence to Number Sentence to Answer (B) (page 175) Word Sentence Number Sentence Answer (a) What do you get when you double eleven? 2 112 22 (b) What is thirty-five divided by seven? 35 7 5 (c) What is seven times six? 7 6 42 (d) What is seventeen increased by eight? 17 8 25 (e) What do you get when nine is taken away from fifteen? 15 9 6 (f) What is the sum of twelve and seven? 12 7 19 (g) What do we get when ten is broken into two equal parts? 10 2 5 (h) What is sixteen plus ten? 16 10 26 (i) What is the product of nine and seven? 9 7 63 (j) What is half of twenty-four? 24 2 12 (k) What is thirty-seven less five? 37 5 32 (l) What is six multiplied by eight? 6 8 48 (m) What is three taken from forty-nine? 49 3 46 (n) What is twenty-six increased by eleven? 26 11 37 (o) What do you get when six is removed from twenty-three? 23 6 17 (p) How many nines fit into eighty-one? 81 9 9 (q) What is forty-five decreased by six? 45 6 39 (r) What is eighteen combined with nine? 18 9 27 (s) What do you get when you triple twelve? 3 12 36 (t) Given seven and seventeen, what is their total? 7 17 24 (u) How much more is thirty-six compared to three? 36 3 33 (v) What is a third of twenty-seven? 27 3 9 NSSAL 375 Draft

Word Sentence to Number Sentence to Answer (C) (page 176) Word Sentence Number Sentence Answer (a) Given five hundred and two hundred, what is their total? 500 200 700 (b) What is fifty multiplied by three? 50 3 150 (c) What is three hundred increased by four hundred twenty? 300 420 720 (d) What is forty removed from one hundred? 100 40 60 (e) What is a third of nine thousand? 900 3 300 (f) How many sevens fit into three hundred fifty? 350 7 50 (g) What is seventy times eighty? 70 80 5600 (h) What is the sum of eleven and eighty? 11 80 91 (i) How much more is ninety compared to thirty? 90 30 60 (j) What is five thousand plus eight thousand? 5000 8000 13000 (k) What is two hundred sixty decreased by twenty? 260 20 240 (l) What do you get when you double four thousand? 2 4000 8000 (m) What is six hundred increased by two hundred thirty? 600 230 830 (n) What do you get when you triple forty? 3 40 120 (o) What is one thousand nine hundred less eight hundred? 1900 800 1100 (p) What is half of sixteen thousand? 16000 2 8000 (q) What is two hundred eighty divided by seven? 280 7 40 (r) What do you get when ten is taken away from ninety? 90 10 80 (s) What is sixty combined with eighty? 60 80 140 (t) What do we get when six is broken into six equal parts? 6 6 1 (u) What is seventy taken from ninety-six? 96 70 26 (v) What is the product of six and seven thousand? 6 7000 42000 What are the Possibilities? (A) (pages 177 to 179) 1. 0 and 5, 1 and 4, 2 and 3 2. 1 and 18, 2 and 9, 3 and 6, 1 and 20, 2 and 10, 4 and 5 NSSAL 376 Draft

3. 4 and 2, 6 and 3, 8 and 4 4. 9 and 4, 8 and 3, 7 and 2, 6 and 1, 5 and 0 5. 1 and 4, 2 and 2, 1 and 5, 1 and 6, 2 and 3 6. 6 and 9, 7 and 8, 7 and 9, 8 and 8, 8 and 9, 9 and 9 7. 12 and 3, 16 and 4, 20 and 5, 24 and 6 8. 6 and 4, 6 and 3, 5 and 3, 5 and 2, 4 and 2, 4 and 1, 3 and 1, 3 and 0, 2 and 0 9. 2 and 5, 1 and 8, 1 and 6, 2 and 3, 1 and 4, 1 and 2 10. 1 and 7, 3 and 5, 1 and 9, 3 and 7, 5 and 5 11. 18 and 9, 14 and 7, 10 and 5 12. 10 and 6, 8 and 4, 6 and 2, 4 and 0 What are the Possibilities? (B) (pages 180 and 181) 1. 2 and 8, 4 and 4, 4 and 6, 4 and 8, 6 and 6, 6 and 8, 8 and 8 2. 1 and 3, 1 and 5, 1 and 7, 1 and 9, 3 and 5, 3 and 7, 3 and 9 3. 3 and 11, 5 and 9, 7 and 7 4. 8 and 5, 7 and 4, 6 and 3, 5 and 2 5. 2 and 12, 3 and 8, 4 and 6 6. 2 and 6, 2 and 8, 2 and 10, 2 and 12, 4 and 4, 4 and 6 Does It Make Sense? (pages 182 and 183) 1. Does not make sense; one song from itunes costs around $1, not $9 2. Does not make sense; she purchased 7 litres of milk, not 8 litres. 3. Makes sense 4. Does not make sense; she ran 42 kilometres, not 36 kilometres NSSAL 377 Draft

