Place Value Objectives To develop place-value concepts and connect place value in money with place value in base-10 blocks. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Count by 1s, 10s, and 100s. [Number and Numeration Goal 1] Model and write 3- and 4-digit numbers using base-10 blocks and money. [Number and Numeration Goal 2] Make exchanges with base-10 blocks and relate that to exchanges with money. [Measurement and Reference Frames Goal 4] Key Activities Children identify and represent place value and numbers using base-10 blocks, compare the use of base-10 blocks to the use of money to represent place value, and practice place-value exchanges. Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal 3] Ongoing Assessment: Informing Instruction See page 766. Key Vocabulary flat long cube place value big cube Materials Math Journal 2, pp. 253 and 254 Home Link 10 7 Math Masters, pp. 320 and 321 (optional); p. 415 transparencies of Math Masters, pp. 320 and 321 (optional) base-10 blocks (1 big cube, 9 flats, 9 longs, 9 cubes) 24 pennies, 39 dimes, thirty-nine $1 bills, and one $10 bill per group: 1 six-sided die, 1 ten- or twelve-sided die slate Reviewing Ballpark Estimation Math Journal 2, p. 255 calculator Children make ballpark estimates, find the exact answers, and compare their estimates to the exact answers. Math Boxes Math Journal 2, p. 256 Children practice and maintain skills through Math Box problems. Home Link Math Masters, p. 322 Children practice and maintain skills through Home Link activities. READINESS Building Base-10 Structures per group: base-10 blocks, quarter-sheets of paper Children build base-10 block structures and identify their values as numbers. EXTRA PRACTICE Writing and Comparing Numbers Math Masters, pp. 322A and 322B Children practice place value with whole numbers. ELL SUPPORT Using Base-10 Blocks for Place Value Children use base-10 blocks to discuss the relationships between values. Advance Preparation For the Math Message, label and display a centimeter cube, a long, a flat, and a big cube for children to refer to as they complete the problems. For a mathematics and literacy connection, obtain a copy of How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen Nolan (Scholastic Inc., 1995). Teacher s Reference Manual, Grades 1 3 pp. 56, 57 764 Unit 10 Decimals and Place Value
Getting Started Mental Math and Reflexes Pose number stories involving estimation. Have children record amounts on an Exit Slip (Math Masters, page 415). Suggestions: About how much change should I get? I bought a 6-pack of soda for $1.99. I gave the cashier a $5 bill. About $3.00 I bought a bag of potato chips for $2.39. I gave the cashier $3.00. About 60 I bought a bag of grapes for $3.23 and a bag of chips for $0.99. I gave the cashier a $10 bill. About $5.80, or about $6.00 Mathematical Practices SMP1, SMP2, SMP5, SMP6, SMP7 Content Standards 2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.4, 2.NBT.8 Math Message 1 long = 10 cubes 1 flat = 10 longs = 100 cubes 1 big cube = 10 flats = 100 longs = 1,000 cubes Home Link 10 7 Follow-Up Briefly review area answers. Have children share strategies for solving one addition or subtraction problem. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Quickly review Math Message responses. Discuss relationships among base-10 blocks: each is 10 times larger than the next smaller one, and 1_ the size of the next larger one. 10 Ongoing Assessment: Recognizing Student Mental Math Achievement and Reflexes Use Mental Math and Reflexes to assess children s ability to estimate change. Children are making adequate progress if they can correctly estimate the first problem. Some children may be able to do all three problems. [Operations and Computation Goal 3] Representing 3- and 4-Digit Numbers with Base-10 Blocks (Math Masters, pp. 320 or 321) WHOLE-CLASS Ask three volunteers to form a line at the front of the room. The first child on the left, as viewed by the class, holds 3 flats for all to see, the one in the middle holds up 5 longs, and the child on the right holds 2 cubes. Tell children to assume that the cube is ONE. What is the place value of each digit? 