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

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1 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 will distinguish between the place values of a digit in 1-, 2-, and 3-digit numbers, and they will understand the value of each digit. Students will read and write 3-digit numbers using words and numerals, and understand the connection between number words, expanded form, and base ten block representations. Students will also compare 3-digit numbers using the symbols <, >, and = with base ten blocks and using place value. Students will add and subtract 3-digit numbers using base ten blocks and using the standard algorithm, with and without regrouping. NOTE: BLM Place Value Bingo has two spinner circles, which look like pie charts. A pencil and paper clip can be used to operate these spinners. With the piece of paper resting on a desk, hold the pencil vertically so that the sharp end faces down, goes through one end of the paper clip, and presses against the center of the spinner circle. The paper clip rests on top of the piece of paper, with one end anchored at the center of the spinner circle by the pencil. Flick the other end of the paper clip. The paper clip should spin around the pencil, and eventually stop on one of the sectors of the spinner circle. Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-1

2 NBT3-1 Place Value Ones, Tens, and Hundreds Pages Standards: preparation for 3.NBT.A.2 Goals: Students will identify the place value of digits in 2- and 3-digit numbers, and understand the value of the digits. Prior Knowledge Required: Knows the number words one, ten, hundred, and their corresponding numerals (1, 10, 100) Vocabulary: digit, hundreds, hundreds digit, hundreds place, ones, ones digit, ones place, place value, tens, tens digit, tens place Materials: BLM Place Value Cards (p. C-78) BLM Place Value Bingo (p. C-79) bingo chips, paper clips, pencils (MP.6) Review of Place Value. Photocopy BLM Place Value Cards and cut out the three cards. Write the number 347 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? (no) Is 3 the ones digit? (no) Have a volunteer put the card below the correct digit. (below the 7) Invite volunteers to position the other cards correctly. Cards can be affixed to the board temporarily using tape or sticky tack. Erase the 3 and take away the hundreds card. ASK: Are these cards still in the right place? (yes) Write the 3 back in, put the hundreds card back beneath the 3, erase the 7, and remove the ones card. ASK: Are these cards still in the right place? (no) Have a volunteer reposition the cards correctly. (tens card under 3, ones card under 4). Repeat this process with the 3 and 7 (i.e., erase the 4). Write 989 on the board and ask students to identify the place value of the underlined digit. (hundreds) 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 the lesson. Repeat with several 2- and 3-digit numbers that have an underlined digit. 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: 401, 124, 847. (hundreds, ones, tens) Continue until students can identify place value correctly and confidently. Include examples where you ask for the place value of the digit 0. Example: 108, 970, 302 (tens, ones, tens) C-2 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

3 Place Value Chart. Introduce the place value chart and have a volunteer write the digits from the number 231 in the correct columns (answers are in italics): Hundreds Tens Ones Use the words ones place, tens place, and hundreds place or use the word column if students have learned it. Repeat with the following examples, this time having students signal the correct digit for each place value: 458, 703, 241, 89, 5, 333. Exercises: Write the digits from the number in the place value chart. a) 932 b) 426 c) 502 d) 47 Hundreds Tens Ones Answers: a) Hundreds: 9, Tens: 3, Ones: 2; b) Hundreds: 4, Tens: 2, Ones: 6; c) Hundreds: 5, Tens: 0; Ones: 2; d) Hundreds: 0, Tens: 4, Ones: 7 Write 836 on the board. SAY: The number 836 is a 3-digit number. What is the place value of the digit 8? (hundreds) If necessary, point to each digit as you count aloud from the right: ones, tens, hundreds. SAY: The 8 is in the hundreds place, so it stands for 800. What does the digit 3 stand for? (30) The 6? (6) Exercises: Fill in the blank. a) In the number 427, the digit is in the hundreds place. b) In the number 385, the digit is in the tens place. c) In the number 102, the digit is in the ones place. d) In the number 347, the digit 4 stands for. e) In the number 598, the digit 5 stands for. f) In the number 273, the digit 3 stands for. Answers: a) 4, b) 8, c) 2, d) 40, e) 500, f) 3 ASK: What does the digit 6 stand for in 608? (600) In 306? (6) In 762? (60) In 506? (6) Exercises: What does the digit 4 stand for? a) 345 b) 408 c) 514 d) 647 Answers: a) 40, b) 400, c) 4, d), 40 ASK: In the number 831, what does the digit 3 stand for? (30) The 1? (1) The 8? (800) Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-3