5. Makes sense. 6. Does not make sense; can't have 100 roommates in an apartment. 7. Make sense. 8. Does not make sense; by the end of the year there were 23 students, rather than 21 9. Makes sense. 10. Makes sense. 11. Does not make sense; the total mass was 17 kg, not 30 kg. 12. Does not make sense; the total distance is 1800 km, not 18 000 km. 13. Does not make sense; a brand new 50 inch flat screen television would be anywhere from $700 to $1200, not $100. 14. Makes sense. 15. Does not make sense; it should be 4 apples and 6 oranges, rather than 4 oranges and 6 apples. 16. Does not make sense; she may have brought in $460, but her profit was $230. Put the Numbers in Where It Makes Sense (A) (page 185) 1. Lei and Jun are siblings. Lei is 4 years younger than Jun. If Jun is 31 years old, then Lei is 27 years old. 2. Marcus has dime and nickels in his pocket. If he has 7 nickels and 2 dimes, then he has a total of 55 cents. 3. Very few men attended the show. If there were 3 men and 24 women, then there 8 times as many women as men. 4. Normally 12 people attend the neighborhood watch meeting. That number increased slightly by 3 such that 15 people attended. 5. Anne had 40 dollars but spent most of her money on a 35 dollar top (after taxes). She now has 5 dollars left in her purse. 6. Bashir had 36 candies to split evenly between his 3 children. Each child got 12 candies; enough to ruin their supper. NSSAL 378 Draft

7. If there are 60 minutes in an hour, then we know that there are 180 minutes in 3 hours. 8. Ryan, who prefers running, ran for 25 minutes and biked for 15 minutes. That means he trained for a total of 40 minutes. 9. The mechanic ordered 40 containers of engine oil at a cost of 3 dollars per container. The total cost was 120 dollars. 10. 4 room mates got together to purchase an 800 dollar couch. If they all paid the same amount, then each pays 200 dollars. Put the Numbers in Where It Makes Sense (B) (page 186) 1. Tanya has 3 dimes and 2 quarters in her purse. That means she has 80 cents of change in her purse. 2. Bill and Ajay are friends. Bill is 3 years older than Ajay. If Bill is 50 years old, then Ajay is 47 years old. 3. Kim bought 12 apples and 4 oranges. Therefore she bought 3 times as many apples as oranges, or 8 more apples than oranges. 4. Three friends equally share the cost of a 21 dollar pizza that was divided into 6 pieces. Each pays 7 dollars and gets 2 pieces. 5. Ryan had 30 dollars but spent most of his money on a 19 dollar DVD (after taxes). He now has 11 dollars left. 6. If there are 24 hours in one day, then there are 48 hours in 2 days. 7. The room temperature was 18 degrees Celsius. If it is turned up slightly by 3 degrees, then the new temperature is 21 degrees. 8. There were 300 millilitres of water in a container. If only 50 millilitres is poured out, then the container still has 250 millilitres. 9. There are 8 SUVs and 32 cars in the lot. Therefore there are 4 times as many cars as SUVs, or 24 more cars than SUVs. 10. The store owner ordered 25 packages of printer paper at a cost of 2 dollars per package. His bill (before taxes) was 50 dollars. NSSAL 379 Draft

Put the Numbers in Where It Makes Sense (C) (page 187) 1. The cereal, the more expensive item, cost 5 dollars, and the dish soap cost 3 dollars. The total cost was 8 dollars. 2. The jar contained 40 candies. If you ate 30, which is most of the candy, then that would leave 10 in the jar. 3. The flour, which weighs 60 kg, must be divided evenly amongst 3 families. Each family was pleased to get 20 kg. 4. The DVD cost 18 dollars. The socks cost 10 dollars. The DVD was 8 dollars more expensive than the socks. 5. The corner store owner sold 30 bottles of pop. If each sold for 3 dollars, then his total pop sales were 90 dollars. 6. Tom drove for 2 more hours than Ed. Tom drove 9 hours, and Ed drove for 7 hours. 7. Kim worked 8 hours on Monday and less on Tuesday. If she got 7 hours on Tuesday, then her total was 15 hours. 8. Hinto had 3 nickels and 2 quarters. He had a total of 65 cents in nickels and quarters. 9. The friends on his Facebook account increased by 24, going from 70 to 94. 10. There 4 times as many children at the movie compared to adults. There were 20 adults and 80 children. Put the Numbers in Where It Makes Sense (D) (pages 188 and 189) 1. A cinema in a movie theatre can hold 120 people. Unfortunately that day, only half of the cinema was full meaning only 60 people are viewing the movie. The theatre charges 6 dollars for child tickets and 10 dollars for adult tickets. The total earnings for that showing in that cinema were 456 dollars. 2. Attendance for the annual blues concert is normally 850 people. This year, the number attending grew by 75, meaning that a total of 925 people attended. If individual tickets sold for 40, the promoters expected to bring in 3000 dollars more than last year just in ticket sales. 3. Taylor works at a hardware store where he makes 15 dollars per hour. Typically he works 38 hours per week, just shy of full time hours, and brings in 570 dollars (before deductions). If he works an additional 5 hours a week, he will make 75 dollars more (before deductions). NSSAL 380 Draft