3 hundreds, 5 tens, and 2 ones Have children write the number represented by these base- 10 blocks on their slates. Have them say the number aloud. 352 Write 300 + 50 + 2 = 352 on the board. Explain to children that writing a number model that shows the value of each digit in a number is called expanded notation. NOTE It is not expected that children use the term expanded notation. It is important, however, for them to know that multidigit numbers can be written as a sum of the values of each digit. Choose a fourth child to stand first in line on the left and hold a big cube. Children write the new number and say it aloud. 1,352 Discuss the change that results from adding the big cube to the collection. The number increases by 1,000. Write 1,000 + 300 + 50 + 2 = 1,352 on the board. Name Date Time Place-Value Chart Ten- Thousands Hundreds Tens Ones Thousands Math Masters, page 320 Name Date Time Í dimes Î pennies Place-Value Mat 10s 1s Math Masters, page 321 Lesson 765
Date Materials Student Page Time Money Exchange Game Directions 1 six-sided die 1 ten- or twelve-sided die 24 pennies, 39 dimes, thirty-nine $1 bills, and one $10 bill per player Players 2 or 3 Skill Make exchanges between coins and bills Object of the Game To be the first to trade for $10 Directions 1. Each player puts 12 pennies, 12 dimes, twelve $1 bills, and one $10 bill in the bank. 2. Players take turns. Players use a six-sided die to represent pennies. Players use a ten- or twelve-sided die to represent dimes. 3. Each player rolls the dice. takes from the bank the number of pennies and dimes shown on the faces of the dice. puts the coins in the correct columns on his or her Place-Value Mat on journal page 254. 4. Whenever possible, a player replaces 10 coins or bills of a lower denomination with a coin or bill of the next higher denomination. 5. The first player to trade for a $10 bill wins. If there is a time limit, the winner is the player with the largest number on the mat when time is up. Date Math Journal 2, p. 253 NOTE There are many names for base-10 blocks. The following names are used in Everyday Mathematics: cube (centimeter cube) for the smallest cube, long for the strip of 10 cm cubes, flat for the block consisting of 100 cm cubes. This leaves open the possibility of using the cube, the long, or the flat as the unit (ONE) for decimal and fraction work. Í dimes Î pennies Place-Value Mat 1s 10s Student Page Time Repeat the activity with other 3- and 4-digit numbers less than 2,000. Then reverse the procedure: Write a 3- or 4-digit number on the board and ask children in the line to represent the number with base-10 blocks. Write a number model to represent the base-10 blocks on the board. Repeat with several other numbers as needed. Ongoing Assessment: Informing Instruction Watch for children who are having difficulty recording numbers on their slates. Have them write the numbers on a place-value chart or mat (Math Masters, pages 320 or 321). Reviewing the Role of 0 as a Placeholder WHOLE-CLASS Continue the routines from the previous activity, but have one or more children in the line be empty-handed, representing the digit 0 in those places. Children write the numbers on their slates with zeros in the appropriate places. Reverse the procedure: Write 3- or 4-digit numbers containing one or more zeros on the board and ask children to represent those numbers with base-10 blocks. Comparing Place Value with Base-10 Blocks and Money WHOLE-CLASS DISCUSSION $10 1,000s Point out the