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


 Bernadette Jordan
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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 3digit numbers, and they will understand the value of each digit. Students will read and write 3digit numbers using words and numerals, and understand the connection between number words, expanded form, and base ten block representations. Students will also compare 3digit numbers using the symbols <, >, and = with base ten blocks and using place value. Students will add and subtract 3digit 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 C1
2 NBT31 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 3digit 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. C78) BLM Place Value Bingo (p. C79) 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 3digit 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) C2 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 3digit 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 C3
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 3digit 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. C1, 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) C4 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 C5
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 2digit 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 2digit 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 2digit number where the sum of the digits is 11. k) Write a 2digit number where the digits are the same and the sum of the digits is 14. l) Write a 3digit number where the digits are the same and the sum of the digits is 15. Is there a 2digit 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 2digit number with a tens digit eight less than its ones digit. o) Write a 3digit number where all three digits are odd. p) Write a 3digit 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 C6 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
7 NBT32 Base Ten Blocks Pages Standards: preparation for 3.NBT.A.2 Goals: Students will represent numbers with base ten materials. Prior Knowledge Required: Understands place value Vocabulary: base ten blocks, digit, hundreds block, hundreds digit, ones block, ones digit, tens block, tens digit, Materials: transparency and overhead projector (if available) base ten blocks (of two different colors, if available) BLM Hundreds Chart and Base Ten Materials (p. C80) BLM Hundreds Charts up to 200 (p. C81) Base ten models for 1 and 2digit numbers. Photocopy BLM Hundreds Chart and Base Ten Materials onto a transparency, if available. Demonstrate how to find by taking 3 ones blocks and then another 4 ones blocks and placing them on the chart in order, so that the last block is on square 7. ASK: How can I find by using ones blocks and the hundreds chart? How is the counting already done for you when you put the ones blocks on the chart in order? Emphasize that students can see the answer by looking under the last ones block. Tell your students that instead of using 10 ones blocks to cover a row, you find it easier to use one bigger block. Show them a tens block and ask if anyone remembers what the block is called. Show them how 10 ones blocks can be joined together to make 1 tens block. Provide your students with BLM Hundreds Charts up to 200, as well as 10 tens blocks and 9 ones blocks each. Have students use 3 tens blocks and 5 ones blocks and cover the squares from the top chart in order. (The hundreds charts are 10 cm x 10 cm so that a ones block will cover a grid square exactly. If the ones blocks you are using are larger than 1 cubic centimeter, you may need to enlarge BLM Hundreds Charts up to 200 when printing.) ASK: How many squares are covered? (35) PROMPT: Which number do you see under the last ones block? (35) Repeat for several examples. (41, 23, 59, 74, 99) ASK: What number do you get if you use 2 tens blocks and 0 ones blocks? (20) What number do you get if you use 5 tens blocks? (50) 7 tens blocks? (70) 10 tens blocks? (100) Base ten models for 3digit numbers. Tell your students that we used a tens block instead of 10 separate ones blocks. ASK: What can we use instead of 10 tens blocks? (a hundreds block) Show them how 10 tens blocks can be put side by side to make 1 hundreds block. Place the 10 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C7
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 3digit 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 C8 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 C9
10 NBT33 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. C82) 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. C10 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 C11