4 Exercises: Fill in the blanks. a) In 982, the digit 9 stands for, the digit 8 stands for, and the digit 2 stands for. b) In 173, the digit 1 stands for, the digit 7 stands for, and the digit 3 stands for. c) In 547, the digit 5 stands for, the digit 4 stands for, and the digit 7 stands for. d) In 628, the digit 6 stands for, the digit 2 stands for, and the digit 8 stands for. Answers: a) 900, 80, 2; b) 100, 70, 3; c) 500, 40, 7; d) 600, 20, 8 ASK: What does 0 stand for in 340? (0) In 403? (0) In 809? (0) Emphasize that 0 always stands for 0, no matter what position it is in. Finally, ASK: In the number 856, what is the tens digit? (5) The ones digit? (6) The hundreds digit? (8). Repeat, having students signal their answers, for 350, 503, 455, 770, and 820. Activities Collaborative Place Value Bingo. Draw a large 3 3 table (the bingo card) on the board and fill each cell with a 3-digit number. Example: Ahead of time, write the word hundreds on a small piece of paper, and fold it twice so that the word cannot be seen; do the same with the words tens and ones. Place these 3 folded pieces of papers in a container. Similarly, write each of the digits from 0 to 9 on a separate small piece of paper, and put these ten folded pieces of paper in another container. Have a volunteer draw (without peeking) a folded piece of paper from the digits container and a folded piece of paper from the place value container. The student then calls out what was drawn: for example, if 3 and tens are drawn, the student says, 3 in the tens place. Have all students scan the bingo card to see if they can find a number with a 3 in the tens place. If there is such a number on the bingo card (in this case, 132) they circle the number. Otherwise, no number gets circled. Fold and return the pieces of paper to their respective containers, and repeat with a new volunteer. The whole class wins if three numbers are circled in a row. (For a faster game, allow rows, columns, and diagonals for the class to win, or declare a win if students circle four numbers anywhere on the bingo card.) 2. Students who finish Activity 1 early might enjoy playing bingo individually, using the spinners provided on BLM Place Value Bingo to determine a digit and a place value. Students will need 9 bingo chips, 1 paper clip, and 1 pencil. (See Unit Introduction, p. C-1, for instructions on using these spinners with a pencil and paper clip.) You can fill in the numbers on the bingo card yourself, or have students strategically choose numbers before their first spin. Now, if the digits spinner turns up 7 and the place value spinner turns up tens, the student has to scan the nine numbers in the chart to see if any of them have a 7 in the tens place. If so, the student places a bingo chip on the number. Play continues until there are 3 bingo chips in a row or column (or until there are 4 bingo chips anywhere on the card). (end of activity) C-4 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

5 Extensions (MP.6) 1. In the number 467, the digit 4 stands for 400. Teach students alternatives to the phrase stands for. For example: the digit 4 means 400, the digit 4 represents 400, the digit 4 is short for 400, the digit 4 has a value of 400. If you choose to use the latter phrase, make sure students understand the difference between the value of a digit and place value. Have students practice these phrases in oral and written form for a variety of numbers. 2. Write the following numbers on the board: 350, 503, 435, 537, 325, and 753. Ask students to identify which digit, the 5 or the 3, is worth more in each number. Students should be using the phrases stands for, has a value of, is short for, and so on. Sample answer: In 350, the 5 stands for 50 and the 3 stands for 300, so the digit 3 is worth more. (MP.7) 3. Teach students the Egyptian system for writing numerals to help them appreciate the utility of place value. 1 = (stroke) 10 = (arch) 100 = (coiled rope) Write the following numbers using both the Egyptian and the Arabic systems: Invite students to study the numbers for a moment. 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 the Arabic system, a single digit (7) tells you how many ones there are. Review the ancient Egyptian symbols for 1, 10, and 100 and ask students to write a few numbers the Egyptian way and to translate those Egyptian numbers into regular numbers (using Arabic numerals). Emphasize that the order in which you write the symbols doesn t matter: 234 = = ASK: Does the order in which you write regular digits matter? (yes) Is 234 the same as 342? (no) In the Egyptian way, does the value of a symbol depend on its place? (no) In our way, does the value of a digit depend on its place? (yes) Are the ones, tens, and so on always in the same place in our system? (yes) In the Egyptian system? (no) Why is our way called a place value system? Have students write a number that is really long to write the Egyptian way (e.g., 798). ASK: How is our system more convenient? Why is it helpful to have a place value system i.e., a system where the ones, tens, and so on are always in the same place? Explain that having a place value system allows you to use the same symbol to mean many different values. The digit 7, for example, can mean 7 ones, 7 tens or 7 hundreds depending on where it is in the number. Students might want to invent their own number system using the Egyptian system as a model. Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-5