similarities between base-10 blocks and money, comparing cubes and pennies, longs and dimes, flats and dollars, and so on. Discuss how both groups of materials make trades using a 10-for-1 rule, represent larger numbers the same way, and represent numbers in more than one way. Also discuss the differences between base-10 blocks and money: Relationships among base-10 blocks are reflected in the size of the blocks, but relationships among denominations of coins and bills are not reflected in size; money is used inside and outside of school, but base-10 blocks are usually used only at school. Playing the Money Exchange Game (Math Journal 2, pp. 253 and 254; Math Masters, p. 321) SMALL-GROUP $1 dollars 100s Explain the rules of the Money Exchange Game. You may wish to use an overhead transparency of Math Masters, page 321 to model the game. Then divide the class into groups of 2 or 3 players and have children play the game. Math Journal 2, p. 254 766 Unit 10 Decimals and Place Value
2 Ongoing Learning & Practice Reviewing Ballpark Estimation (Math Journal 2, p. 255) Children complete this journal page by finding a ballpark estimate for each problem. They then solve the problem using a calculator. When most children have completed this journal page have them compare their estimates with their exact answers and discuss any discrepancies. If necessary, encourage children to estimate and solve the problem again. Math Boxes (Math Journal 2, p. 256) Date Ballpark Estimates Time Fill in the unit box. Then, for each problem: Unit Make a ballpark estimate before you add. Write a number model for your estimate. Use your calculator and solve the problem. Write the exact answer in the box. Compare your estimate to your answer. 1. Ballpark estimate: 148 + 27 4. Ballpark estimate: 143 + 41 2. Ballpark estimate: 3. Ballpark estimate: 150 + 30 = 180 160 + 30 = 190 130 + 40 = 170 175 163 + 32 195 133 + 35 168 5. Ballpark estimate: 184 + 23 6. Ballpark estimate: 140 + 40 = 180 180 + 20 = 200150 + 180 = 330 184 Student Page 207 154 + 183 337 Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 10-6 and 10-10. The skill in Problem 6 previews Unit 11 content. Math Journal 2, p. 255 Home Link (Math Masters, p. 322) Home Connection Children identify digits in specified places in 3- and 4-digit numbers, read the numbers to someone at home, and write 3- and 4-digit numbers represented by sets of base-10 blocks. Date Math Boxes 1. What number is shown by the blocks? 347 3. In the morning, it was 62 F. By afternoon, the temperature was 75 F. How much did the temperature rise? 13 Change Start End 62 F +13 F 75 F Number model: 62 + 13 = 75 5. Which object is shaped like a cone? Circle the best answer. A shoe box B party hat C paper towel roll D globe 256 two hundred fifty six 229_262_EMCS_S_SMJ_G2_U10_57640X.indd 256 Student Page 11 Time Math Journal 2, p. 256 2. Kelly has $10. Her lunch total was $8.75. How much change will she get? 4. Cross out the names that don t belong. 10 ten cents, 1_ 10 of a dollar, $10.00, Í, ÂÂ, $0.01, 1_ 100 of a dollar, 1_ 2 of a dollar 116 118 88 90 57 $1.25 6. 4 ladybugs. 5 spots on each ladybug. How many spots? 20 Fill in the diagram and write a number model. lady bugs 4 spots per lady bug Sample answers: 4 5 = 20; 5 + 5 + 5 + 5 = 20 spots in all 5 20 112 113 3/18/11 3:53 PM Name Date Time HOME LINK Place Value Family Note In this lesson, your child has been studying place value, or the value of digits in numbers. Listen as your child reads the numbers in Problems 1 6. You might ask your child to pick a few of the numbers and tell you the place value of each of the digits. For example, in 462, the value of 4 is 400, the value of 6 is 60, and the value of 2 is 2. 10 Please return this Home Link to school tomorrow. In each number: Circle the digit in the hundreds place. Underline the digit in the thousands place. Example: 9,342 1. 4 6 2 2. 1, 3 2 6 3. 5, 0 0 6 4. 8 6 9 5. 2, 3 0 4 6. 4, 5 6 7 7. Read the numbers in Problems 1 6 to someone at home. Write the numbers represented by the base-10 blocks. 8. = 9. = 247 1,183 10. = 1,204 Practice Solve. Home Link Master 158 188 29 380 11. 134 + 24 = 12. 152 + 36 = 13. 67-38 = 14. 164 + 216 = Math Masters, p. 322 py g g p 293-347_EMCS_B_MM_G2_U10_576949.indd 322 2/25/11 2:29 PM Lesson 767
