Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction"

Transcription

1 Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review place value to 1,000,000 and understand the relative sizes of numbers in each place. Students will also practice representing numbers with base ten materials, and convert between numbers and expanded form. Students will order sets of two or more numbers, and will find the greatest and least number possible using the digits given. Students will add and subtract with and without regrouping, use pictures and charts to solve word problems, and recognize what is given and what they need to find in a word problem. Finally, students will round to the closest ten, hundred, or thousand, and estimate sums and differences by rounding each addend to the nearest ten, hundred, or thousand. Number and Operations in Base Ten C-1

2 NBT5-1 Place Value Pages STANDARDS 5.NBT.A.3, 5.NBT.A.1 Vocabulary expanded form hundreds hundred thousands millions ones place value ten thousands tens thousands Goals Students will identify the place value and the actual value of digits in numbers up to 7 digits, and learn to write number words for numbers with up to 7 digits. PRIOR KNOWLEDGE REQUIRED Knows the number words one, ten, hundred, thousand, ten thousand, hundred thousand, million, and their corresponding numerals MATERIALS BLM Place Value Cards (p. C-58) scissors tape or sticky tack Introduce place value. Photocopy BLM Place Value Cards and cut out the five cards. Write the number 65,321 on the board, leaving extra space between all the digits, and hold the ones card under the 3. ASK: Did I put the card in the right place? Is 3 the ones digit? Have a volunteer put the card below the correct digit. Invite volunteers to position the other cards correctly. Cards can be temporarily affixed to the board using tape or sticky tack. Exploring more about place value. Write 23,989 on the board and ask students to identify the place value of the underlined digit. (NOTE: If you give each student a copy of BLM Place Value Cards, individuals can hold up their answers. Have students cut out the cards before you begin.) Repeat with several numbers that have an underlined digit. Include whole numbers with anywhere from 1 to 5 digits. (MP.6) Vary the question slightly by asking students to find the place value of a particular digit without underlining it. (Example: Find the place value of the digit 4 in these numbers: 24,001, 42,305, 34,432, 32,847.) Continue until students can identify place value correctly and confidently. Include examples where you ask for the place value of the digit 0. Write 28,306 on the board. SAY: The number 28,306 is a 5-digit number. What is the place value of the digit 2? (If necessary, point to each digit as you count aloud from the right: ones, tens, hundreds, thousands). SAY: The 2 is in the ten thousands place, so it stands for 20,000. What does the digit 8 stand for? (8,000) the 3? (300) the 0? (0 tens or just 0) the 6? (6) ASK: What is the value of the 6 in 2,608? (600) in 36,504? (6,000) in 63,504? (60,000) in 6,504? (6,000) ASK: In the number 6,831, what does the digit 3 stand for? (30) the 6? (6,000) the 1? (1) The 8? (800) C-2 Teacher s Guide for AP Book 5.1

3 ASK: What is the value of the 0 in 340? (0) in 403? (0) in 8,097? (0) Write out the corresponding addition statements so students see that 0 always has a value of 0, no matter what position it is in. ASK: In the number 7,856, what is the tens digit? (5) the thousands? (7) ones? (6) hundreds? (8) Repeat for 3,050, 455, 77,077. Introduce hundred thousands and millions place value. Follow the same procedure as in the previous lesson to introduce the place values hundred thousands and millions. Write the correct spelling for all place values on the board. Exercises: Identify the place value of the digit 3 in each number. a) 312,607 b) 453,207 c) 3,762,906 d) 7,401,235 Answers: a) 300,000, b) 3,000, c) 3,000,000, d) 30 Determining how many times as much or as many. Review the concept how many times as many if necessary. Begin with twice as many by having students solve word problems such as: Carrie has three tickets to a concert. Rob has twice as many as Carrie. How many tickets does Rob have? Draw three tickets on the board and write Carrie s name beside them. Then write Rob s name to the right of Carrie s and SAY: I know that Rob has twice as many tickets as Carrie, so I just have to draw Carrie s number of tickets twice. Carrie Rob Have students solve word problems with three times as many and emphasize that you have to draw the lesser number of objects three times to make the greater number. ASK: How many times as much money is a dollar worth than a dime? (10) than a nickel? (20) than a penny? (100) How many times as much money is a dime worth than a nickel? (2) than a penny? (10) How many times as much money is a quarter worth than a nickel? (5) a dollar worth than a quarter? (4) How many times as many blocks are in a hundreds block than in a tens block? (10) than a ones block? (100) How many times as many blocks are in a thousands block than in a hundreds block? (10) than a tens block? (100) than a ones block? (1,000) Remind students that we can speak of numbers as being twice as many or three times as many or four times as many as another number. Exercises: Fill in the blanks. a) 12 = 3, so 12 is times as many as 3. b) 20 = 4, so 20 is times as many as 4. Number and Operations in Base Ten 5-1 C-3

4 c) 100 = 10, so 100 is times as many as 10. d) 1,000 = 10, so 1,000 is times as many as 10. e) 30,000 = 300, so 30,000 is times as many as 300. f) 4,000 is times as many as 40. g) 400,000 is times as many as 400. Answers: a) 4, b) 5, c) 10, d) 100, e) 100, f) 100, g) 1,000 ASK: What is the value of the first 1 in the number 1,716? (1,000) What is the value of the second 1? (10) How many times as many is the first 1 worth than the second 1? (100) How many tens blocks would you need to make a thousands block? (100) Repeat with more numbers in which the digit 1 is repeated (examples: 1,341, 11, 101, 21,314). ASK: What is the value of the first 3 in 3,231? (3,000) the second 3? (30) How many times as many is the first 3 worth than the second 3 in 3,231? (100) Exercises: Copy and complete the chart. Add rows for b) through d). First Number Second Number How many times as many? a) 3, b) 5,000 and 50 c) 500,000 and 5,000 d) 800,000 and 8 Answers: b) 100, c) 100, d) 100,000 Bonus: Give students who finish quickly greater numbers with the two threes moving farther and farther apart, ending with a number such as: 823,450,917,863,401 Have students fill in a chart like the following: (MP.7, MP.8) Number How many places to the right of the first 3 is the second 3? How many times as many is the first 3 worth than the second 3? How many 0s are in the number from the previous column? 3, , ,383 1,233 Make up your own number What pattern do you notice? Does the pattern help you solve the Bonus problem? Answer: The second 3 is 9 places over from the first 3 in the Bonus, so to write how many times as many the first 3 is worth than the second 3, write 1 with 9 zeroes: 1,000,000,000. C-4 Teacher s Guide for AP Book 5.1

5 Reading and writing multi-digit numbers. Write on the board: 32,000 ASK: How many thousands are there? Show students how to write thirty-two thousand. Exercises: Write number words for multiples of 1,000. a) 17,000 b) 20,000 c) 489,000 d) 638,000 e) 704,000 Answers: a) seventeen thousand, b) twenty thousand, c) four hundred eighty-nine thousand, d) six hundred thirty-eight thousand, e) seven hundred four thousand Exercises: Write the number words for 5-digit and 6-digit numbers. a) 23,802 b) 254,006 c) 30,109 d) 140,019 e) 632,540 Answers: a) twenty-three thousand eight hundred two, b) two hundred fifty-four thousand six, c) thirty thousand one hundred nine, d) one hundred forty thousand nineteen, e) six hundred thirty-two thousand five hundred forty Write out the place value words for numbers with up to 12 digits: ones tens hundreds thousands ten thousands hundred thousands millions ten millions hundred millions billions ten billions hundred billions Point out that after the thousands, there is a new word at every three place values. This is why we put commas between every three digits in numbers so that we can see when a new word will be used. This helps us to quickly identify and read multi-digit numbers. Demonstrate this using the number 3,456,720,603, which is read as three billion four hundred fifty-six million seven hundred twenty thousand six hundred three. Then write another multi-digit number on the board 42,783,089,320 and ASK: How many billions are in this number? (42) How many millions? (783) How many thousands? (89) Then read the whole number together. Extensions 1. Identify and write the numbers given specific criteria and constraints. a) Write a number between 12,730 and 12,370. b) Write a 5-digit even number with the tens digit 6. c) Write an odd number greater than 9,860. d) Write a number with the tens digit one more than the ones digit. Number and Operations in Base Ten 5-1 C-5

6 Harder (MP.1) e) Write a 5-digit number with the tens digit eight less than the ones digit. f) Write a 6-digit number in which the first three digits are odd. g) Write a number between 50 and 60 with both digits the same. h) Write a 3-digit even number with all its digits the same. i) Find the sum of the digits in each of these numbers: 37, 48, 531, 225, 444, 372. j) Write a 3-digit number in which all digits are the same and the sum of the digits is 15. k) Which number has the tens digit one less than the ones digit: 324,540, 880, 11,034, 909? l) Write a 4-digit number in which the digits are all equal and the sum of the digits is 12. Make up more such questions, or have students make up their own. Sample answers: a) 12,573, b) 10,468, c) 9,957, d) 4,187, e) 81,619, f) 131,589 Answers: g) 55; h) 222, 444, 666, or 888; i) 10, 12, 9, 9, 12, 12; j) 555, k) 11,034, l) 3,333 (MP.7) 2. Which has a greater place value in the following numbers, the 3 or the 6? How many times as many is the digit worth? a) 63 b) 623 c) 6,342 d) 36 e) 376 f) 3,006 g) 6,731 h) 7,362 i) 9,603 j) 3,568 k) 3,756 l) 3,765 If students need help, ask them how they could turn each question into a problem they already know how to solve. For example, if it was 323 instead of 623, you would know how to solve it. (the first 3 is worth 100 times as many as than the second 3) How is 623 different from 323? (6 is two times as many as 3, so the 6 is worth 200 times as many as the 3) Answers: a) 6, 20 times; b) 6, 200 times; c) 6, 20 times; d) 3, 5 times; e) 3, 50 times; f) 3, 500 times; g) 6, 200 times; h) 3, 5 times; i) 6, 200 times; j) 3, 50 times; k) 3, 500 times; l) 3, 50 times; m) 6, 200 times C-6 Teacher s Guide for AP Book 5.1