6 4. Have students identify and write numbers according to specific criteria. NOTE: Some of the examples use the words even, odd, and sum, which are taught formally later. Examples: a) Write a number between 30 and 40. b) Write an even number with a 6 in the tens place. c) Write a number that ends with a zero. d) Write a 2-digit number. e) Write an odd number greater than 70. f) Write a number with a tens digit one more than its ones digit. g) Write a 2-digit number where the digits are the same. h) Write a number between 50 and 60 where the digits are the same. i) Find the sum of the digits in each of these numbers: 37, 48, 531, 225, 444, 372. j) Write a 2-digit number where the sum of the digits is 11. k) Write a 2-digit number where the digits are the same and the sum of the digits is 14. l) Write a 3-digit number where the digits are the same and the sum of the digits is 15. Is there a 2-digit number where the digits are the same and the sum of the digits is 15? Make up more such questions, or have students make up their own. Bonus: m) Which number has a tens digit one less than its ones digit: 34, 47, 88, 90? n) Write a 2-digit number with a tens digit eight less than its ones digit. o) Write a 3-digit number where all three digits are odd. p) Write a 3-digit number where the ones digit is equal to the sum of the hundreds digit and the tens digit. Sample answers: a) 37; b) 364; c) 170; d) 13; e) 73; f) 65; g) 88; h) 55; i) 10, 12, 9, 9, 12, 12; j) 47; k) 77; l) 555, no; Bonus: m) 34; n) 19; o) 375; p) 459 C-6 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

8 tens blocks on top of the hundreds block. (If possible, use one color for the tens blocks and a different color for the hundreds block.) Give your students 2 hundreds blocks to add to their 10 tens blocks and 9 ones blocks. ASK: What number do you get if you place a hundreds block on the first hundreds chart and then 3 tens blocks and 7 ones blocks in order on the next hundreds chart? (137) Repeat with: a) 1 hundreds block, 5 tens blocks, 4 ones blocks (154) b) 1 hundreds block, 6 tens blocks, 2 ones blocks (162) c) 1 hundreds block, 7 tens blocks, 5 ones blocks (175) d) 1 hundreds block, 3 tens blocks (130) e) 1 hundreds block, 10 tens blocks (200) f) 2 hundreds blocks (200) (MP.2) Show models of base ten blocks without using the hundreds chart and have students tell you what number is represented. Example: 3 hundreds blocks, 0 tens blocks, 5 ones blocks. (305) Show base ten models of the following numbers, and have students write what number is represented: 412, 352, 160, 27, 518, 231. Drawing base ten models. Demonstrate drawing a base ten model for 145 on grid paper: Shade the blocks and ASK: How many little squares are shaded altogether? (145) Have students draw base ten models for other 2- and 3-digit numbers. Students can use grid paper to draw models as shown in the above diagram; however, some students might have difficulty drawing such base ten models. Teach students a faster way to sketch base ten models on paper without grid markings: Hundreds Block Tens Block Ones Block Some students may prefer to simply draw straight lines for tens, and dots for ones: Tens Block Ones Block C-8 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

9 Let students choose their method for sketching base ten models, and have them practice with many examples: 45, 60, 74, 104, 251, 300, 260. (MP.1) Activity Give your students ones, tens, and hundreds blocks. Students could work in groups. Have students sketch their answers, so you can verify that they have successfully completed the work. a) Show 17, 31, 252, and 346 with base ten blocks. b) Show 22 using exactly 13 blocks. c) Show 31 using 13 blocks. d) Show 315 using exactly 36 blocks. HINT: For b), c), and d), start with a standard model and trade for blocks of equal value. Answers: b) 1 tens blocks and 12 ones blocks; c) 2 tens blocks and 11 ones blocks, d) 31 tens blocks and 5 ones blocks (end of activity) Extensions (MP.7) 1. Draw sketches of base ten models where the hundreds, tens, and ones blocks are out of order. Have students identify the number being modeled. Examples: a) b) Answers: a) 235, b) 123 (MP.7) 2. Write equations on the board in which one side is a base ten model sketch and the other side is a number. Examples: a) = 214 b) = 125 Ask the students whether the equations are true or false. Vary the examples so that some are true and some are false. For those that are false, have the students draw missing base ten blocks or cross out extra base ten blocks to make the equations true. Answers: a) true, b) false Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-9