12 Exercises: Write the number for the expanded form. a) = b) = c) = d) = Answers: a) 530, b) 705, c) 208, d) 380 (MP.1) Write on the board: = = = 892 Challenge students to say how to fill in the blanks. For each question, PROMPT: What is missing, the ones, tens, or hundreds? (ones, 5; tens, 70; hundreds, 800) Exercises: Fill in the blank. a) = 534 b) 641 = c) 812 = d) = 742 e) = 420 f) = 402 Answers: a) 4, b) 40, c) 800, d) 40, e) 20, f) 2 Expanded form and base ten sketches. Remind students how to draw rough sketches of base ten models (see Lesson NBT32, p. C7). Have students write various numbers in expanded form and then draw a rough sketch of a base ten model. Examples: 732, 456, 57. (MP.4) Tell your students that you read one book with 300 pages and another book with 70 pages. ASK: How many pages did I read altogether? Have a volunteer write the corresponding addition sentence ( = 370). Exercises: Use expanded form to answer the question. a) A store has 100 red bikes, 40 blue bikes, and 6 green bikes. How many bikes does the store have altogether? b) On a class field trip, there were 200 children, 10 parent volunteers, and 7 teachers. How many people went on the field trip? (MP.1) Bonus: In a school in Buffalo with 498 children, 400 students are from the United States, and 90 students are from Canada. How many students are from neither the United States nor Canada? (498 = ) Solutions: a) = 146, b) = 217, Bonus: 498 = , so there are 8 students who are from neither the United States nor Canada. Activity I have, Who has? Using BLM Make Up Your Own Cards, make enough cards so that everyone in the class can have one. Use expanded form and base ten sketches to make the cards. For example, the student has the following card: I have Who has? C12 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
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 C13
14 NBT34 Writing and Reading Number Words Pages Standards: preparation for 3.NBT.A.2 Goals: Students will read and write number words for any number between 0 and 999. Prior Knowledge Required: Understands place value Vocabulary: digit, expanded form, number word, numeral Materials: BLM Blank Checks (p. C83) BLM Number Word Search (p. C84, see Extension 1) BLM Number Word Crossword Puzzle (p. C85, see Extension 2) BLM Crossword without Clues (p. C86, see Extension 3) (MP.6) Number words from 0 to 10. Write the numerals 0 to 10 vertically on the board. ASK: Are these numbers written as numerals or as number words? (numerals) What are the number words for these numerals? Have the students help you write the number words zero, one, two, and so on beside the corresponding numerals. Ensure students understand the difference between numerals (numbers written with symbols, as in 3 ) and number words (as in three ). Number words from 11 to 19. Write the following words on the board, all in a row: fourteen thirteen seventeen sixteen nineteen fifteen Ask the class to read the words out loud together. Ask volunteers to write the corresponding numerals under the words. (14, 13, 17, 16, 19, 15) ASK: What number does the word teen remind you of? (ten) Guide them by asking them to look at the letters is teen spelled almost the same as a number they know? Tell them that fourteen is = 14. ASK: Where can you see four in fourteen? Where can you see a word that looks like ten in the word fourteen? Have volunteers demonstrate the first two parts of both exercises below before having all students complete the rest. (MP.8) Exercises: 1. Fill in the blanks with the correct number words. a) fourteen = + ten b) seventeen = seven + c) nineteen = + d) = six + ten Answers: a) four; b) ten; c) nine, ten; d) sixteen C14 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
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 1digit number in the word for the 2digit 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 1digit 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 C15
16 Have volunteers fill in the blanks by looking carefully at the beginning letters and asking themselves what 1digit number those letters remind them of. ASK: Which ones digit do these numbers all have? (0) Which letters do the words all end with? ( ty ) Tell students that any number word ending with ty will always mean a number having a ones digit 0. Ask volunteers to guess how the following number words are written as numbers: eighty, ninety. (80, 90) Challenge them to find a 2digit number having the ones digit 0 whose number word doesn t end with ty. (10) Exercises: Write the numerals for each number word. a) thirty thirteen three b) twenty two twelve c) four fourteen forty d) eighteen eighty eight e) seven ninety thirteen eighty nine fourteen f) nineteen sixty forty fifteen twelve eight Answers: a) 30, 13, 3; b) 20, 2, 12; c) 4, 14, 40; d) 18, 80, 8; e) 7, 90, 13, 80, 9, 14; f) 19, 60, 40, 