7 NBT5-2 Representation in Expanded Form Pages STANDARDS 5.NBT.A.3 Goals Students will practice representing numbers with base ten materials, and convert between numbers and expanded form. Vocabulary digit hundreds block numeral ones block place value tens block PRIOR KNOWLEDGE REQUIRED Knows place values for ones, tens, hundreds, thousands, and ten thousands Is familiar with base ten materials Knows the number words for place values of one, ten, hundred, thousand, ten thousand, hundred thousand, million, and their corresponding numerals MATERIALS 5 hundreds blocks per student 25 tens blocks per student 15 ones blocks per student Thousands block Hundreds block Tens block Ones block Introduce the standard way to represent numbers using blocks. As students group and manipulate base ten materials throughout the lesson, monitor the models they create on their desks and/or have students sketch their answers on paper so you can verify their understanding. Students can work individually or in small groups. Give each student three tens blocks and fifteen ones blocks. Ask them to make the number 17 and to explain how their model represents that number. PROMPTS: How many tens blocks do you have? (1) How many ones are in a tens block? (10) How many ones are there altogether? (17) Repeat with more 2-digit numbers (examples: 14, 19, 28, 34, 32, 25). Then give each student 3 hundreds blocks and have them make 3-digit numbers (examples: 235, 129, 316). Use prompts, if needed, to help students break down their models. For the number 235, ASK: How many ones are in the hundreds blocks? (200) tens blocks? (30) ones blocks? (5) How many ones are there altogether? (235) Have students work in pairs to make the following: 12 using exactly 12 blocks, 22 using 13 blocks, 25 using 16 blocks, and 31 using 13 blocks. Some of these models will be non-standard (example: 22 using 13 blocks = 1 tens block and 12 ones blocks, instead of the standard 2 tens blocks and 2 ones blocks). Encourage students to make a standard model first, then ask themselves whether they need more blocks or fewer blocks. (they will always need more blocks) Which blocks can they trade to keep the value the same but increase the number of blocks? (answers will vary) Number and Operations in Base Ten 5-2 C-7

8 Review how to draw the base ten blocks, especially the thousands cube, as shown on p. 13 in the AP Book. Have students draw models for various 4-digit numbers (examples: 2,541, 1,082, 3,204). Review expanded form. ASK: How much is the 4 worth in 459? (400) the 5? (50) the 9? (9) Have a volunteer write the expanded form of 459 on the board. (459 = ) Exercises: Write the numbers in expanded form. a) 352 b) 896 c) 784 Answers: a) 352 = ; b) 896 = ; c) 784 = Ensure that all students have written at least the first one correctly. Review expanded form of numbers that contain 0. Ask a volunteer to write 350 in expanded form on the board. (350 = ) Have another volunteer write the expanded form of 305. (305 = ) Exercises: Write the numbers in expanded form. a) 207 b) 270 c) 702 d) 720 Answers: a) 207 = ; b) 270 = ; c) 702 = ; d) 720 = Proceed to 4- and 5-digit numbers, then to 6- and 7-digit numbers Exercises: Write the numbers in expanded form. a) 6,103 b) 7,064 c) 29,031 d) 30,402 e) 234,401 f) 7,032,530 g) 8,411,206 Answers: a) 6,103 = 6, ; b) 7,064 = 7, ; c) 29,031 = 29, ; d) 30,402 = 30, ; e) 234,401 = 200, , , ; f) 7,032,530 = 7,000, , ; g) 8,411,206 = 8,000, , , Review expanded form using number words. Write on the board: 32,427 = ten thousands + thousands + hundreds + tens + ones Have a volunteer fill in the blanks. Repeat with the numbers 4,589; 38,061; 5,770, 804; 40,300. Proceed to 6- and 7-digit numbers, adding the words millions and hundred thousands. Then model writing the words millions, hundred thousands, ten thousands, thousands, hundreds, tens, and ones, as you write the expanded form of the number 8,642,503: 8,642,503 = 8 millions + 6 hundred thousands + 4 ten thousands + 2 thousands + 5 hundreds + 0 tens + 3 ones C-8 Teacher s Guide for AP Book 5.1

9 (MP.7) Exercise: Fill in the blanks, then rewrite the number words in the correct order. 5,423,891 = ones + hundred thousands + tens + ten thousands + thousands + millions + hundreds Answer: 5 millions + 4 hundred thousands + 2 ten thousands + 3 thousands + 8 hundreds + 9 tens + 1 one Writing numbers from the expanded form. ASK: What is ? Is there a 0 in the number? How do you know? What would happen if we didn t write the 0 digit because we thought the 0 didn t matter, and we just wrote the 5 and the 7 as 57? Does = 57? (no) Emphasize that in expanded form we do not need to write the 0 because expanded form is an addition statement (or sum) and the 0 does not add anything. But the 0 means something in multi-digit numbers. It makes sure that each digit s place value is recorded properly. Mathematicians call 0 a place holder because of this. Exercises: Add. a) b) c) d) e) f) 4, g) 5, h) 7, i) 80, j) 60, Bonus: 30, ,000, Answers: a) 302, b) 230, c) 405, d) 504, e) 740, f) 4,378, g) 5,061, h) 7,003, i) 80,300, j) 60,049, Bonus: 8,030,410 Give students examples of 3-, 4-, 5-, 6-, and 7-digit sums for which they need to fill in the blanks (examples: = 253; 50, = 54,020; 7,000, = 7,040,300) Bonus: Provide examples in which the order of the addends differs from the order of the digits. (example: 4,327 = ,000) ASK: What is the sum of the digits in 234? (9) in 5,121? (9) Ask students to find a number that has digits with a sum of 11. Encourage students to find more than one answer. (137; 5,132; 902; 830; 416; 623; 3,044) Have students make (or sketch) models of their numbers using base ten materials. ASK: How many blocks did you need? How can you find the number of blocks from the digits? Exercises: What is the sum of the tens digit and the thousands digit? a) 2,735 b) 5,745 c) 39,602 d) 412,777? Answers: a) 5, b) 9, c) 9, d) 9 Challenge students to find a number with sum of the tens digit and the thousands digit equal to 11. (7,148; 9,020; 8,932; 6,456) Number and Operations in Base Ten 5-2 C-9

10 Review the concept of twice as many and three times as many. Exercises 1. Which digit is twice the ones digit? a) 432 b) 6,723 c) 45,621 d) 308,754 e) 67, Which digit is three times the tens digit? a) 513 b) 89,736 c) 907,508 d) 36,422 Answers: 1. a) 4, b) 6, c) 2, d) 8, e) 0; 2. a) 3, b) 9, c) 0, d) 6 Exercises: Do these problems individually. a) Write a number whose hundreds digit is twice its ones digit. b) In the number 4,923, find a digit that is twice another digit. c) In the number 265,321, which digit is exactly three times the tens digit? d) Write an odd number whose ten thousands digit is twice its hundreds digit. Answers: a) 613 (answers may vary), b) 4, c) 6, d) 80,413 (answers may vary) Extensions (MP.1) 1. Write an odd number whose ten thousands digit is twice its hundreds digit. Sample answer: 61, Solve these puzzles using base ten blocks: a) I am greater than 20 and less than 30. My ones digit is one more than my tens digit. b) I am a 2-digit number: Use 6 blocks to make me. Use twice as many tens blocks as ones blocks. c) I am a 3-digit number. My digits are all the same. Use 9 blocks to make me. d) I am a 2-digit number. My tens digit is 5 more than my ones digit. Use 7 blocks to make me. e) I am a 3-digit number. My tens digit is one more than my hundreds digit and my ones digit is one more than my tens digit. Use 6 blocks to make me. f) Show 1,123 using exactly 16 blocks. (There are 2 answers.) g) I am a 4-digit number. My digits are all the same. Use 12 blocks to make me. C-10 Teacher s Guide for AP Book 5.1