10 NBT3-3 Expanded Form Pages Standards: preparation for 3.NBT.A.2 Goals: Students will understand how to represent numbers in expanded form, and how to recognize a number written in expanded form. Prior Knowledge Required: Understands place value Vocabulary: digit, expanded form, hundreds, numeral, ones, tens Materials: BLM Make Up Your Own Cards (p. C-82) Write the expanded form when given the numeral. Show the base ten model drawing for 145 again: ASK: How many little squares are colored? (145) Point to the hundreds block, the tens blocks, and the ones blocks, and ask in turn how many little squares are colored from each type of block. Then write on the board: 145 = Repeat this exercise with the following numbers: 361, 218, 427, 659. Explain that this is called expanded form with numerals. Tell the students that we use the word numeral to denote a number written as a symbol, as in 10 rather than the word ten. Ask a volunteer to write the expanded form for 145 using the words hundreds, tens, and ones. (145 = 1 hundred + 4 tens + 5 ones; point out that the s on the word hundreds is dropped here since 145 has only 1 hundred). Explain that this is called expanded form with numerals and words. Point out that in the expanded form using numerals and words, you are counting how many of each type of block you need to make a number. In the expanded form using numerals only, you are counting how many ones in each type of block are used to make the number. C-10 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

11 Exercises: 1. Fill in the blanks. a) 325 = hundreds + tens + ones b) 413 = hundreds + ten + ones c) 937 = hundreds + tens + ones d) 108 = hundred + tens + ones Answers: a) 3, 2, 5; b) 4, 1, 3; c) 9, 3, 7; d) 1, 0, 8 2. Fill in the blanks. a) 479 = b) 218 = c) 173 = d) 546 = Bonus: e) 791 = f) 316 = Answers: a) hundreds, tens, ones; b) hundreds, tens, ones; c) hundreds, tens, ones; d) hundreds, tens, ones; Bonus: e) tens, one, hundreds; f) ones, hundreds, tens (MP.7) Have students draw base ten models for several numbers and record the expanded form in two different ways (using numerals and words or numerals only). Examples: 135, 241, 129, 302. Have students expand several numbers using numerals only. Examples: 348, 640, 301. (348 = , 640 = , 301 = ). Ensure students understand that when we have a 0 digit, we do not need to include 0 in the expanded sum. For example, we write 405 = , not Similarly, we would normally write 405 = 4 hundreds + 5 ones, even though it is important to understand that there are 0 tens. Write the numeral for the expanded form. Have students write the numeral for several sums written in expanded form. Write on the board: = Ask students what should be written in the blanks. PROMPT: What is the hundreds digit? (2) The tens digit? (7) The ones digit? (6) Exercises: Write the number for the expanded form. a) = b) = c) = d) = Answers: a) 436, b) 765, c) 288, d) 813 Write on the board: = = Ask students what should be written in the blanks for each question. PROMPT: What is the hundreds digit? The tens digit? The ones digit? ASK: How are these two examples different? (the first has 0 in the ones place, the second has 0 in the tens place) Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-11

13 The student says, I have 348, who has 213? and the person with then says, I have 213, who has depending on which base ten model is on the bottom of that card. Play continues until everyone gets a turn. You might arrange it so that the bottom of the last card matches with the top of the first card, so that students know when they get back to the first card. (end of activity) Extensions (MP.6) 1. Have students determine numbers written in expanded form when the hundreds, tens, and ones are out of order. For example: a) = b) = c) 5 tens + 6 ones + 7 hundreds = Answers: a) 435, b) 650, c) 756 (MP.6) 2. Have students fill in the blanks for numbers in expanded form where the blanks are out of order. For example: a) = 547 b) + 60 = 69 c) ones + tens + 1 hundred = 198 Answers: a) 500; b) 9; c) 8, 9 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-13