4. Tanya has 3 teenage children. Montez, the oldest, is 18 years old. Tylena, the youngest, is 13 years old. Kiana, the middle child, is 2 years older than Tylena, making her 15 years old. Tanya, the mother, is 43 years old. 5. A group of seniors wants to charter buses to go on a trip. They check with the local charter company and learn that each bus can take 50 people and that the company charges 800 dollars a day for the bus and driver. Since 140 seniors wish to take the trip, then that means that they will need to charter 3 buses. Unfortunately that means that 10 seats on the buses will be unused. If the seniors are planning on taking a two day trip, the total cost for chartering the buses is 4800 dollars (before taxes). 6. A tank initially held 600 litres of water. A pump that removes water from the tank at a rate of 20 litres per minute is switched on ten minutes. That means that 200 litres have been removed, leaving 400 litres in the tank. If someone comes after the pump was switched off and pours 50 litres of water into the tank, the tank will now hold 450 litres of water. 7. Two brothers, Brian and Dave, work for the same company. Brian makes 3 dollars more per hour than Dave. Since Brian makes 16 dollars per hour, that means that Dave makes 19 dollars per hour. That means that in a 40 hour work week, Brian will make 760 dollars before deductions, and David will make 640 dollars before deductions. 8. There were 9 times as many people at the Rolling Bones concert than at the Tragically Flipped concert. If 7000 people were at the Flip concert, then that means that 63 000 people were at the Bones concert. The Bones charged 100 dollars per ticket, while the Flip only charged 40 dollars per ticket. That means that the Bone brought in 6 020 000 dollars more in ticket sales for their concert. Not Enough Information is Provided (page 190) 1. We need to know if all of the marbles are the same size and made of the same material (i.e. they all have the same mass). We also need to know how many marbles are in the jar. 2. We need to know the cans are sold individually or in a six-pack. If they are individual cans, we need to know the cost of each can (They would all be of the same cost if they are the same brand and same size). If they are in a six-pack, then we just look at the price on the six-pack. 3. We need to know how many friends helped out. We also need to know if they all worked the same number of hours and did similar tasks. If so then each would be entitled to an equal share of the $600. 4. We need to know two things. How much water did the container initially hold? For what length of time was the water being removed? NSSAL 381 Draft

5. We need to know how many hotdogs, pops, and chips are sold. We also need to know the fire fall's cost for those items; we can't figure out how much is made (i.e. profits) without considering the initial costs. 6. We need to know how many children Jun has and how many days each is planning on attending the camp. Word Problems with Too Much Information (pages 191 and 192) Correct Solution Extra Information 1. (a) 10 5 5 notebook costs $3 2. (c) 8 2 16 bag of potato chips costs $3 3. (b) 24 16 40 carry-on bag weighs 10 kg 4. (d) 8 6 2 4 children 5. (c) 20 5 4 10 pencils 6. (d) 6 8 48 7 men 7. (b) 2 6 8 3 hours 8. (a) 30 12 18 $23 sweatshirt 9. (b) 90 3 30 run 15 km 10. (d) 6 4 24 cycles at 20 kilometres per hour World Problems (A) (pages 195 and 196) 1. 5 + 6 = 11 2. 20-6 = 14 3. 5 7 = 35 4. 28 4 = 7 5. 35-13 = 12 6. 27 3 = 9 7. 8 + 7 = 15 8. 3 40 = 120 9. 10 + 9 = 19 10. 900 3 = 300 11. 28-15 = 13 12. 19-12 = 7 13. 5 9 = 45 14. 100 10 = 10 15. 60 + 39 = 99 16. 60 9 = 540 17. 17-4 = 13 18. 12 + 14 = 26 19. 480 6 = 80 20. 4 10 = 40 World Problems (B) (pages 197 to 199) 1. 3640-1780 = 1860 2. 237 + 19 = 256 3. 498 6 = 83 4. 27 15 = 405 5. 24 + 19 + 5 = 48 6. 1920-650 = 1270 7. 207 9 = 23 8. 8454 + 7461 = 15 915 9. 85 16 = 1360 10. 1365 3 = 455 11. 89 + 47 = 136 12. 257-118 = 139 13. 196-68 = 128 14. 1260 9 = 140 15. 31 25 = 775 NSSAL 382 Draft