15, 12, 8 Exercises: Write the number word ending. a) 30 = thir b) 20 = twen c) 13 = thir d) 17 = seven e) 40 = for f) 80 = eigh g) 18 = eigh h) 19 = nine i) 90 = nine Answers: a) ty, b) ty, c) teen, d) teen, e) ty, f) ty, g) teen, h) teen, i) ty Finally, have students write the full number words. Exercises: Write the number word. a) 20 = b) 19 = c) 90 = d) 17 = e) 13 = f) 80 = g) 50 = h) 15 = i) 11 = j) 18 = k) 12 = l) 70 = Answers: a) twenty, b) nineteen, c) ninety, d) seventeen, e) thirteen, f) eighty, g) fifty, h) fifteen, i) eleven, j) eighteen, k) twelve, l) seventy Reading number words from 0 to 99. Write twenty on the board and ask a volunteer to write the corresponding numeral. (20) Ask the student to state what the number word twentythree means. Can the student think of an addition sentence from this word? ( = 23) Remind students that this is the expanded form. Repeat for twentyseven and twentyone. Exercise: Write the numeral for the given number word. a) twentytwo b) twentyfive c) twentynine d) twentysix Answers: a) 22, b) 25, c) 29, d) 26 C16 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
17 Write on the board: thirtysix 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 thirtysix stands for? What addition sentence can you write from this? ( = 36) Have a volunteer write the numeral for thirtyfive with the addition sentence. (35 = ) Exercises: Write the numeral and the addition sentence. a) thirtythree b) thirtytwo c) thirtyeight d) thirtyfour e) fortytwo f) eightyone g) fiftyfour h) ninetyseven Answers: a) = 33, b) = 32, c) = 38, d) = 34, e) = 2, f) = 81, g) = 54, h) = 97 Write on the board: 73 = = = = seventythree thirtytwo sixtyone fiftyfour 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) thirtyeight b) fortyfive c) twentysix d) fiftyone e) sixtyseven f) eightynine g) seventyfour h) ninetyone 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) twentyeight b) eighteen c) sixteen d) four e) forty f) fortythree g) zero h) fifty i) fiftyeight j) thirteen k) twelve l) nineteen m) twentynine n) fiftynine o) fortyeight p) twenty q) thirtyone 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 C17
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) fortyzero n) fortythree o) twentyeight p) thirty nine q) eightfive r) seventysix Answers: a) fortyone; b) thirtytwo; c) ninety; d) nine; e) eightynine; f) seventyfour; g) ninetynine; h) zero; i) fifty; j) twentyfive; k) seventeen; l) eleven; Bonus: m) should be forty, no  zero ; n) correct; o) correct; p) the  is missing, should be thirtynine ; 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 3digit 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 3digit numbers. Tell students that they can write out 3digit numbers like 532 by breaking them down. Say the number out loud and invite students to help you write what they hear: five hundred thirtytwo. Point out that there is no dash between five and hundred. C18 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) thirtyfour, b) four, c) fifty, d) eighteen 2. a) 761 = sixtyone b) 840 = forty c) 327 = twentyseven 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 ninetyeight, b) seven hundred forty, c) seven hundred fiftysix, 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) SeventyFour Main Street e) Bulk Sale! Buy Ten for the Price of Five! f) Bus Stop: Route 108 Answers: a) one hundred eightyone; b) sixtyfive; 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) fiftytwo, d) twentyeight, e) three hundred sixtyfive, f) three hundred sixtysix 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 C19
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 C20 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
21 NBT35 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 3digit numbers. Prior Knowledge Required: Understands expanded form for 2 and 3digit numbers Can read and write number words for 2 and 3digit numbers Can draw base ten models for 2 and 3digit numbers Materials: BLM Blank Checks (p. C83; 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 seventyeight, b) six hundred eleven, c) eight hundred eighteen, d) nine hundred twentythree, e) six hundred fifty, f) six hundred five Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C21
22 Exercises: Write the numeral for the given number word. a) four hundred eightynine b) three hundred twenty c) one hundred four d) sixtyseven e) eleven f) nine hundred twentyfive Answers: a) 489, b) 320, c) 104, d) 67, e) 11, f) 925 Review of base ten blocks. Write 1, 2, and 3digit 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 3digit number. My digits are all the same. Use 12 blocks to make me. c) I am a 2digit number. My tens digit is 5 more than my ones digit. Use 7 blocks to make me. d) I am a 3digit 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 2digit 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? C22 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 NBT34. 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 fortyeight, 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 NBT34. Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C23