15 2. Circle the beginning letters that are the same in both number words. a) six sixteen b) five fifteen c) nine nineteen d) four fourteen e) three thirteen f) two twelve g) seven seventeen h) eight eighteen Answers: a) six, b) fi, c) nine, d) four, e) th, f) tw, g) seven, h) eight ASK: Which of these pairs have the entire 1-digit number in the word for the 2-digit number? (four and fourteen, six and sixteen, seven and seventeen, eight and eighteen, nine and nineteen) ASK: Why is the pair eight and eighteen a bit different from these other pairs? (because eight ends with t, and there is only one t in eighteen ) Exercises: Circle the digits that are the same in both numbers. a) 6 16 b) 5 15 c) 9 19 d) 4 14 e) 3 13 f) 2 12 g) 7 17 h) 8 18 Answer: a) 6, b) 5, c) 9, d) 4, e) 3, f) 2, g) 7, h) 8 Point out that the number word eleven is a special case, because even though eleven = one + ten, the beginning letters of one do not match the beginning letters of eleven. (MP.8) Exercises: Fill in the blank. a) sixteen = + ten b) seventeen = + ten c) nineteen = nine + d) thirteen = + ten e) fourteen = + ten f) fifteen = + ten g) twelve = + ten h) eleven = + ten i) eighteen = eight + Answers: a) six, b) seven, c) ten, d) three, e) four, f) five, g) two, h) one, i) ten Number words for multiples of 10 from 20 to 90. Write on the board: twenty = 20 two = 2 ASK: What two beginning letters do these number words have in common? ( tw ) What digit is in both numbers? (2) Write on the board: thirty ASK: Can anyone think of a word for a 1-digit number that also starts with th? (three) Write: thirty = _ 0 three = 3 Have a volunteer fill in the blank. (3) Write on the board: forty = _ 0 fifty = _ 0 seventy =_ 0 sixty =_ 0 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-15

17 Write on the board: thirty-six Underneath the word thirty, write the numeral 30 ; underneath the six, write 6. You might draw arrows connecting thirty to 30 and six to 6. ASK: What numeral do you think the number word thirty-six stands for? What addition sentence can you write from this? ( = 36) Have a volunteer write the numeral for thirty-five with the addition sentence. (35 = ) Exercises: Write the numeral and the addition sentence. a) thirty-three b) thirty-two c) thirty-eight d) thirty-four e) forty-two f) eighty-one g) fifty-four h) ninety-seven Answers: a) = 33, b) = 32, c) = 38, d) = 34, e) = 2, f) = 81, g) = 54, h) = 97 Write on the board: 73 = = = = seventy-three thirty-two sixty-one fifty-four 15 = = = = fifteen eighteen thirteen sixteen If available, use colored chalk or an overhead projector and write the parts in bold in a different color. Point to each question and ASK: Where do you see the first digit of the number in the number word at the beginning or at the end? Which number words have the first digit at the beginning? (twenty and higher) Which number words have the first digit at the end? (thirteen to nineteen) Exercises: Write the numeral for the number word. a) thirty-eight b) forty-five c) twenty-six d) fifty-one e) sixty-seven f) eighty-nine g) seventy-four h) ninety-one Answers: a) 38, b) 45, c) 26, d) 51, e) 67, f) 89, g) 74, h) 91 Exercises: Write the numeral for the number word. a) twenty-eight b) eighteen c) sixteen d) four e) forty f) forty-three g) zero h) fifty i) fifty-eight j) thirteen k) twelve l) nineteen m) twenty-nine n) fifty-nine o) forty-eight p) twenty q) thirty-one r) eleven Answers: a) 28, b) 18, c) 16, d) 4, e) 40, f) 43, g) 0, h) 50, i) 58, j) 13, k) 12, l) 19, m) 29, n) 59, o) 48, p) 20, q) 31, r) 11 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-17