Same Numbers, Similar Context, Different Math (A) (pages 200 and 201) 1. (a) 5 20 100 dollars (b) 20 5 4 dollars (c) 20 5 15 women (d) 20 5 25 women 2. (a) 40 8 5 times as heavy (b) 40 8 32 kg (c) 40 8 320 kg (d) 40 8 48 kg 3. (a) 30 5 25 hours (b) 30 5 35 hours (c) 30 5 6 times (d) 30 5 150 hours 4. (a) 50 10 60 people (b) 10 50 500 learners (c) 50 10 40 students (d) 50 10 5 vans Same Numbers, Similar Context, Different Math (B) (pages 202 and 203) 1. (a) 40 + 10 = $50 (b) 10 40 = $400 (c) 40-10 = $30 (d) 40 10 = $4 (e) (2 40) + (3 10) = $110 (f) 40 - (2 10) = $20 (g) (3 40) - (9 10) = $30 2. (a) 20 2 = 40 pills (b) 20 2 = 10 days (c) 20-2 = 18 pills (d) 20 + 2 = 22 pills (e) 20 - (3 2) = 14 pills (f) (3 20) + (4 2) = 68 pills (g) 20 (2 2) = 5 days 3. (a) 5 + 30 = 35 employees (b) 5 30 = 150 employees (c) 30-5 = 25 employees (d) 30 5 = 6 employees (e) 3 (5 + 30) = 105 employees (f) (5 20) + (30 10) = $400 (g) 30 + (4 5) = 50 employees NSSAL 383 Draft

More than One Question (pages 204 and 205) 1. (a) 5 3 8 litres (b) 5 3 2 litres (c) 12 8 4 litres (d) 12 5 7 litres 2. (a) 3 2 6 sheep (b) 14 2 12 (c) 14 2 7 pigs (d) 2 14 6 7 29 animals (e) 2 14 6 22 animals or 29 7 22 animals 3. (a) 4 3 12 motorcycles (b) 3 12 15 vehicles (c) 5 3 15 tires (d) 12 3 9 (e) 12 4 3 times Food Chart A (page 206) 1. 3 + 2 = 5 grams 2. 8-5 = 3 grams 3. 2 20 = 40 grams 4. 16 2 = 8 times larger 5. 1 + 12 + 10 = 23 grams 6. (2 18) 9 = 4 times larger 7. 24 - (5 3) = 9 grams Food Chart B (pages 207 and 208) 1. 40 + 75 = 115 kilocalories 2. (2 15) 10 = 3 times larger 3. 476-140 = 336 milligrams 4. 4 129 = 516 milligrams 5. 155 + 95 + 155 = 405 kilocalories 6. (3 233) - (2 75) = 549 milligrams 7. (2 60) + (3 35) + 20 = 245 grams 8. (2 140) (4 10) = 7 times larger 9. (220 + 40) - (165 + 65) = 30 grams 10. (60 + (2 20)) (15 + 35) = 2 times larger Keeping Track of New Stock (A) (page 209) 1. 40 10 = 4 times larger 2. 30-20 = 10 units 3. 18 + 4 = 22 units 4. 3 20 = 60 units 5. 30-10 = 20 units 6. 20 4 = 5 times larger 7. 10 + 4 + 15 = 29 units 8. 15 5 = 3 units NSSAL 384 Draft

Keeping Track of the New Stock (B) (page 210) 1. (2 40) + (2 10) = 100 units 2. (34-22) + (18-15) = 9 units 3. (40-34) - (20-18) = 4 units 4. (24-10) - (13-4) = 5 units 5. (34 + 13) - 24 = 23 units 6. 3 (30-24) = 18 units 7. (10-0) (20-15) = 2 times larger 8. (34-22) (40-34) = 2 times larger How Much Do They Have? (A) (page 212) Anne s Money: 50 or $0.50 Jake s Money: 90 or $0.90 Meera s Money: $2.45 Ryan s Money: $3.80 Yoshi s Money: $4.65 How Much Do They Have? (B) (page 213) Dave s Money: 95 or $0.95 Shelly s Money: 65 or $0.65 Maurita s Money: $1.80 Jun s Money: $4.30 Lei s Money: $5.50 How Much Do They Have? (C) (page 214) Andrew s Cash: $70 Mary s Cash: $45 Kara s Cash: $50 Montez s Cash: $120 Shima s Cash: $140 How Much Do They Have? (D) (page 215) Hamid s Cash: $55 Tanya s Cash: $40 Samir s Cash: $80 Mark s Cash: $135 Hatsu s Cash: $175 How Much Do They Have? (E) (page 216) Sasha s Money: $8.25 Hinto s Money: $11.70 Lisa s Money: $24.20 Tiva s Money: $7.40 Meera s Money: $53.30 NSSAL 385 Draft

Emptying the Junk Drawer (pages 217 and 218) Bills or Change Number of Each Value in Dollars $20 bills 1 20 $10 Bills 1 10 $5 Bills 3 15 Toonies ($2 coins) 4 8 Loonies ($1 coins) 3 3 Quarters (25 coins) 7 1.75 Dimes (10 coins) 10 1.00 Nickels (5 coins) 12 0.60 Total: 59.35 If you found three more nickels, five more quarters, and four more loonies, how much would you have in total? Answer: $64.75 Least to Most Expensive (page 222) 1. Two Slice Toaster Litre of Milk Refrigerator Electric Fry Pan 2 1 4 3 2. Silver Earrings Leather Jacket Pair of Socks Pencil 3 4 2 1 3. Power Drill Winter Gloves Fingernail Clippers Mattress (Queen) 3 2 1 4 4. Hardcover Book Birthday Card Prescription Glasses Pair of Winter Boots 2 1 4 3 5. Coffee Table Kitchen Stove Can Opener Electric Kettle 3 4 1 2 6. Four Winter Tires 20 inch Television DVD Player Four Litres of Oil 4 3 2 1 NSSAL 386 Draft