24 NBT36 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 3digit 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 1digit numbers to ensure that students are comfortable with the phrases greater than and less than. Comparing 2digit numbers by matching tens. Model the numbers 43 and 26 using base ten materials: C24 Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten
25 ASK: Which number has more tens blocks, 43 or 26? (43) Which has more ones blocks? (26) Hmmm, 43 has more tens blocks, but 26 has more ones blocks how can we know which number is bigger? Show students how to match the 2 tens blocks of 26 with 2 tens blocks of 43. ASK: After matching the 2 tens blocks of 26, how many ones are left over in the number 26? (6) Can we use these 6 ones blocks to match with one of the remaining tens blocks of 43? (no) Point out that the remaining 6 ones blocks of 26 are not enough to make another tens block. ASK: Which number is greater, 43 or 26? (43) Why? (because 43 has more tens) ASK: If two 2digit numbers have different tens digits, which number is greater? Ensure students understand that the number with more tens is the larger number. Exercises: Use base ten blocks to model the numbers. Circle the greater number. a) b) c) d) Answers: a) 56, b) 45, c) 46, d) 55 Model the numbers 54 and 57. ASK: Which number has more tens, 54 or 57? Students should see that the number of tens match. ASK: How do we know which number is greater? Explain to students that if the number of tens match, you need to compare the number of ones blocks. ASK: Which number has more ones blocks, 54 or 57? (57) So which number is greater, 54 or 57? (57) Exercises: Use base ten blocks to model the numbers. Circle the greater number. a) b) c) d) Answers: a) 58, b) 62, c) 37, d) 51 Summarize the above exercises. ASK: If two 2digit numbers have the same tens digit, how can you tell which number is greater? (the number with the greater ones digit will be greater) If the numbers have different tens digits, how can you tell which number is greater? (the number with a greater tens digit will be greater). 2digit numbers are larger than 1digit numbers. Guide students to see that 2digit numbers are larger than 1digit numbers. Model the numbers 7 and 15. SAY: 7 is a 1digit number. Does 7 have any tens blocks? (no) ASK: Does any 1digit number have enough ones to make a tens block? (no) SAY: 15 is a 2digit number. How many tens blocks are in 15? (1) Does a 2digit number always have at least one tens block? (yes) Which number is bigger, 7 or 15? (15) Why? (15 has more tens) Why is a 2digit number always greater than a 1digit number? Students should see that 2digit numbers have 1 or more tens, while 1digit numbers have no tens. Exercises: Use base ten blocks to model the numbers. Circle the greater number. a) 6 13 b) c) 12 9 d) Answers: a) 13, b) 62, c) 12, d) 48 Comparing 3digit numbers. Ask volunteers to make (or draw rough sketches of) base ten models for the numbers 238 and 153. ASK: Which number has more hundreds blocks? Tens blocks? Ones blocks? Which number do you think is greater? Match the hundreds block of 153 with one of the hundreds blocks of 238. ASK: How many tens are left over in 153? (5) How Teacher s Guide for AP Book 3.1 Unit 2 Number and Operations in Base Ten C25
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 3digit 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 3digit numbers have different hundreds digits, which number is greater? (the one with more hundreds) If two 3digit 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) 3digit numbers are larger than 2digit numbers. Guide students to see that 3digit numbers are larger than 2digit numbers. Model the numbers 47 and 125. SAY: 47 is a 2digit number. Does 47 have any hundreds blocks? (no) ASK: Does any 2digit number have enough tens and ones to make a hundreds blocks? (no) SAY: 125 is a 3digit number. How many hundreds blocks are in 125? (1) Does a 3digit 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 3digit number always greater than a 2digit number? Students should see that 3digit numbers have 1 or more hundreds, while 2digit numbers have no hundreds. C26 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 twodigit numbers. Ask students to say how they know which number is greater. You might make one of the numbers in nonstandard 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 C27
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