Name Date Time Teaching Master Place Value Write the number for each group of base-10 blocks. 3 Differentiation Options 1. 2. 3. 4. 346 530 604 READINESS Building Base-10 Structures SMALL-GROUP 5 15 Min To explore place value using a concrete model, have children build a base-10 structure with flats, longs, and cubes. The cube is ONE. Children work together to count the value of each structure and record it on a quarter-sheet of paper. Then children arrange the sheets in order from least to greatest value. Copyright Wright Group/McGraw-Hill 1,326 5. Circle the largest number. 4,343 Then explain how you 4,563 know what number 4,543 is the largest. 4,463 Answers vary. EXTRA PRACTICE Writing and Comparing Numbers (Math Masters, pp. 322A and 322B) 5 15 Min Math Masters, p. 322A To provide children additional practice with writing and comparing numbers, have them complete Math Masters, pages 322A and 322B. ELL SUPPORT Using Base-10 Blocks for Place Value 5 15 Min Name Date Time Teaching Master Place Value continued To provide language support for place value concepts, do the following activity. Show each of the base-10 blocks, draw a sketch of each one on the board, and label them with their names and values. Have children place 10 cubes on top of 1 long. Point out that 10 cubes are the same as 1 long. 10 cubes and 1 long have the same value. Next, place 10 longs on top of 1 flat. Point out that 10 longs are the same as 1 flat. 10 longs and 1 flat have the same value. Write in expanded form. Example: 56 50 + 6 6. 63 7. 457 8. 893 9. 1,538 10. 2,341 11. 4,906 60 + 3 400 + 50 + 7 800 + 90 + 3 1,000 + 500 + 30 + 8 2,000 + 300 + 40 + 1 4,000 + 900 + 6 Write the number. 12. 900 + 20 + 5 13. 800 + 70 + 6 925 14. 9,000 + 20 + 4 15. 1,000 + 3 9,024 876 1,003 Do your own. Write a number. Write the number in expanded form. 16. Answers vary. 17. Math Masters, p. 322B 322A-322B_EMCS_B_MM_G2_U10_576949.indd 322B 3/18/11 2:28 PM 768 Unit 10 Decimals and Place Value
Name Date Time HOME LINK Place Value Family Note In this lesson, your child has been studying place value, or the value of digits in numbers. Listen as your child reads the numbers in Problems 1 6. You might ask your child to pick a few of the numbers and tell you the place value of each of the digits. For example, in 462, the value of 4 is 400, the value of 6 is 60, and the value of 2 is 2. 10 Please return this Home Link to school tomorrow. In each number: Circle the digit in the hundreds place. Underline the digit in the thousands place. Example: 9,342 1. 4 6 2 2. 1, 3 2 6 3. 5, 0 0 6 4. 8 6 9 5. 2, 3 0 4 6. 4, 5 6 7 7. Read the numbers in Problems 1 6 to someone at home. Write the numbers represented by the base-10 blocks. 8. = 247 9. = 10. = Practice Solve. Copyright Wright Group/McGraw-Hill 11. 134 + 24 = 12. 152 + 36 = 13. 67-38 = 14. 164 + 216 = 322
Name Date Time Place Value Write the number for each group of base-10 blocks. 1. 2. 3. 4. Copyright Wright Group/McGraw-Hill 5. Circle the largest number. 4,343 Then explain how you 4,563 know what number 4,543 is the largest. 4,463 322A
Name Date Time Place Value continued Write in expanded form. Example: 56 50 + 6 6. 63 7. 457 8. 893 9. 1,538 10. 2,341 11. 4,906 Write the number. 12. 900 + 20 + 5 13. 800 + 70 + 6 14. 9,000 + 20 + 4 15. 1,000 + 3 Do your own. Write a number. Write the number in expanded form. 16. 17. Copyright Wright Group/McGraw-Hill 322B