7. Small Flashlight Delivery Pizza Reclining Chair Table Lamp 1 2 4 3 8. Hair Dryer Coffee Mug Chocolate Bar Toaster Oven 3 2 1 4 9. Paperback Novel Big Concert Ticket Spring Jacket Bus Toll 2 4 3 1 10. Love Seat Dish Soap 10 kg Turkey Four Litres of Milk 4 1 3 2 What Are the Three Items Worth? (page 223) Item: Price Item: Price 1. Hammer $10 2. Box of Cereal $6 Florescent Light Bulb $3 A Pair of Jeans $50 Can of Pop $1 T-shirt $12 Item: Price Item: Price 3. Sofa $600 4. Fast-food Hamburger $3 A Pair of Sunglasses $20 A Pair of Work Boots $90 Microwave Oven $150 Knapsack for School $40 Item: Price Item: Price 5. A Man's Haircut $25 6. Tube of Toothpaste $3 Loaf of Bread $2 Small Waste Paper Basket $15 An Adult Bicycle $250 Winter Coat $120 What Is It Worth? (A) (page 224) Item Approximate Price (Number) Approximate Price (Words) (a) Ride-on Lawn Mower $2149 Two thousand, one hundred forty-nine (b) DVD/Blu-ray Player $99 Ninety-nine (c) Toaster $17 Seventeen (d) HD Video Camera $329 Three hundred twenty-nine (e) Compact Car $14 900 Fourteen thousand, nine hundred (f) 42 inch Flat Screen TV $549 Five hundred firty-nine (g) Tank of Gas (Compact Car) $50 Fifty NSSAL 387 Draft

What Is It Worth? (B) (page 225) Item Approximate Price (Number) Approximate Price (Words) (a) Washing Machine $469 Four hundred sixty-nine (b) Hair Dryer $21 Twenty-one (c) Minivan $22 900 Twenty-two thousand, nine hundred (d) Fast Food Meal for One $8 Eight (e) Gasoline Push Mower $239 Two hundred thirty-nine (f) Child's Bicycle $69 Sixty-nine (g) Four Person Hot Tub $3599 Three thousand, five hundred ninetynine Which Measurement Is Reasonable? (page 229) 1. The length of an adult's arm: (a) 65 centimetres 2. The length of three city blocks: (d) 1 kilometre 3. The amount of lemonade that could be held in a pitcher: (c) 2 litres 4. The weight of a ten year old boy: (b) 34 kilograms 5. The amount of water in a drinking glass: (c) 350 millilitres 6. The height of a three-story apartment building: (a) 12 metres 7. The weight of a compact car: (b) 1800 kilograms 8. The length of a man's fingernail on his pinkie finger: (d) 1 centimetre 9. The distance from Halifax, Nova Scotia to Truro, Nova Scotia: (d) 100 kilometres 10. The amount of gasoline that can be held in a compact car's gas tank: (c) 40 litres Telling Time (A) (page 230) (a) 4:50 (b) 11:00 (c) 2:00 (d) 7:25 (e) 1:15 (f) 9:55 (g) 3:35 (h) 12:05 (i) 6:05 NSSAL 388 Draft

Telling Time (B) (page 231) (a) 7:40 (b) 2:15 (c) 10:10 (d) 1:20 (e) 11:05 (f) 3:45 (g) 8:50 (h) 5:10 (i) 12:15 Telling Time (C) (page 232) (a) 5:20 (b) 1:30 (c) 9:00 (d) 11:15 (e) 3:50 (f) 12:20 (g) 2:25 (h) 10:20 (i) 7:55 Telling Time (D) (page 233) (a) 4:10 (b) 12:35 (c) 9:15 (d) 2:40 (e) 11:25 (f) 5:45 (g) 10:30 (h) 8:10 (i) 6:40 Telling Time (E) (page 234) (a) 5:50 (b) 6:20 (c) 1:45 (d) 4:15 (e) 6:30 (f) 9:10 (g) 2:50 (h) 10:40 (i) 8:15 Telling Time (F) (page 235) (a) 3:10 (b) 10:45 (c) 4:30 (d) 8:25 (e) 5:55 (f) 12:50 (g) 9:35 (h) 7:15 (i) 1:55 How Much Time Hass Passed? (A) (pages 238 and 239) (a) Start Time: 6:20 (b) Start Time: 2:00 Finish Time: 6:30 Finish Time: 2:40 Time Passed: 0 hour(s), 10 minutes Time Passed: 0 hour(s), 40 minutes (c) Start Time: 4:15 (d) Start Time: 9:10 Finish Time: 4:30 Finish Time: 10:10 Time Passed: 0 hour(s), 15 minutes Time Passed: 1 hour(s), 0 minutes NSSAL 389 Draft