11 Answers: a) 23, 24, 25, 26, 27, 28, or 29; b) 42, c) 333, d) 61, e) 123, f) 11 hundreds blocks + 2 tens blocks + 3 ones blocks or 1 thousands block + 12 tens blocks + 3 ones blocks, g) 3, Solve these puzzles by only imagining the base ten blocks. Use base ten blocks for harder questions if necessary. Questions (a) through (e) have more than one answer share your answers with a partner. a) I have more tens than ones. What number could I be? b) I have the same number of ones and tens blocks. What number could I be? c) I have twice as many tens blocks as ones blocks. What 2-digit number could I be? d) I have six more ones than tens. What number could I be? e) I have an equal number of ones, tens, and hundreds, and twice as many thousands as hundreds. What number could I be? f) I have one set of blocks that make the number 13 and one set of blocks that make the number 22. Can I have the same number of blocks in both sets? g) I have one set of blocks that make the number 23 and one set of blocks that make the number 16. Can I have the same number of blocks in both sets? Answers: a) Answers can be any number in which the tens digit is higher than the ones digit, such as 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, etc. As the tens digit increases by one, the number of ones digits that can be used also increases by one; b) 11, 22, 33, 44, 55, 66, 77, 88, 99; c) 21, 42, 63, 84; d) 17, 28, 39; e) 2,111, 4,222, 8,444; f) yes, they can both have 4 blocks: 13 = 1 tens block + 3 ones blocks, 22 = 2 tens blocks + 2 ones blocks; g) no (MP.3) 4. Make a chart to investigate how many base ten blocks are needed to make different numbers. Use these example numbers in the chart: 84, 23, 916, 196, 1,003, 200, 4,321, 9,022. When students are done the chart, ASK: a) Do all 3-digit numbers need more blocks than all 2-digit numbers? (no) Are all 3-digit numbers greater than all 2-digit numbers? (yes) Why is this the case? (3-digit numbers are hundreds and 2-digit numbers are tens) b) How can you find the number of base ten blocks needed just by looking at the digits? (add the digits) c) What is the greatest number of base ten blocks needed for a 1-digit number? (9) a 2-digit number? (18) a 3-digit number? (27) a 4-digit number? (36) Describe the pattern. (all are multiples of 9) Number and Operations in Base Ten 5-2 C-11

12 d) Make an organized list to find all 2-digit numbers that need the exact number of blocks. i) 1 block ii) 2 blocks iii) 3 blocks iv) 15 blocks Answers: i) 10; ii) 11, 20; ii) 12, 21, 30; iv) 69, 78, 87, 96 e) Make an organized list to find all 3-digit numbers that need the exact number of blocks. i) 1 block ii) 2 blocks iii) 3 blocks iv) 4 blocks v) 5 blocks Answers: i) 100; ii) 101, 110, 200; iii) 102, 111, 120, 201, 210, 300; iv) 103, 112, 121, 130, 202, 211, 220, 301, 310, 400; v) 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 320, 401, 410, Which of the following are correct representations of 352? a) b) 1 hundred + 20 tens + 2 ones c) 2 hundreds + 15 tens + 2 ones d) 34 tens + 12 ones Answers: a) and c) represent 352 Make up more problems like this and have students make up problems of their own. C-12 Teacher s Guide for AP Book 5.1

13 NBT5-3 Comparing and Ordering Pages Multi-Digit Numbers STANDARDS 5.NBT.A.3 Goals Students will order sets of two or more numbers, and will find the greatest and least number possible using the digits given. Vocabulary expanded form greater than > less than < PRIOR KNOWLEDGE REQUIRED Can compare pairs of numbers Knows place values for ones, tens, hundreds, thousands, and ten thousands Knows the number words for place values of one, ten, hundred, thousand, ten thousand, hundred thousand, million, and their corresponding numerals MATERIALS grid paper (optional) 3 dice per pair of students 3 small boxes, bags, or other containers per pair of students 1-digit to 5-digit number cards, 1 per student (MP.7) Comparing numbers that differ by only one digit. Write the numbers 435 and 425 in expanded form on the board. ASK: Which number is greater? (435) How can you easily tell from the expanded form that 435 is greater than 425? (30 is more than 20, and everything else is the same) Circle the 30 and 20 to emphasize this. 435 = = Exercises: Use expanded form to identify the greater number. a) 352 or 452 b) 405 or 401 c) 398 or 358 d) 541 or 241 Answers: a) 452, b) 405, c) 398, d) 541 Point out that you can compare the numbers 435 and 425 just by looking at the digits that are different. SAY: Since the tens digits are the only ones that are different, the number with the greater tens digit is greater Exercises: Circle the digits that are different, then write the greater number. a) 542 b) 706 c) 3,240 d) 432, , ,706 Answers: a) hundreds digit, 642; b) ones digit, 706; c) hundreds digit, 3,540; d) ten thousands digit, 432,706 Number and Operations in Base Ten 5-3 C-13

14 Comparing numbers that differ by more than one digit. Tell students that you want to compare two 3-digit numbers. Write on the board: ASK: Which number has more hundreds? (342) more tens? (257) more ones? (257) Which number do you think is greater the one with the most hundreds, the most tens, or the most ones? (most hundreds) Why? (hundreds are greater than tens and ones) Encourage students who have trouble seeing that the number with the most hundreds is greater to think in terms of money in which a hundred cents is a dollar, ten cents is a dime, and 1 cent is a penny. The question then becomes: Which is more money: 3 dollars, 4 dimes, and 2 pennies; or 2 dollars, 5 dimes, and 7 pennies? The money amount that has more dollars is greater. Exercises: Circle the greater number. a) 731 or 550 b) 642 or 713 c) 519 or 382 Answers: a) 731, b) 713, c) 519 Encourage students who are struggling to compare the number of hundreds more easily by writing the second number below the first number on grid paper, if necessary. 582 = = Now tell students that you want to compare 582 and 574. Demonstrate how to split the numbers, as shown in the margin. SAY: The hundreds are the same, so you just have to compare 82 and 74. ASK: Which is greater, 82 or 74? (82) How do you know? (it has more tens) Point out that when comparing any two numbers, start at the left and circle the first digits that are different those will tell you which number is greater. Have volunteers circle the first, left-most digits that are different in these pairs of numbers: a) 632 b) 873 c) 2,741 d) 352, , ,631 Exercises: Write the greater number in each pair above. Answers: a) 641, b) 873, c) 2,750, d) 352,418 Exercises: Counting from the left, underline the first digit that is different. Then circle the greater number. a) 718 and 523 b) 5,234 and 6,234 c) 9,843,275 and 9,846,192 d) 874,321 and 874,132 Answers: a) 718, b) 6,234, c) 9,846,192, d) 874,321 NOTE: Have students who are struggling use grid paper to line up the place values ones with ones, tens with tens, and so on. Example: C-14 Teacher s Guide for AP Book 5.1

15 Remind students that < means is less than because the wider end is on the right, so the lesser number is first. Similarly, > means is greater than because the wider end is on the left so the greater number is first. Exercises: Write < or > for each pair of numbers. a) 32, ,329 b) 912,401 91,401 c) 8,322,407 8,322,415 d) 62,713 68,290 Answers: a) 32,417 < 276,329; b) 912,401 > 91,401; c) 8,322,407 < 8,322,415; d) 62,713 < 68,290 (MP.1) Write on the board: (MP.3) Ask students to make all the possible 3-digit numbers from these digits. (358, 385, 538, 583, 835, 853) Tell them to try to do it in an organized way. Take suggestions for how to do that. (start with the hundreds digit; write all the numbers that have the hundreds digit 3 first, then work on the numbers with the hundreds digit 5, then 8) How many numbers are there altogether? (6, 2 starting with each digit) Which of these numbers is greatest? (835) Which is least? (358) Have students reflect: Could they have found the greatest number using these digits without listing all the possible numbers? SAY: I want to find the greatest number possible using each of the digits 1, 3, 5, and 8 once. Do I need to find all the numbers I can make from these digits to find the greatest number? (no, you can simply write the numbers in order from greatest to least starting from the left) Exercises: Create the greatest possible number using each digit once. a) 2, 9, 7, 8, 4 b) 4, 4, 8, 3, 2 c) 3, 7, 0, 6, 1 Answers: a) 98,742, b) 84,432, c) 76,310 Then ask students to find the least possible number using those same digits. (Note that a number cannot begin with the digit 0, so the least number in c) is 10,367.) Finally, ask students to use the same digits to find a number in between the greatest and least possible numbers. Exercises: Order the groups of three 4-digit numbers from least to greatest. a) 3,458, 3,576, 3,479 b) 4,987, 6,104, 6,087 c) 4,387, 2,912, 3,006 Answers: a) 3,458, 3,479, 3,576; b) 4,987, 6,087, 6,104; c) 2,912, 3,006, 4,387 Combine 3-digit and 4-digit numbers and have students order them from least to greatest (example: 3,407, 410, 740). Have students order similar groups of 5-digit numbers. Bonus: Have students order longer lists of numbers. Number and Operations in Base Ten 5-3 C-15

16 Finally, combine numbers with different numbers of digits. For example, have students order from least to greatest 2,354, 798, 54,211. (798, 2,354, 54,211) Have students use the digits 0 to 9 each once so that, >,. ASK: Can you place the digits so that, >,? (no, a 6-digit number is always greater than a 4-digit number) Exercises 1. Use the digits 0, 1, and 2 to create a number that is: a) more than 200 b) between 100 and 200 c) a multiple of Use the digits 4, 6, 7, and 9 to create a number that is: a) between 6200 and 6500 b) larger than 8000 c) an even number between 9500 and Use the digits 0, 3, 4, 7, and 8 to create a number that is: a) a multiple of 10 b) between 73,900 and 75,000 c) more than 40,000 and less than 70, Find the correct digit. a) < < b) < < ACTIVITIES 1 2 (MP.3) 1. Students work with a partner. Partner 1 rolls 3 dice. Partner 2 makes the greatest possible number with the digits Partner 1 rolled. Partners then switch roles. HARDER: Students work in pairs and compete with each other to make the greatest (or least, or closest to 500) 3-digit number. Use three small boxes, bags, or other containers for the hundreds, tens, and ones digit, but choose where to put each roll before doing the next roll. For example, if Partner 1 is trying for the least number and rolls a 2, Partner 2 might choose to place it in the hundreds box. If the next roll is a 1, Partner 2 will want to move the 2 but will not be allowed to. 2. Students use number cards to line up for lunch in order from greatest to least. The number cards should range from 1-digit to 5-digit numbers. Discuss with students how they can organize themselves into groups. Are there any groups in which all the numbers in one group will be greater than all the numbers in other groups? If necessary, prompt students with questions such as: Are all the 2-digit numbers greater than all the 1-digit numbers? How do you know? Should the 2-digit numbers go before the 1-digit C-16 Teacher s Guide for AP Book 5.1