18 Writing number words from 0 to 99. Tell students you want to write the number word for 45. PROMPT: What does the 4 stand for? (40) Write on the board: 45 forty- ASK: what does the 5 stand for? Have a volunteer fill in the blank. (five) Exercises: Write the number word for the numeral. a) 41 b) 32 c) 90 d) 9 e) 89 f) 74 g) 99 h) 0 i) 50 j) 25 k) 17 l) 11 Bonus: Is the number word written correctly? If not, find the mistake and write the number word correctly. m) forty-zero n) forty-three o) twenty-eight p) thirty nine q) eight-five r) seventy-six Answers: a) forty-one; b) thirty-two; c) ninety; d) nine; e) eighty-nine; f) seventy-four; g) ninetynine; h) zero; i) fifty; j) twenty-five; k) seventeen; l) eleven; Bonus: m) should be forty, no - zero ; n) correct; o) correct; p) the - is missing, should be thirty-nine ; q) should be eightyfive, the y is missing; r) correct Number words for multiples of 100. Once students have mastered writing numbers up to 99, tell them that writing hundreds is even easier. There is no special word for three hundreds like there is for three tens: 30 = = thirty, but 300 = = three hundred (not three hundreds) SAY: You just write what you see: three hundred. There s no special word to remember. Have volunteers write the number words for 3-digit multiples of 100: 200, 300, 500. (two hundred, three hundred, five hundred) Remind them not to include a final s even when there is more than one hundred. Have volunteers write the numerals given number words for multiples of 100: two hundred, six hundred, nine hundred, one hundred, five hundred, and eight hundred. (200, 600, 900, 100, 500, 800) Exercises: 1. Write the number word for the numeral. a) 400 b) 600 c) 900 d) 800 e) 700 f) 100 Answers: a) four hundred, b) six hundred, c) nine hundred, d) eight hundred, e) seven hundred, f) one hundred 2. Write the numeral for the number word. a) three hundred b) one hundred c) four hundred d) seven hundred Answers: a) 300, b) 100, c) 400, d) 700 Number words for 3-digit numbers. Tell students that they can write out 3-digit numbers like 532 by breaking them down. Say the number out loud and invite students to help you write what they hear: five hundred thirty-two. Point out that there is no dash between five and hundred. C-18 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

19 Also, emphasize that the word and should not appear in these number words: for example, 301 is written as three hundred one, not as three hundred and one. Exercises: Fill in the blanks. 1. a) 134 = one hundred b) 904 = nine hundred c) 650 = six hundred d) 718 = seven hundred Answers: a) thirty-four, b) four, c) fifty, d) eighteen 2. a) 761 = sixty-one b) 840 = forty c) 327 = twenty-seven d) 205 = five Answers: a) seven hundred, b) eight hundred, c) three hundred, d) two hundred 3. a) 898 = b) 740 = c) 756 = d) 601 = Answers: a) eight hundred ninety-eight, b) seven hundred forty, c) seven hundred fifty-six, d) six hundred one Number words from 0 to 999. Write some typical text from signs and banners and have students replace any number words with numerals and vice versa. Exercises: Write the number word for the numeral, or the numeral for the number word. a) New York 181 miles b) Speed Limit: 65 miles/hour c) Maximum Height 6 feet d) Seventy-Four Main Street e) Bulk Sale! Buy Ten for the Price of Five! f) Bus Stop: Route 108 Answers: a) one hundred eighty-one; b) sixty-five; c) six; d) 74; e) 10, 5; f) one hundred eight Exercises: Write the correct number word to complete the sentence. a) There are months in a year. b) There are days in a week. c) There are weeks in a year. d) February normally has days. e) A year normally has days. f) A leap year has days. Answers: a) twelve, b) seven, c) fifty-two, d) twenty-eight, e) three hundred sixty-five, f) three hundred sixty-six Activity At students can use Method 1 to write the number word corresponding to a given numeral in the correct place on a check, or use Method 2 to read a given number word and write the corresponding numeral. You may select the number range (e.g., 0 to 100, 0 to 1000). Alternatively, you can draw checks on the board, where you fill in the numeral amount and have students write the number in words, or vice versa, and then do the same with BLM Blank Checks. (end of activity) Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-19

20 Extensions 1. Provide copies of BLM Number Word Search. Encourage students to use the message they find after finishing the puzzle to check that they did the puzzle correctly. Selected Answer: 2. winter, spring, and, summer 2. Give students BLM Number Word Crossword Puzzle. Answers: Across: 2. six, 4. nine, 7. seventeen, 8. eighty, 10. forty, 11. zero; Down: 1. one, 2. seventy. 3. fifteen, 5. twenty, 6. ten, 9. three (MP.1) 3. Give students BLM Crossword without Clues. Answers: 1. 4 letters: nine, zero; 5 letters: forty, three; 6 letters: eighty, twenty; 7 letters: fifteen, seventy; 9 letters: seventeen; 2. seventeen is the only word in a group by itself (9 letters) see solved puzzle below for where it fits; 3. t t w e z s e v e n t e e n t w o n r n t f o r t y e i g h t y h r s e f i f t e e n x i s e v e n t y e C-20 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