(e) Start Time: 11:00 (f) Start Time: 2:00 Finish Time: 12:15 Finish Time: 3:45 Time Passed: 1 hour(s), 15 minutes Time Passed: 1 hour(s), 45 minutes (g) Start Time: 4:15 (h) Start Time: 10:30 Finish Time: 5:45 Finish Time: 12:15 Time Passed: 1 hour(s), 30 minutes Time Passed: 1 hour(s), 45 minutes How Much Time Hass Passed? (B) (pages 240 and 241) (a) Start Time: 11:05 (b) Start Time: 9:35 Finish Time: 11:40 Finish Time: 10:40 Time Passed: 0 hour(s), 35 minutes Time Passed: 1 hour(s), 5 minutes (c) Start Time: 6:50 (d) Start Time: 5:20 Finish Time: 9:10 Finish Time: 7:40 Time Passed: 2 hour(s), 10 minutes Time Passed: 2 hour(s), 20 minutes (e) Start Time: 1:45 (f) Start Time: 6:40 Finish Time: 4:10 Finish Time: 8:25 Time Passed: 2 hour(s), 45 minutes Time Passed: 1 hour(s), 45 minutes (g) Start Time: 11:00 (h) Start Time: 11:15 Finish Time: 1:30 Finish Time: 2:40 Time Passed: 2 hour(s), 30 minutes Time Passed: 3 hour(s), 25 minutes How Much Time Hass Passed? (C) (pages 242 and 243) (a) Start Time: 3:10 (b) Start Time: 5:45 Finish Time: 3:50 Finish Time: 8:15 Time Passed: 0 hour(s), 40 minutes Time Passed: 2 hour(s), 30 minutes (c) Start Time: 4:15 (d) Start Time: 12:20 Finish Time: 6:50 Finish Time: 4:15 Time Passed: 2 hour(s), 35 minutes Time Passed: 3 hour(s), 55 minutes (e) Start Time: 11:40 (f) Start Time: 10:30 Finish Time: 12:50 Finish Time: 1:15 Time Passed: 1 hour(s), 10 minutes Time Passed: 2 hour(s), 45 minutes (g) Start Time: 10:45 (h) Start Time: 9:15 Finish Time: 2:50 Finish Time: 12:35 Time Passed: 4 hour(s), 5 minutes Time Passed: 3 hour(s), 20 minutes NSSAL 390 Draft

Orthographic Projections (A) (pages 246 to 249) 1. Front View Back View Right View Left View Top View Bottom View 2. Front View Back View Right View Left View Top View Bottom View 3. Front View Back View Right View Left View Top View Bottom View NSSAL 391 Draft

4. Front View Back View Right View Left View Top View Bottom View 5. Front View Back View Right View Left View Top View Bottom View 6. Front View Back View Right View Left View Top View Bottom View NSSAL 392 Draft

Orthographic Projections (B) (pages 250 and 251) 1. Front View Back View Right View Left View Top View Bottom View 2. Front View Back View Right View Left View Top View Bottom View 3. Front View Back View Right View Left View Top View Bottom View NSSAL 393 Draft

4. Front View Back View Right View Left View Top View Bottom View NSSAL 394 Draft

Isometric Projections (pages 253 to 256) 1. 2. 3. 4. 5. 6. 7. 8. 9. NSSAL 395 Draft

Edges, Faces and Vertices (A) (page 259) Faces Edges Vertices 1. 5 9 6 2. 5 8 5 3. 6 12 8 4. 4 6 4 5. 7 15 10 6. 8 18 12 7. 6 10 6 8. 8 12 6 9. 9 17 10 Edges, Faces and Vertices (B) (page 260) Faces Edges Vertices 1. 9 16 9 2. 6 12 8 3. 10 24 16 4. 7 15 10 5. 7 12 7 6. 8 18 12 7. 8 13 7 8. 9 21 14 9. 11 27 18 Nets (pages 266 and 267) 1. F 2. C 3. B 4. E 5. A 6. D The diagrams below have been scaled down. NSSAL 396 Draft

Describe the Faces (pages 268 to 276) 1. (a) Six Faces Two of the faces are identical parallelograms. Two of the faces are identical squares. Two of the faces are identical rectangles. (b) Five Faces Four of the faces are identical isosceles triangles. Last face is a square. (c) Six Faces Four of the faces are identical rectangles. Two of the faces are identical rhombuses. (d) Five Faces Three of the faces are identical squares. Two of the faces are identical equilateral triangles. 2. (a) Six Faces Four of the faces are identical rectangles. Two of the faces are identical squares. (b) Five Faces Two of the faces are identical isosceles right triangles. The three remaining faces are rectangles but they are not of the same size. (c) Six Faces Two of the faces are identical parallelograms. Two of the faces are identical rectangles. The last two faces are identical rectangles. (d) Six Faces Two of the faces are identical rectangles. Another two faces are identical rectangles. The last two faces are identical rectangles. NSSAL 397 Draft