17 numbers, or after? Who should go right before the 2-digit numbers? Who should go first? Before having any group go, ensure that all the groups know which order they go in. ASK: Who belongs in the first group? Have them show their cards. Repeat with the second, third, fourth, and fifth groups. Extensions (MP.1) 1. How many whole numbers are greater than 4,000 but less than 4,350? Explain how you know. Answer: 349 numbers; any number from 4,001 to 4, What is the greatest 6-digit number you can create so that: a) the number is a multiple of 5 b) the ten thousands digit is twice the tens digit Answers: a) 999,995; b) 989, Write the number 98,950 on the board and challenge students to find all the greater numbers that use the same digits. Answers: 99,058; 99,085; 99,508; 99,580; 99,805; 99, Write the number 75,095 on the board. Have each student find a number that differs from it in only one digit. Have them ask a partner whether their number is greater or less than 75,095. Whose number is greatest? Have them work in groups of 4, 5, or 6 to order all the numbers they made. Sample answers: The greatest number is 95,095, the least number is 15,095, and the closest number is 75,094 or 75,096. Number and Operations in Base Ten 5-3 C-17

18 NBT5-4 Regrouping Pages STANDARDS preparation for 5.NBT.B.7 Goals Students will write numbers as sums of ones, tens, hundreds, and thousands in different ways. Vocabulary digits number sentence place value regrouping PRIOR KNOWLEDGE REQUIRED Is familiar with base ten materials Knows place values for ones, tens, hundreds, thousands, and ten thousands Knows the number words for place values of one, ten, hundred, thousand, ten thousand, hundred thousand, million, and their corresponding numerals Review base ten blocks. Draw on the board: ASK: How many ones blocks are there altogether? (34) Ask for strategies for counting the blocks. (count by fives, then by ones, or count by sevens, then by ones; using multiplication: multiply 7 by 5, then subtract 1, or multiply 5 by 6, then add 4, or multiply 7 by 4, then add 6) ASK: Do we have enough to trade for a tens block? (yes) How do you know? (because there are more than 10 ones blocks) How many tens blocks can we trade for? (3) How do you know? (there are more than 30 blocks) Have a volunteer group sets of 10. Where do you see that number in 34? (the 3 represents the number of tens) What does the 4 tell you? (the number of ones left over) Draw base ten models with more than ten ones and have students practice trading ten ones blocks for a tens block. They should draw models to record their trades in their notebooks. Example: 4 tens + 19 ones = 5 tens + 9 ones Students should also be comfortable translating these pictures into number sentences: = = = 59 C-18 Teacher s Guide for AP Book 5.1

19 Using regrouping. ASK: What number is 6 tens + 25 ones? How can we regroup the 25 ones to solve this question? 25 = 2 tens + 5 ones = , so 6 tens + 25 ones = tens 25 ones This means 6 tens + 25 ones = 8 tens + 5 ones, as summarized by this chart: Tens Ones = = 5 Have students practice using a chart like this to regroup numbers. Then have them regroup numbers without using the chart: 3 tens + 42 ones = tens + ones Continue with problems that require: 1) regrouping tens to hundreds (example: 4 hundreds + 22 tens). 2) regrouping ones to tens and tens to hundreds. Include numbers with 9 tens and more than 10 ones, so they will not have to regroup tens to hundreds until after they regroup the ones (example: 2 hundreds + 9 tens + 14 ones). Use this to explain the importance of grouping the ones first you can only tell if there are enough tens to make a hundred after you have grouped all the ones into tens. 3) regrouping hundreds to thousands. 4) regrouping thousands to ten thousands, hundreds to thousands, tens to hundreds, and ones to tens. Again, include examples with 9 hundreds and more than 10 tens, or 9 thousands, 9 hundreds, 9 tens, and more than 10 ones. Examples: a) 3 ten thousands + 4 thousands + 15 hundreds + 5 tens + 3 ones b) 4 ten thousands + 17 thousands + 9 hundreds + 18 tens + 2 ones c) 5 ten thousands + 12 thousands + 9 hundreds + 3 tens + 38 ones d) 4 ten thousands + 9 thousands + 13 hundreds + 14 tens + 7 ones e) 5 ten thousands + 12 thousands + 19 hundreds + 5 tens + 12 ones f) 9 ten thousands + 8 thousands + 16 hundreds + 34 tens + 11 ones g) 7 ten thousands + 5 thousands + 9 hundreds + 12 tens + 8 ones h) 6 ten thousands + 9 thousands + 9 hundreds + 24 tens + 7 ones i) 8 ten thousands + 9 thousands + 9 hundreds + 9 tens + 26 ones j) 8 ten thousands + 9 thousands + 13 hundreds + 8 tens + 25 ones Number and Operations in Base Ten 5-4 C-19

20 Extensions 1. Show the regrouping in Questions 2 and 3 on AP Book p. 17 with base ten blocks. 2. Teach students the Egyptian system for writing numerals to help them appreciate the utility of place value. Write the following numbers using both the Egyptian and our Arabic systems: Invite students to study the numbers for a moment, then ASK: What is different about the Egyptian system for writing numbers? (It uses symbols instead of digits. You have to show the number of ones, tens, and so on individually if you have 7 ones, you have to draw 7 strokes. In our system, a single digit (7) tells you how many ones there are.) Review the ancient Egyptian symbols for 1, 10, and 100, and introduce the symbols for 1,000 and 10,000: 1 = (stroke) 10 = (arch) 100 = (coiled rope) 1,000 = (lotus leaf) 10,000 = (finger) Ask students to write a few numbers the Egyptian way and to translate those Egyptian numbers into regular numerals. Emphasize that the order in which you write the symbols does not matter: 234 = Have students write a number that is very long to write the Egyptian way. (example: 798) ASK: How is our system more convenient? Why is it helpful to have a place value system in which the ones, tens, and so on are always in the same place? Students might want to invent their own number system using the Egyptian system as a model. Answer: To show 999 we need just 3 symbols, but the Egyptian way needs 27 symbols. 3. If you teach students Egyptian writing, you can then ask them to show regrouping using Egyptian writing. C-20 Teacher s Guide for AP Book 5.1

21 NBT5-5 Multi-Digit Addition Pages STANDARDS 5.NBT.B.7 Goals Students will add up to 6-digit numbers with and without regrouping. Vocabulary algorithm expanded form place value chart regrouping standard notation for addition PRIOR KNOWLEDGE REQUIRED Is familiar with base ten materials Knows place values for ones, tens, hundreds, thousands, and ten thousands Knows place values for ones, tens, hundreds, thousands, and ten thousands MATERIALS 1 die per pair of students Review regrouping when using base ten materials for addition. Tell students you want to add 27 and 15. Begin by drawing base ten models of 27 and 15 on the board: 27 = 15 = Then write the addition statement and combine the two models to represent the sum: = ASK: How many ones do we have in total? (12) how many tens? (3) Replace 10 ones with 1 tens block. ASK: Now how many ones do we have? (2) How many tens? (4) How many do we have altogether? (42) = Exploring addition with regrouping using place value charts. Use a tens and ones chart to summarize how you regrouped the ones: Tens Ones After combining the base ten materials 4 2 After regrouping 10 ones blocks as 1 tens block Number and Operations in Base Ten 5-5 C-21

22 Exercises: Draw the base ten materials and the tens and ones charts for each addition statement. a) 36 b) 28 c) 46 d) Bonus e) 32 f) Selected solution: a) 7 tens blocks + 11 ones blocks = 8 tens blocks + 1 ones block = 81 Answers: b) 65, c) 82, d) 47, Bonus: e) 91, f) 74 Using standard notation for addition with regrouping 2 digits. Ask students if they really need the base ten materials or if they can add without them. Draw the chart on the board: Tens Ones Add each digit separately 8 3 Regroup 10 ones as 1 ten: = = SAY: When you use a chart, you can add the tens and ones first, then regroup. When you do the sum directly, you regroup right away: = 13, which is 1 ten + 3 ones, so you put the 3 in the ones column and add the 1 to the tens column. Demonstrate the first step of writing the sum of the ones digits: Ask students how many ones there are when you add the ones digits, and how you are regrouping them. Tell them that when we regroup ten ones for a ten, we put the 1 on top of the tens column. Mathematicians call this process carrying the 1. Ask students for reasons why this name is appropriate for the notation. Have students do the first step for several problems, then move on to problems in which students need to do both steps. Some students may need to begin by having the first step done for them so they can focus only on completing the second step. C-22 Teacher s Guide for AP Book 5.1