21 NBT3-5 Number Representations Summary Pages Standards: preparation for 3.NBT.A.2 Goals: Students will practice interchanging between the various number representations covered thus far (number words, base ten blocks, and expanded form) for 1-, 2-, and 3-digit numbers. Prior Knowledge Required: Understands expanded form for 2- and 3-digit numbers Can read and write number words for 2- and 3-digit numbers Can draw base ten models for 2- and 3-digit numbers Materials: BLM Blank Checks (p. C-83; see Extension 4) Review of expanded form. Have a volunteer do Exercises 1.a) and 2.a) below and then have all students do the remaining exercises. Exercises: 1. Fill in the blank. a) = b) = c) = d) = e) = f) = Answers: a) 437, b) 359, c) 807, d) 43, e) 688, f) For each part of Exercise 1, write the number in expanded form using numerals and words. Selected answer: a) 4 hundreds + 3 tens + 7 ones Demonstrate the first exercise below and then have students do the remaining exercises. (MP.7) Exercises: Fill in the blank. a) = 679 b) = 548 c) = 555 d) = 250 e) = 205 f) = 916 Answers: a) 70, b) 500, c) 5, d) 50, e) 5, f) 10 Review of number words. Have a volunteer do the first exercise below and then have all students do the remaining exercises. Exercises: Write the number word for the given numeral. a) 578 b) 611 c) 818 d) 923 e) 650 f) 605 Answers: a) five hundred seventy-eight, b) six hundred eleven, c) eight hundred eighteen, d) nine hundred twenty-three, e) six hundred fifty, f) six hundred five Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-21

22 Exercises: Write the numeral for the given number word. a) four hundred eighty-nine b) three hundred twenty c) one hundred four d) sixty-seven e) eleven f) nine hundred twenty-five Answers: a) 489, b) 320, c) 104, d) 67, e) 11, f) 925 Review of base ten blocks. Write 1-, 2-, and 3-digit numbers on the board and have student volunteers draw base ten models (sketches). Remind students of a fast way to make sketches: Hundreds Block Tens Block Ones Block Exercises: Draw base ten sketches for the following numbers: a) 314 b) 278 c) 83 d) 401 e) 189 f) 15 Selected answer: a) Extensions (MP.6) 1. Ask students to explain and show with base ten blocks the meaning of each digit in a number with all digits the same (e.g., 333). 2. Have students 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 3-digit number. My digits are all the same. Use 12 blocks to make me. c) I am a 2-digit number. My tens digit is 5 more than my ones digit. Use 7 blocks to make me. d) 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. Answers: a) 23, b) 444, c) 61, d) Have students solve these puzzles by only imagining the base ten blocks. NOTE: Parts a) through d) have more than one answer emphasize this by asking students to share their answers. 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? (MP.3) e) You have one set of blocks that make the number 13 and one set of blocks that make the number 22. Can you have the same number of blocks in both sets? (MP.3) f) You have one set of blocks that make the number 23 and one set of blocks that make the number 16. Can you have the same number of blocks in both sets? C-22 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

23 Selected answers: e) Yes, standard models i.e., 4 blocks each; f) No. There are only two possibilities for 16: 7 blocks and 16 blocks. There are only three possibilities for 23: 5 blocks, 14 blocks, 23 blocks. So there is no match. 4. See Activity from Lesson NBT3-4. Show students a copy of a check and explain why it s important to write the amount using both words and numerals. Show them how easy it is to change a number such as to by adding the digit 1. On the other hand, it would be very difficult to add one hundred before the word forty-eight, especially if you write fortyeight starting at the far left. Write sample checks on the board with the amount written in numeral form and have students fill in the number word in the appropriate spot, and vice versa. Or do this exercise using BLM Blank Checks, as in the Activity from Lesson NBT3-4. Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-23