(e) Five Faces Two of the faces are identical rectangles. Two of the faces are identical isosceles triangles. The last face is a square. (f) Six Faces Two of the faces are identical trapezoids. Three of the faces are rectangles but they are not of same size. The last face is a square. (g) Five Faces Two of the faces are identical scalene right triangles Two of the faces are rectangles but they are not of the same size The last face is a square. (h) Six Faces Four of the faces are identical trapezoids. The two remaining faces are squares but they are not of the same size 3. (a) 4 identical rectangles 6 cm 2 identical squares 14 cm 6 cm (b) 2 identical scalene right triangles 1 square 6 cm 6 cm 8 cm 10 cm 10 cm 2 rectangles, but of different sizes 10 cm 10 cm 6 cm 8 cm 10 cm NSSAL 398 Draft

(c) 4 identical isosceles triangles 24 mm 24 mm 1 square 15 mm 15 mm 15 mm (d) 2 identical rectangles 4 m 9 m 2 more identical rectangles 9 m 16 m 2 more identical rectangles 4 m 16 m (e) 3 identical isosceles triangles 11 cm 11 cm 7 cm 1 equilateral triangle 7 cm 7 cm 7 cm NSSAL 399 Draft

(f) 2 identical trapezoids 5 m 6 m 4 m 9 m 1 square 9 m 9 m 3 rectangles but of different sizes 4 m 5 m 9 m 9 m 6 m 9 m (g) 2 identical hexagons (All edges are 8 cm long.) 8 cm 6 identical rectangles 8 cm 30 cm NSSAL 400 Draft

(h) 4 identical isosceles triangles 13 cm 13 cm 4 identical rectangles 10 cm 4 cm 10 cm 1 square 10 cm 10 cm (i) 2 identical equilateral triangles 5 m 5 m 5 m 3 identical rectangles 2 m 5 m (j) 3 identical isosceles triangles 10 cm 10 cm 6 cm Another 3 identical isosceles triangles 8 cm 8 cm NSSAL 401 6 cm Draft

(k) 2 identical octagons (All edges are 2 m in long.) 2 m 8 identical squares 2 m 2 m (l) 2 identical trapezoids 4 cm 10 cm 10 cm 8 cm Another 2 identical trapezoids 2 cm 10 cm 10 cm 4 cm 2 rectangles, but of different sizes 8 cm 4 cm 4 cm 2 cm NSSAL 402 Draft

Geometry Crossword (pages 277 and 278) V E R T E X Q N Q U A D R I L A T E R A L I T I L P S A P E O R T H O G R A P H I C A N M E H R I G H T E R I S O S C E L E S A A T A M L G R L B T L O I S U R R E N C Q S C A L E N E L U P C O F A C E E O C T A G O N R Z A R H E X A G O N N A I G M D L E D G E NSSAL 403 Draft

Reflections (A) (page 279) Very Challenging (Only give to your strongest learners) NSSAL 404 Draft

Reflections (B) (page 280) Very Challenging (Only give to your strongest learners) NSSAL 405 Draft

Reflections (C) (page 281) Very Challenging (Only give to your strongest learners) NSSAL 406 Draft

What's the Number? (page 283 and 284) (a) 2247 (b) 1358 (c) 3132 (d) 524 (e) 4019 (f) 2308 (g) 1420 (h) 3080 Express the Number Different Ways (pages 285 and 286) (a) Number: 1435 Expanded Form: 1000 + 400 + 30 + 5 Using Words: one thousand, four hundred thirty-five (b) Number: 2561 Expanded Form: 2000 + 500 + 60 + 1 Using Words: two thousand, five hundred sixty-one (c) Number: 5214 Expanded Form: 5000 + 200 + 10 + 4 Using Words: five thousand, two hundred fourteen (d) Number: 4186 Expanded Form: 4000 + 100 + 80 + 6 Using Words: four thousand, one hundred eighty-six (e) Number: 6042 Expanded Form: 6000 + 40 + 2 Using Words: six thousand, forty-two (f) Number: 1709 Expanded Form: 1000 + 700 + 9 Using Words: one thousand, seven hundred nine (g) Number: 3470 Expanded Form: 3000 + 400 + 70 Using Words: three thousand, four hundred seventy NSSAL 407 Draft

Express with the Fewest Number of Manipulatives (pages 287 to 294) 1. (a) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 2 11 16 3 2 6 Number: 326 (b) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 1 22 18 3 3 8 Number: 338 (c) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 3 10 29 4 2 9 Number: 429 NSSAL 408 Draft

(d) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 0 26 23 2 8 3 Number: 283 (e) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 4 16 8 5 6 8 Number: 568 (f) New Representation: Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 1 20 31 3 3 1 Number: 331 NSSAL 409 Draft

2. (a) Original Representation New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 3 17 13 4 8 3 Number: 483 Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 2 22 18 4 3 8 Number: 438 Flats (Hundreds) Original Representation Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 1 25 32 3 8 2 Number: 382 3. (a) New Representation (b) New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 6 5 7 6 4 9 Number: 657 Number: 649 (c) New Representation (d) New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 9 2 3 4 8 7 Number: 923 Number: 487 NSSAL 410 Draft