23 Include examples in which the numbers add up to more than 100 (examples: , ). Exercises: Add the numbers. a) b) c) d) e) f) g) Bonus: Answers: a) 85, b) 84, c) 90, d) 85, e) 113, f) 114, g) 87, Bonus: 166 Adding 3-digit numbers using expanded form. Have volunteers draw on the board base ten models for 152 and 273. Tell students that you want to add these numbers. ASK: How many hundreds, tens, and ones are there altogether? (3 hundreds + 12 tens + 5 ones) Do we need to regroup? (yes) How do you know? (the tens digit is more than 9) How can we regroup? (since there are 12 tens, we can trade 10 of them for 1 hundred) After regrouping, how many hundreds, tens, and ones are there? (4 hundreds + 2 tens + 5 ones) What number is that? (425) Write out and complete the following statements as you work through the example: 153 hundred + tens + ones hundreds + tens + ones hundreds + tens + ones After regrouping: hundreds + tens + ones Have students add more pairs of 3-digit numbers. Provide examples in the following sequence: either the ones or the tens need to be regrouped (examples: , ). both the ones and the tens need to be regrouped (examples: , ). the tens need to be regrouped, but you don t realize it until you regroup the ones (examples: , ) Using standard notation for addition with regrouping 3 digits. Now show students the standard algorithm alongside a hundreds, tens, and ones chart for the first example you did together ( ): Hundreds Tens Ones = = Number and Operations in Base Ten 5-5 C-23

24 Point out that after regrouping the tens, you add the 1 hundred that you carried over from the tens at the same time as the hundreds from the two numbers, so you get hundreds. Have students add more 3-digit numbers using the chart and the algorithm at first, then using only the algorithm. Do examples in the same sequence as before: either the ones or tens need to be regrouped; both the ones and tens need to be regrouped; the tens need to be regrouped after the ones have been regrouped. Exercises: Add using the standard algorithm. a) b) c) d) e) f) g) h) Bonus: Answers: a) 575, b) 815, c) 1,490, d) 1,769, e) 953, f) 1,486, g) 905, h) 1,000, Bonus: 1,995 Adding 4-, 5-, 6-digit numbers. When students have mastered 3-digit numbers, repeat the lesson with 4-digit numbers, then with 5-digit numbers. Do not assume that students will be so familiar with the method that you can skip steps in the process. Use a chart alongside the algorithm to start, and provide examples in which different digits need to be regrouped. Finally, include both 4- and 5-digit numbers as addends in the same sum (example: 32, ,736). Exercises 1. Add the 4-digit numbers. a) 1, ,217 b) 3, ,590 c) 6, ,258 d) 1, ,958 e) 4, ,347 f) 4, ,325 Bonus: 3, , ,132 Answers: a) 8,575, b) 6,563, c) 14,953, d) 9,193, e) 13,005, f) 10,000, Bonus: 11, Add the 5-digit and 6-digit numbers. a) 81, ,584 b) 13, ,756 c) 94, ,647 d) 862, ,857 e) 394, ,656 f) 146, ,925 Bonus: g) 15, , ,209 h) 3,789, ,654,987 Answers: a) 94,557, b) 93,241, c) 113,005, d)1,061,452, e) 810,004, f) 1,000,000, Bonus: g) 75,214, h) 9,444,443 C-24 Teacher s Guide for AP Book 5.1

25 ACTIVITIES 1 2 Game for two players: 1. Each player makes a copy of this grid: + 2. Players take turns rolling a die and writing the number rolled in one of their own grid boxes. The winner is the player who creates two 3-digit numbers with the greatest sum. Variations: the addends have different numbers of digits (example: 3 digits and 4 digits, 3 digits and 5 digits, both 5 digits) add 3 numbers instead of 2 the winner is the player whose sum is closest to a given number, such as 400 the winner is the player who has the least sum Extensions 1. Add the numbers. a) b) 3, , ,132 c) 15, , ,209 d) 17, , ,117 Answers: a) 1,995, b) 11,834, c) 75,214, d) 78,309 (MP.3) (MP.1) 2. When students are comfortable adding 3-, 4-, and 5-digit numbers, review with the class what a palindrome is. Ask a volunteer to articulate what the rule is for determining whether a number is a palindrome. (a palindrome is a number whose digits are in the same order when written from right to left, as when written from left to right) Write on the board: ,532 2,332 4,332 12,334,321 Point to each number, one at a time, and ask students whether the number is a palindrome. (yes, no, yes, yes, no, no) Students can signal their answers by giving a thumbs up or thumbs down. Repeat with several more numbers. When students are comfortable with the new terminology, ask them to list the 2-digit palindromes. (11, 22, 33, and so on to 99) Tell them that you are going to show them how to turn any number into a palindrome by using addition. Write the number 13 on the board and ask students Number and Operations in Base Ten 5-5 C-25

26 to find numbers you can add to 13 to make a palindrome. (9, 20, 31, 42, 53, 64, 75, 86) Tell students that one of these numbers can be obtained from the original 13 in a very easy way. Which number is that? (31) How can we obtain 31 from 13? (use the same digits, but in reverse order) Have students add these numbers to their reverse: 35, 21, 52 (example: = 88). Do they always get a palindrome? (yes) Challenge students to find a 2-digit number for which a palindrome does not result by adding it to its reverse. Tell them to follow the same process with their resulting number. For example, if they started with 69, they will see that = 165 is not a palindrome, so they could repeat the process with 165 ( = 726). Ask how many have palindromes now. Have students continue repeating the process until they end up with a palindrome. Starting with 69 (or 96), the sequence of numbers they get will be: 69 (or 96), 165, 726, 1,353, 4,884. Have students repeat the process starting with various 2-digit numbers (examples: 54, 74, 37, 38, 56, 28), then with multiple-digit numbers (examples: 341, 576, 195, 197, 8,903, 9,658, 18,271). Tell students that most numbers will eventually become palindromes, but that mathematicians have not yet proven whether all numbers will. Over 2,000,000 steps have been tried (using a computer, of course) on the number 196, and mathematicians have still not found a palindrome. (MP.1) Ask students to find a number that will not become a palindrome, even after five or ten steps. 3. Systematically list all palindromes from 100 to 200 (it s easy to give a rule for these) or from 100 to 1,000. Answers: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191; a general rule for these 3-digit numbers might be 1d1, where d can be any digit. (MP.1, MP.3) 4. ASK: When you add two palindromes, do you always get a palindrome? When do you get a palindrome and when do you not? Can you change the question slightly to make it have a yes answer? (When you add two palindromes whose digits are all less than 5, do you always get another palindrome?) 5. Find a number that, when added to its reverse, results in the following number. a) 584 b) 766 c) 1,251 d) 193 Which one is not possible? Explain how you know. Answers: a) 292, b) 383, c) 625, d) not possible because the difference between ones and hundreds is more than 1 C-26 Teacher s Guide for AP Book 5.1

27 NBT5-6 Multi-Digit Subtraction Pages STANDARDS 5.NBT.B.7 Goals Students will subtract with and without regrouping. Vocabulary borrowing minuend regrouping standard algorithm PRIOR KNOWLEDGE REQUIRED Understands subtraction as taking away Is familiar with base ten materials Knows place values for ones, tens, hundreds, thousands, and ten thousands Knows the number words for place values of one, ten, hundred, thousand, ten thousand, hundred thousand, million, and their corresponding numerals Can separate the tens and the ones MATERIALS base ten blocks cards numbered 1 to 8, one set per student Review subtraction without regrouping. Tell students that you want to use base ten materials to subtract Have a volunteer draw a base ten model of 48 on the board. SAY: I want to take away 32. How many tens blocks should I remove? (3) Demonstrate crossing them out. ASK: How many ones blocks should I remove? (2) Cross those out, too. ASK: What do I have left? How many tens? (1) How many ones? (6) What is 48 32? (16) Have student volunteers do other problems on the board with no regrouping (examples: 97 46, 83 21, 75 34). (51, 62, 41) Have classmates explain the steps the volunteers are following. Then have students create and solve similar problems in their notebooks. Check students work to make sure the first number is not less than the second number to avoid negative results. Give students examples of base ten models with the subtraction shown and have them complete tens and ones charts: Tens Ones Have students create and subtract more 2-digit numbers (no regrouping) using the chart and base ten models together. Number and Operations in Base Ten 5-6 C-27

28 When students have mastered this, have them subtract by writing out the tens and ones (as in Question 2 on p. 22 in the AP Book): 46 = 4 tens + 6 ones - 13 = 1 ten + 3 ones = 3 tens + 3 ones = 33 Then have students separate the tens and ones using only numerals (as in Question 3 on p. 23 in the AP Book): 36 = = = = 12 Now ask students to subtract: (MP.3) ASK: Which strategy did you use? Is there a quick way to subtract without using base ten materials, or tens and ones charts, or separating the tens and ones? (yes subtract each digit from the one above) What are you really doing in each case? (subtracting the ones from the ones, and the tens from the tens, and putting the resulting digits in the right places) Have students draw a base ten model of 624 and show how to subtract 310. Have them subtract using the standard algorithm (example: by lining up the digits) and check to see whether they got the same answer both ways. Repeat with 4- and 5-digit numbers that do not require regrouping (example: 34,586 12,433). Ask students how they learned to subtract Have a volunteer demonstrate on the board. ASK: Can you use the same method to subtract 46 28? (no) Why not? (there aren t enough ones) Should you be able to subtract 28 from 46? (yes) If you have 46 things, does it make sense to take away 28 of them? (yes) Challenge students to think of a way to change the problem to one that looks like a problem they did last time. Tell them that they are allowed to change one of the numbers, then adjust their answers. Have them work in pairs. Possible answers may include: find 46 26, then subtract 2 more because you didn t subtract enough find 48 28, then subtract 2 because you added 2 to get 48 find 46 20, then subtract 8 because you didn t subtract enough (you can find 26 8 by counting down) find 38 28, then find by counting down Have volunteers come to the board to show their strategies and how they needed to adjust their answer. Restate, add to, or correct students explanations when necessary. Then have all students solve similar C-28 Teacher s Guide for AP Book 5.1

NBT4-1 Place Value Ones, Tens, Hundreds, Page 24

NBT4-1 Place Value Ones, Tens, Hundreds, Page 24 NBT4-1 Place Value Ones, Tens, Hundreds, Page 24 and Thousands STANDARDS 4.NBT.A.2 Goals Students will identify the place value of digits in 2-, 3-, and 4-digit numbers. Vocabulary hundreds ones place

More information

Unit 6 Number and Operations in Base Ten: Decimals

Unit 6 Number and Operations in Base Ten: Decimals Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,

More information

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.