24 NBT3-6 Comparing Numbers with Base Ten Models Pages Standards: preparation for 3.NBT.A.1 Goals: Students will use base ten blocks to compare pairs of 1-, 2-, and 3-digit numbers and determine which number is greater. Prior Knowledge Required: Can identify the numeral for a base ten block representation Can make or sketch a base ten model for a number Vocabulary: base ten blocks, greater than, hundreds, less than, ones, ones place, tens, regrouping, tens place Materials: base ten blocks Less than and greater than. Emphasize that to say that one number is greater than another means the first number represents more objects than the second e.g., 4 dollars is more money than 3 dollars, 4 meters is longer than 3 meters, 4 goals is more than 3 goals, 4 minutes is more time than 3 minutes. It is crucial that students understand that 4 of anything is more than 3 of the same thing, and so it makes sense to compare the numbers 3 and 4 by saying that 4 is more than 3. The correct mathematical expression is 4 is greater than 3, and students should get used to using the phrases greater than and less than. Write on the board: 4 is 5 Have volunteers say either greater than or less than as appropriate (in this case, less than is correct). Repeat with several pairs of 1-digit numbers to ensure that students are comfortable with the phrases greater than and less than. Comparing 2-digit numbers by matching tens. Model the numbers 43 and 26 using base ten materials: C-24 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

26 many ones blocks are there? (3) Can this be enough to make another hundreds block? (no) So, which number is greater, 238 or 153? (238) Teach the students how to compare two 3-digit numbers by comparing first the hundreds, then the tens (if the hundreds are the same), and then the ones (if the hundreds and tens are the same). Make or draw base ten models to compare 153 and 147: 153 same more tens 147 SAY: We first compare the hundreds. Which number has more hundreds, 153 or 147? (they both have 1 hundred) Since they have the same number of hundreds, how do we check which number is greater? (compare the tens) Which number has more tens? (153 has more tens than 147) Do we need to compare the ones now? (no, we already know 153 is the greater number) Repeat with several examples where the numbers differ in the hundreds, tens or ones digits. Examples: 235 and 239, 125 and 213, 136 and 152, 108 and 105 Exercises: Use base ten blocks to model the numbers. Circle the greater number. a) b) c) d) Answers: a) 236, b) 261, c) 129, d) 184 (MP.8) Summarize the above exercises. ASK: If two 3-digit numbers have different hundreds digits, which number is greater? (the one with more hundreds) If two 3-digit numbers have the same hundreds digit, how do we check which one is greater? (look at the tens) What if the tens are different, then which number is greater? (the one with more tens) What if the tens are also the same? How do we check which number is greater? (look at the ones) If the ones are different, which number is greater? (the number with more ones) If all 3 digits are the same, what can we say about the numbers? (the numbers are equal) 3-digit numbers are larger than 2-digit numbers. Guide students to see that 3-digit numbers are larger than 2-digit numbers. Model the numbers 47 and 125. SAY: 47 is a 2-digit number. Does 47 have any hundreds blocks? (no) ASK: Does any 2-digit number have enough tens and ones to make a hundreds blocks? (no) SAY: 125 is a 3-digit number. How many hundreds blocks are in 125? (1) Does a 3-digit number always have at least one hundreds block? (yes) Which number is bigger, 47 or 125? (125) Why? (125 has more hundreds) Why is a 3-digit number always greater than a 2-digit number? Students should see that 3-digit numbers have 1 or more hundreds, while 2-digit numbers have no hundreds. C-26 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten

27 Exercises: Use base ten blocks to model the numbers. Circle the greater number. a) b) c) d) Answers: a) 143, b) 612, c) 212, d) 148 Extensions 1. Have students compare numbers with base ten models where the blocks are not in order. Students should write the number represented and then circle the larger number. Include examples where the two models represent the same number. In such cases, students should write the word equal or the symbol = rather than circle either number. Example: 123 = Create base ten models of a pair of two-digit numbers. Ask students to say how they know which number is greater. You might make one of the numbers in non-standard form, as shown in the first number in the example below: To compare the numbers, students could remodel the first number in standard form by regrouping 10 ones blocks as 1 tens block. 3. Ask students to create base ten models of two numbers where one of the numbers a) is 30 more than the other. b) is 50 less than the other. c) has a hundreds digit equal to 6 and is 310 more than the other. Sample answers: a) 480, 450; b) 214, 264; c) 628, 318 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C-27

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