(e) New Representation (f) New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 5 8 8 7 6 5 Number: 588 Number: 765 (g) New Representation (h) New Representation Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) Flats (Hundreds) Rods (Tens) Unit Tiles (Ones) 8 5 4 7 4 7 Number: 854 Number: 747 (i) Flats (Hundreds) New Representation Rods (Tens) Unit Tiles (Ones) 6 4 8 Number: 648 Adding (pages 295 to 298) 1. (a) 1 3 5 3 (b) 4 4 2 3 (c) 5 2 1 2 (d) 2 2 6 3 4 8 7 3 7 3 4 9 (e) 3 4 4 2 (f) 3 3 2 2 (g) 1 1 2 4 2 6 (h) 1 3 2 4 4 7 6 6 4 2 6 8 1 5 8 NSSAL 411 Draft

2. Tens Ones (a) 3 1 5 4 8 5 (b) 2 4 5 3 Tens Ones 6 8 (c) 1 6 2 6 Tens Ones 7 8 NSSAL 412 Draft

(d) 1 1 2 3 6 3 Hundreds Tens Ones 2 5 9 3. (a) 85 (b) 78 (c) 48 (d) 88 (e) 89 (f) 49 (g) 286 (h) 358 (i) 499 (j) 784 (k) 983 (l) 746 (m) 2786 (n) 3499 (o) 5168 Adding with Regrouping (pages 299 to 304) 1. (a) (b) (c) Step 1 Step 2 Step 3 4 6 Break the 14 ones Exchange 10 ones for 3 8 into a group of 10 a rod. ones and a group of 4 ones. 1 3 4 2 9 4 5 6 Break the 13 ones into a group of 10 ones and a group of 3 ones. Break the 11 ones into a group of 10 ones and a group of 1 ones. Exchange 10 ones for a rod. Exchange 10 ones for a rod. 1 4 3 8 1 1 3 5 1 4 2 7 6 8 4 9 4 3 5 6 1 NSSAL 413 Draft

2. (a) 1 3 2 6 9 Steps 1 and 2 Step 3 Tens Ones Tens Ones 6 5 (b) 1 2 1 5 8 Steps 1 and 2 Step 3 Tens Ones Tens Ones 4 3 (c) 1 3 4 9 7 Steps 1 and 2 Step 3 Tens Ones Tens Ones 8 6 3. (a) 61 (b) 60 (c) 96 (d) 84 (e) 53 (f) 137 (g) 92 (h) 80 (i) 126 NSSAL 414 Draft

4. (a) 145 (b) 96 (c) 56 (d) 51 (e) 90 (f) 73 (g) 108 (h) 95 (i) 163 Subtracting (pages 305 to 309) 1. (a) 8 5 8 4 (b) 5 1 6 3 (c) 7 3 5 4 (d) 6 4 7 2 3 4 4 3 7 3 2 5 (e) 5 2 3 3 (f) 2 1 6 3 9 5 (g) 2 2 8 1 7 6 3 0 1 3 4 7 1 2. Tens Ones (a) 7 4 5 2 2 2 (b) 8 3 6 6 Tens Ones 5 0 NSSAL 415 Draft

(c) 2 7 9 Hundreds Tens Ones 1 2 6 1 5 3 (d) 2 5 8 Hundreds Tens Ones 4 3 2 1 5 3. (a) 53 (b) 12 (c) 26 (d) 50 (e) 71 (f) 29 (g) 52 (h) 2 (i) 10 (j) 142 (k) 235 (l) 157 (m) 482 (n) 503 (o) 62 (p) 2415 (q) 5432 (r) 2070 (s) 7620 (t) 1043 (u) 5361 Subtracting with Regrouping (pages 310 to 316) 1. (a) 7 16 8 6 3 8 4 8 (b) 6 14 7 4 5 7 1 7 (c) 8 12 9 2 6 8 2 4 NSSAL 416 Draft

(d) 1 13 2 3 6 1 5 2 8 4 (e) 1 14 2 4 7 8 1 1 6 6 (f) 7 14 2 8 4 2 3 5 4 9 2. (a) 7 14 8 4 2 9 5 5 (b) 8 11 9 1 7 6 1 5 (c) 5 13 6 3 3 8 2 5 (d) 7 12 8 2 6 2 5 3 5 7 3 (e) 3 15 4 5 6 2 6 6 1 9 0 (f) 8 16 7 9 6 5 6 9 2 2 7 3. (a) 5 16 6 6 1 8 4 8 (b) 4 11 5 1 3 7 1 4 (c) 7 8 4 3 3 5 (d) 8 14 9 4 6 8 2 6 (e) 6 7 2 3 4 4 (f) 6 12 7 2 9 3 6 1 3 6 8 (g) 4 16 5 6 9 3 9 0 1 7 9 (h) 4 9 6 2 6 5 2 3 1 (i) 7 13 6 8 3 6 5 8 2 5 NSSAL 417 Draft