Unit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

More information

Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction

Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Unit 2 Number and Operations in Base Ten: Place Value, Addition, and Subtraction Introduction In this unit, students will review the place value system for reading and writing numbers in base ten. Students

More information

OA4-13 Rounding on a Number Line Pages 80 81

OA4-13 Rounding on a Number Line Pages 80 81 OA4-13 Rounding on a Number Line Pages 80 81 STANDARDS 3.NBT.A.1, 4.NBT.A.3 Goals Students will round to the closest ten, except when the number is exactly halfway between a multiple of ten. PRIOR KNOWLEDGE

More information

Unit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals

Unit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals Unit 4 Number and Operations in Base Ten: Multiplying and Dividing Decimals Introduction In this unit, students will learn how to multiply and divide decimals, and learn the algorithm for dividing whole

More information

OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

More information

NS4-99 Decimal Tenths

NS4-99 Decimal Tenths WORKBOOK 4:2 PAGE 263 NS4-99 Decimal Tenths GOALS Students will learn the notation for decimal tenths. Students will add decimal tenths with sum up to 1.0. Students will recognize and be able to write

More information

NF5-12 Flexibility with Equivalent Fractions and Pages 110 112

NF5-12 Flexibility with Equivalent Fractions and Pages 110 112 NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.

More information

Using Proportions to Solve Percent Problems I

Using Proportions to Solve Percent Problems I RP7-1 Using Proportions to Solve Percent Problems I Pages 46 48 Standards: 7.RP.A. Goals: Students will write equivalent statements for proportions by keeping track of the part and the whole, and by solving

More information

Adding Integers on a Number Line

Adding Integers on a Number Line NS7-5 Adding Integers on a Number Line Pages 36 37 Standards: 7.NS.A.1b Goals: Students will add integers using a number line. Students will interpret addition of integers when the integers are written

More information

OA3-23 Patterns in Multiplication of Odd Numbers

OA3-23 Patterns in Multiplication of Odd Numbers OA-2 Patterns in Multiplication of Odd Numbers Pages 0 1 Standards:.OA.D. Goals: Students will find patterns in the multiplication of odd numbers Students will practice multiplication facts for odd numbers,

More information

Mental Math Addition and Subtraction

Mental Math Addition and Subtraction Mental Math Addition and Subtraction If any of your students don t know their addition and subtraction facts, teach them to add and subtract using their fingers by the methods taught below. You should

More information

MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

More information

EE6-5 Solving Equations with Balances Pages 77 78

EE6-5 Solving Equations with Balances Pages 77 78 EE6-5 Solving Equations with Balances Pages 77 78 STANDARDS 6.EE.B.5, 6.EE.B.6 Goals Students will use pictures to model and solve equations. Vocabulary balance equation expression sides (of an equation)

More information

Gap Closing. Decimal Computation. Junior / Intermediate Facilitator's Guide

Gap Closing. Decimal Computation. Junior / Intermediate Facilitator's Guide Gap Closing Decimal Computation Junior / Intermediate Facilitator's Guide Module 8 Decimal Computation Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5

More information

Unit 6 Geometry: Constructing Triangles and Scale Drawings

Unit 6 Geometry: Constructing Triangles and Scale Drawings Unit 6 Geometry: Constructing Triangles and Scale Drawings Introduction In this unit, students will construct triangles from three measures of sides and/or angles, and will decide whether given conditions

More information

Topic: 1 - Understanding Addition and Subtraction

Topic: 1 - Understanding Addition and Subtraction 8 days / September Topic: 1 - Understanding Addition and Subtraction Represent and solve problems involving addition and subtraction. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step

More information

Unit 7 The Number System: Multiplying and Dividing Integers

Unit 7 The Number System: Multiplying and Dividing Integers Unit 7 The Number System: Multiplying and Dividing Integers Introduction In this unit, students will multiply and divide integers, and multiply positive and negative fractions by integers. Students will

More information

Unit 1 Number Sense. All other lessons in this unit are essential for both the Ontario and WNCP curricula.

Unit 1 Number Sense. All other lessons in this unit are essential for both the Ontario and WNCP curricula. Unit Number Sense In this unit, students will study factors and multiples, LCMs and GCFs. Students will compare, add, subtract, multiply, and divide fractions and decimals. Meeting your curriculum Many

More information

Every Day Counts: Partner Games. and Math in Focus Alignment Guide. Grades K 5

Every Day Counts: Partner Games. and Math in Focus Alignment Guide. Grades K 5 Every Day Counts: s and Math in Focus Alignment Guide Grades K 5 7171_Prtnrs_AlgnmtChrt.indd 1 9/22/10 6:04:49 PM Every Day Counts : s s offers 20 simple yet effective games to help students learn, review,

More information

Unit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems

Unit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems Unit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems The material in this unit crosses three strands The Number System (NS), Expressions and Equations (EE), and Ratios and

More information

2 Mathematics Curriculum

2 Mathematics Curriculum New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic C: Read and Write Three Digit Numbers Within 1000 in Unit, Numeral, Expanded, and Word Forms 2.NBT.3, 2.NBT.1 Focus Standard:

More information

NS5-38 Remainders and NS5-39 Dividing with Remainders

NS5-38 Remainders and NS5-39 Dividing with Remainders :1 PAGE 89-90 NS5-38 Remainders and NS5-39 Dividing with Remainders GOALS Students will divide with remainders using pictures, number lines and skip counting. Draw: 6 3 = 2 7 3 = 2 Remainder 1 8 3 = 2

More information

1 Mathematics Curriculum

1 Mathematics Curriculum New York State Common Core 1 Mathematics Curriculum G R A D E GRADE 1 MODULE 1 Topic F Development of Addition Fluency Within 10 1.OA.3, 1.OA.6 Focus Standard: 1.OA.3 Apply properties of operations as

More information

Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.

Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 18 2 5 Lesson 18 Objective: Apply and explain alternate methods for subtracting from multiples of Suggested Lesson Structure Fluency Practice Application Problem

More information

Abercrombie Primary School Progression in Calculation 2014

Abercrombie Primary School Progression in Calculation 2014 Abercrombie Primary School Progression in Calculation 204 What you need to know about calculations Mathematics will be at the core of your child s schooling from the moment they start to the moment they

More information

Addition and Subtraction Games

Addition and Subtraction Games Addition and Subtraction Games Odd or Even (Grades 13) Skills: addition to ten, odd and even or more Materials: each player has cards (Ace=1)10, 2 dice 1) Each player arranges their cards as follows. 1

More information

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17 NS6-0 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE

More information

5th Grade. Division.

5th Grade. Division. 1 5th Grade Division 2015 11 25 www.njctl.org 2 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole Numbers Division

More information

Pre-Algebra Lecture 6

Pre-Algebra Lecture 6 Pre-Algebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals

More information

RP6-23 Ratios and Rates with Fractional Terms Pages 41 43

RP6-23 Ratios and Rates with Fractional Terms Pages 41 43 RP6-2 Ratios and Rates with Fractional Terms Pages 4 4 STANDARDS 6.RP.A.2, 6.RP.A. Vocabulary equivalent ratio rate ratio table Goals Students will understand that ratios with fractional terms can turn

More information

Gap Closing. Multiplying and Dividing. Junior / Intermediate Facilitator's Guide

Gap Closing. Multiplying and Dividing. Junior / Intermediate Facilitator's Guide Gap Closing Multiplying and Dividing Junior / Intermediate Facilitator's Guide Module 5 Multiplying and Dividing Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5

More information

Counting Money and Making Change Grade Two

Counting Money and Making Change Grade Two Ohio Standards Connection Number, Number Sense and Operations Benchmark D Determine the value of a collection of coins and dollar bills. Indicator 4 Represent and write the value of money using the sign

More information

Version 01 7540004661. Part 1 Addition

Version 01 7540004661. Part 1 Addition Version 01 7540004661 Part 1 Addition Survive Math 5 Part 1 Addition Survive Math 5 Addition and Subtraction i This content is Copyright 2005 Open School BC, all rights reserved. Open School BC content

More information

Math Content by Strand 1

Math Content by Strand 1 Math Content by Strand 1 The Base-Ten Number System: Place Value Introduction 2 Learning about whole number computation must be closely connected to learning about the baseten number system. The base-ten

More information

Binary Numbers. Bob Brown Information Technology Department Southern Polytechnic State University

Binary Numbers. Bob Brown Information Technology Department Southern Polytechnic State University Binary Numbers Bob Brown Information Technology Department Southern Polytechnic State University Positional Number Systems The idea of number is a mathematical abstraction. To use numbers, we must represent

More information

Multiplying and Dividing Decimals ALPHA VERSION OCTOBER 2012 Grade 5

Multiplying and Dividing Decimals ALPHA VERSION OCTOBER 2012 Grade 5 Multiplying and Dividing Decimals ALPHA VERSION OCTOBER 2012 Grade 5 Mathematics Formative Assessment Lesson Designed by Kentucky Department of Education Mathematics Specialists to be Field-tested by Kentucky

More information

Math in Focus Vocabulary. First Grade

Math in Focus Vocabulary. First Grade Math in Focus Vocabulary First Grade Chapter Word Definition 1 zero 0 1 one 1 1 two 2 1 three 3 1 four 4 1 five 5 1 six 6 1 seven 7 1 eight 8 1 nine 9 1 ten 10 1 same equal to 1 more 4 eggs is more than

More information

Huntsville City Schools Second Grade Math Pacing Guide

Huntsville City Schools Second Grade Math Pacing Guide Huntsville City Schools Second Grade Math Pacing Guide 2016-2017 Thoughtful and effective planning throughout the school year is crucial for student mastery of standards. Once a standard is introduced,

More information

Hooray for the Hundreds Chart!!

Hooray for the Hundreds Chart!! Hooray for the Hundreds Chart!! The hundreds chart consists of a grid of numbers from 1 to 100, with each row containing a group of 10 numbers. As a result, children using this chart can count across rows

More information

Unit 5 Measurement and Data: US Customary Units

Unit 5 Measurement and Data: US Customary Units Unit 5 Measurement and Data: US Customary Units Introduction In this unit, students will learn about US customary units of length and mass. They will convert between different units in the US customary

More information

Section 1.5 Arithmetic in Other Bases

Section 1.5 Arithmetic in Other Bases Section Arithmetic in Other Bases Arithmetic in Other Bases The operations of addition, subtraction, multiplication and division are defined for counting numbers independent of the system of numeration

More information

Problem-Solving Lessons

Problem-Solving Lessons Grade 4 Problem-Solving Lessons Introduction What is a problem-solving lesson? A JUMP Math problem-solving lesson generally follows the format of a regular JUMP Math lesson, with some important differences:

More information

MULTIPLICATION. Present practical problem solving activities involving counting equal sets or groups, as above.

MULTIPLICATION. Present practical problem solving activities involving counting equal sets or groups, as above. MULTIPLICATION Stage 1 Multiply with concrete objects, arrays and pictorial representations How many legs will 3 teddies have? 2 + 2 + 2 = 6 There are 3 sweets in one bag. How many sweets are in 5 bags

More information

2 Mathematics Curriculum

2 Mathematics Curriculum New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic G: Use Place Value Understanding to Find 1, 10, and 100 More or Less than a Number 2.NBT.2, 2.NBT.8, 2.OA.1 Focus Standard:

More information

1) Make Sense and Persevere in Solving Problems.

1) Make Sense and Persevere in Solving Problems. Standards for Mathematical Practice in Second Grade The Common Core State Standards for Mathematical Practice are practices expected to be integrated into every mathematics lesson for all students Grades

More information

2 Mathematics Curriculum

2 Mathematics Curriculum New York State Common Core 2 Mathematics Curriculum GRADE GRADE 2 MODULE 3 Topic E: Model Numbers Within 1000 with Place Value Disks 2.NBT.A Focus Standard: 2.NBT.A Understand place value. Instructional

More information

Part 3. Number and Operations in Base Ten

Part 3. Number and Operations in Base Ten Part 3 Number and Operations in Base Ten Number and Operations in Base Ten Domain Overview KINDERGARTEN The work in kindergarten forms the foundation for students to develop an understanding of the base

More information

Representing and Renaming Whole Numbers

Representing and Renaming Whole Numbers Module 3 Representing and Renaming Whole Numbers Diagnostic...3 Representing Numbers to 10 000...7 Renaming Numbers to 10 000...15 Representing Numbers to 100 000...20 Renaming Numbers to 100 000...26

More information

1 ENGAGE. 2 TEACH and TALK GO. Round to the Nearest Ten or Hundred

1 ENGAGE. 2 TEACH and TALK GO. Round to the Nearest Ten or Hundred Lesson 1.2 c Round to the Nearest Ten or Hundred Common Core Standard CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. Lesson Objective Round 2- and 3-digit numbers

More information

2 Mathematics Curriculum

2 Mathematics Curriculum New York State Common Core 2 Mathematics Curriculum G R A D E x GRADE 2 MODULE 1 Topic B Mental Strategies for Addition and Subtraction Within 20 2.OA.1, 2.OA.2 Focus Standard: 2.OA.1 Use addition and

More information

What Is Singapore Math?

What Is Singapore Math? What Is Singapore Math? You may be wondering what Singapore Math is all about, and with good reason. This is a totally new kind of math for you and your child. What you may not know is that Singapore has

More information

Five daily lessons. Page 8 Page 8. Page 12. Year 2

Five daily lessons. Page 8 Page 8. Page 12. Year 2 Unit 2 Place value and ordering Year 1 Spring term Unit Objectives Year 1 Read and write numerals from 0 to at least 20. Begin to know what each digit in a two-digit number represents. Partition a 'teens'

More information

Review: Addition and Subtraction of Positive and Negative Numbers

Review: Addition and Subtraction of Positive and Negative Numbers Review: Addition and Subtraction of Positive and Negative Numbers Objective To practice adding and subtracting positive and negative numbers. www.everydaymathonline.com epresentations etoolkit Algorithms

More information

Subtraction Strategies

Subtraction Strategies Subtraction Strategies Objective To review solution strategies for subtraction of multidigit numbers. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

More information

Judi Kinney, Author Jo Reynolds, Illustrations and Graphic Design

Judi Kinney, Author Jo Reynolds, Illustrations and Graphic Design Judi Kinney, Author Jo Reynolds, Illustrations and Graphic Design An Attainment Company Publication 2003 Attainment Company, Inc. All rights reserved. Printed in the United States of America ISBN 1-57861-479-1

More information

Race to 20. Game 9. Overview. Related Lessons. Key Questions. Time. Materials. Extension

Race to 20. Game 9. Overview. Related Lessons. Key Questions. Time. Materials. Extension Game 9 Race to 20 140 Time 20 minutes Materials dice, 1 per pair of students double ten-frame (Reproducible D), 1 per student counters, 25 each of two colors per student Extension dice with a small sticker

More information

Mini-Posters. LES 1 Shopping at the Co-op

Mini-Posters. LES 1 Shopping at the Co-op Mini-Posters LES 1 Shopping at the Co-op Application Situation 1 p. 1 Application Situation 2 p. 48 Application Situation 3 p. 53 Application Situation 4 p. 54 Table of Contents APPLICATION SITUATION 1

More information

Second Grade Math Standards and I Can Statements

Second Grade Math Standards and I Can Statements Second Grade Math Standards and I Can Statements Standard CC.2.OA.1 Use addition and subtraction within 100 to solve one and two-step word problems involving situations of adding to, taking from, putting

More information

Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. materials. materials.

Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. materials. materials. Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. Teaching the Lesson materials Key Activities Children make ballpark estimates for -digit

More information

Parent Packet. HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1

Parent Packet. HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1 Parent Packet HAUPPAUGE MATH DEPARTMENT CCLS Grade 4 MODULE 1 http://www.hauppauge.k12.ny.us/math 2014 2015 School Year Grade 4 Module 1 Place Value, Rounding, and Algorithms for Addition and Subtraction

More information

Unit 6 Measurement and Data: Area and Volume

Unit 6 Measurement and Data: Area and Volume Unit 6 Measurement and Data: Area and Volume Introduction In this unit, students will learn about area and volume. As they find the areas of rectangles and shapes made from rectangles, students will need

More information

Saving Money. Grade One. Overview. Prerequisite Skills. Lesson Objectives. Materials List

Saving Money. Grade One. Overview. Prerequisite Skills. Lesson Objectives. Materials List Grade One Saving Money Overview Students share the book A Chair for My Mother, by Vera B. Williams, to learn about counting and saving money. They complete worksheets on coin counting and saving. Prerequisite

More information

Third Grade Math Games

Third Grade Math Games Third Grade Math Games Unit 1 Lesson Less than You! 1.3 Addition Top-It 1.4 Name That Number 1.6 Beat the Calculator (Addition) 1.8 Buyer & Vendor Game 1.9 Tic-Tac-Toe Addition 1.11 Unit 2 What s My Rule?

More information

Objective: Explore properties of prime and composite numbers to 100 by using multiples.

Objective: Explore properties of prime and composite numbers to 100 by using multiples. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 25 4 3 Lesson 25 Objective: Explore properties of prime and composite numbers to 100 by using multiples. Suggested Lesson Structure Fluency Practice Concept

More information

Common Core State Standards DECONSTRUCTED. Booklet I: Kindergarten to Second Grade, Math FOR INTERNAL USE ONLY

Common Core State Standards DECONSTRUCTED. Booklet I: Kindergarten to Second Grade, Math FOR INTERNAL USE ONLY Common Core State Standards DECONSTRUCTED Booklet I: Kindergarten to Second Grade, Math How to use this booklet You cannot teach a Common Core Standard you must teach the skills inside of each standard.

More information

2 Mathematics Curriculum

2 Mathematics Curriculum New York State Common Core 2 Mathematics Curriculum G R A D E GRADE 2 MODULE 1 Topic C Strategies for Addition and Subtraction Within 100 2.OA.1, 2.NBT.5, 2.OA.2, 1.NBT.4, 1.NBT.5, 1.NBT.6 Focus Standard:

More information

St. Joseph s Catholic Primary School. Calculation Policy April 2016

St. Joseph s Catholic Primary School. Calculation Policy April 2016 St. Joseph s Catholic Primary School Calculation Policy April 2016 Information The following calculation policy has been devised to meet requirements of the National Curriculum 2014 for the teaching and

More information

Roselle Math Curriculum Unit Title: 7 Multiplying and Dividing Decimals Grade: _5_. Common Core Standards, 2010

Roselle Math Curriculum Unit Title: 7 Multiplying and Dividing Decimals Grade: _5_. Common Core Standards, 2010 Essential Question(s) How do decimal numbers impact multiplication and division? Enduring Understanding(s) Decimals can be multiplied and divided in the same way as whole numbers. What strategies can be

More information

Objective To introduce and practice the partial-sums addition algorithm.

Objective To introduce and practice the partial-sums addition algorithm. Objective To introduce and practice the partial-sums addition algorithm. 1 Teaching the Lesson Key Activities Children are introduced to the partial-sums algorithm using base-1 blocks and paper-and-pencil

More information

Unit 7 Measurement and Data: Measuring Length in Metric Units

Unit 7 Measurement and Data: Measuring Length in Metric Units Unit 7 Measurement and Data: Measuring Length in Metric Units Introduction In this unit, students will learn about measuring length, width, height, and distance. Materials Students will need a large number

More information

Contents. Block C Multiplication and division 53. Block B Subtraction, patterns 30 and time

Contents. Block C Multiplication and division 53. Block B Subtraction, patterns 30 and time Contents Page 4 Introduction Page 5 Oral and mental starters Block A Numbers and addition 7 Unit 1 Numbers to 9999 8 Thousands, hundreds, tens and units Reading and writing numbers Using an abacus Comparing

More information

Year 2 Summer Term Oral and Mental Starter Activity Bank

Year 2 Summer Term Oral and Mental Starter Activity Bank Year 2 Summer Term Oral and Mental Starter Activity Bank Objectives for term Recall x2 table facts and derive division facts. Recognise multiples of 5. Recall facts in x5 table. Recall x10 table and derive

More information

Lesson 1 Order of Operations

Lesson 1 Order of Operations Lesson 1 Order of Operations "Operations" means things like add, subtract, multiply, divide Student A solved the following problem: 17-7 x 2 = 20. Is he correct? Why or why not? Lesson 1 Order of Operations

More information

Pocantico Hills School District Grade 1 Math Curriculum Draft

Pocantico Hills School District Grade 1 Math Curriculum Draft Pocantico Hills School District Grade 1 Math Curriculum Draft Patterns /Number Sense/Statistics Content Strands: Performance Indicators 1.A.1 Determine and discuss patterns in arithmetic (what comes next

More information

Arithmetic 2 Progress Ladder

Arithmetic 2 Progress Ladder Arithmetic 2 Progress Ladder Maths Makes Sense Foundation End-of-year objectives page 2 Maths Makes Sense 1 2 End-of-block objectives page 3 Maths Makes Sense 3 4 End-of-block objectives page 4 Maths Makes

More information

Planning Guide. Number Specific Outcomes 8, 9, 10 and 11

Planning Guide. Number Specific Outcomes 8, 9, 10 and 11 Mathematics Planning Guide Grade 5 Working with Decimal Numbers Number Specific Outcomes 8, 9, 10 and 11 This Planning Guide can be accessed online at: http://www.learnalberta.ca/content/mepg5/html/pg5_workingwithdecimalnumbers/index.html

More information

Place Value in Whole Numbers

Place Value in Whole Numbers Place Value in Whole Numbers Objectives To provide practice identifying values of digits in numbers up to one billion; and to provide practice reading and writing numbers up to one billion. www.everydaymathonline.com

More information

Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories.

Change Number Stories Objective To guide children as they use change diagrams to help solve change number stories. Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

More information

Robyn Seifert Decker

Robyn Seifert Decker Robyn Seifert Decker UltraMathPD@gmail.com Place Value Addition Subtraction Problem Solving Fractions If time allows: Multiplication and Division Spiral of change From Prochaska, DiClemente & Norcross,

More information

= > < number and operations in base Ten. Read and Write Whole Numbers... 4 4.NBT.1, 4.NBT.2

= > < number and operations in base Ten. Read and Write Whole Numbers... 4 4.NBT.1, 4.NBT.2 in 3 + + > < > < Module number and operations in base Ten Lesson Read and Write Whole Numbers 4 4NBT, 4NBT2 Common Core State Standards Lesson 2 Compare and Order Whole Numbers 8 4NBT2 Lesson 3 Lesson

More information

Reading and Writing Small Numbers

Reading and Writing Small Numbers Reading Writing Small Numbers Objective To read write small numbers in stard exped notations wwweverydaymathonlinecom epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

More information

Lesson 13 Dividing Multi Digit Numbers Using the Algorithm

Lesson 13 Dividing Multi Digit Numbers Using the Algorithm Lesson 13: Dividing Multi Digit Numbers Using the Algorithm Student Outcomes Students understand that the standard algorithm of division is simply a tally system arranged in place value columns. Classwork

More information

Common Core Mathematics Challenge

Common Core Mathematics Challenge Level: Domain: Cluster: Grade Five Number and Operations Fractions Use equivalent fractions as a strategy to add and subtract fractions. Standard Add and subtract fraction with unlike denominators (including

More information

Lesson 16: Solving and Graphing Inequalities Joined by And or Or

Lesson 16: Solving and Graphing Inequalities Joined by And or Or : Solving and Graphing Inequalities Joined by And or Or Student Outcomes Students solve two inequalities joined by and or or, then graph the solution set on the number line. Classwork Exercise 1 (5 minutes)

More information

Grade 1 Math Expressions Vocabulary Words 2011

Grade 1 Math Expressions Vocabulary Words 2011 Italicized words Indicates OSPI Standards Vocabulary as of 10/1/09 Link to Math Expression Online Glossary for some definitions: http://wwwk6.thinkcentral.com/content/hsp/math/hspmathmx/na/gr1/se_9780547153179

More information

Multiplication and Division

Multiplication and Division E Student Book 6 7 = 4 Name Series E Contents Topic Multiplication facts (pp. 7) 5 and 0 times tables and 4 times tables 8 times table and 6 times tables Date completed Topic Using known facts (pp. 8 )

More information

Title: Place Value Made Simple

Title: Place Value Made Simple Title: Place Value Made Simple Brief Overview: This concept development unit will provide students with the knowledge and understanding of place value of whole numbers (0-1,000,000). s will be able to

More information

Reading and Writing Large Numbers

Reading and Writing Large Numbers Reading and Writing Large Numbers Objective To read and write large numbers in standard, expanded, and number-and-word notations. www.everydaymathonline.com epresentations etoolkit Algorithms Practice

More information

Simply Math. Everyday Math Skills NWT Literacy Council

Simply Math. Everyday Math Skills NWT Literacy Council Simply Math Everyday Math Skills 2009 NWT Literacy Council Acknowledgement The NWT Literacy Council gratefully acknowledges the financial assistance for this project from the Department of Education, Culture

More information

Topic 1: Understanding Addition and Subtraction

Topic 1: Understanding Addition and Subtraction Topic 1: Understanding Addition and Subtraction 1-1: Writing Addition Number Sentences Essential Understanding: Parts of a whole is one representation of addition. Addition number sentences can be used

More information

Using games to support. Win-Win Math Games. by Marilyn Burns

Using games to support. Win-Win Math Games. by Marilyn Burns 4 Win-Win Math Games by Marilyn Burns photos: bob adler Games can motivate students, capture their interest, and are a great way to get in that paperand-pencil practice. Using games to support students

More information

1.1 Place Value of Whole Numbers

1.1 Place Value of Whole Numbers 1.1 Place Value of Whole Numbers Whole Numbers: Whole numbers can be listed as 0,1,2,3,4,5,6,7,8,9,10,11,... The "..." means that the pattern of numbers continues without end. Whole Number Operations Workbook

More information

Unit 2 Number and Operations Fractions: Multiplying and Dividing Fractions

Unit 2 Number and Operations Fractions: Multiplying and Dividing Fractions Unit Number and Operations Fractions: Multiplying and Dividing Fractions Introduction In this unit, students will divide whole numbers and interpret the answer as a fraction instead of with a remainder.

More information

Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on.

Year 1. Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. Year 1 Add with numbers up to 20 Use numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. +1 +1 +1 Children should: Have access to a wide

More information

Unit 3 Operations and Algebraic Thinking: Expressions and Equations

Unit 3 Operations and Algebraic Thinking: Expressions and Equations Unit 3 Operations and Algebraic Thinking: Expressions and Equations Introduction In this unit, students will use the correct order of operations to evaluate expressions involving whole numbers, fractions,

More information

Table of Contents Grade 1

Table of Contents Grade 1 Table of Contents Grade 1 Go Math! Scope and Sequence... 4 Common Core... 5 Domain: 1.OA Operations & Algebraic Thinking... 5 Cluster: 1.OA.A Represent and solve problems involving addition and subtraction...

More information

Calculations Policy. Introduction

Calculations Policy. Introduction Thousands Hundreds Tens Units Tenth Hundredth thousandth Calculations Policy Introduction This Calculations Policy has been designed to support teachers, teaching assistants and parents in the progression

More information

GRADE 4 FLORIDA. Multiplication WORKSHEETS

GRADE 4 FLORIDA. Multiplication WORKSHEETS GRADE 4 FLORIDA Multiplication WORKSHEETS Multiplication facts 5 and 0 times tables The 5 and 0 times tables are easier if you learn them together. Answer the 5 times table: Count in 5s down the ladders:

More information