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

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1 Objectives To review making ballpark estimates; and to review the counting-up and trade-first subtraction algorithms. Teaching the Lesson materials Key Activities Children make ballpark estimates for -digit subtraction problems. They review the counting-up and trade-first subtraction algorithms. Key Concepts and Skills Use place-value concepts to apply the counting-up and trade-first algorithms. [Number and Numeration Goal ] Use basic facts to solve extended fact problems involved in trade-first subtraction. [Operations and Computation Goal ] Use base-0 blocks to model and solve subtraction problems. [Operations and Computation Goal ] Make ballpark estimates as a check for reasonableness of answers. [Operations and Computation Goal ] Key Vocabulary counting-up method trade-first method Math Journal, pp. 47 and 0 Home Link 7 Teaching Master (Math Masters, p. ) base-0 blocks overhead base-0 blocks (optional) Number-Grid Poster (optional) See Advance Preparation Ongoing Assessment: Informing Instruction See page 43. Ongoing Assessment: Recognizing Student Achievement Use journal page 0. [Operations and Computation Goal ] Ongoing Learning & Practice materials Children write equivalent names for numbers in name-collection boxes. Children play Number-Grid Difference. Children practice and maintain skills through Math Boxes and Home Link activities. 3 Differentiation Options Math Journal, pp. 4 and 49 Student Reference Book, p. 30 Home Link Master (Math Masters, p. 4) Teaching Master (Math Masters, p. ) Game Master (Math Masters, p. 4) number cards 0 9, 4 of each pennies or counters; calculator materials READINESS Children play Base-0 Trading Game. ENRICHMENT Children make posters showing a variety of subtraction strategies. Teaching Aid Master (Math Masters, p. 4) base-0 blocks; dice large paper; crayons Additional Information Advance Preparation Plan to spend a total of two days on this lesson. Technology Assessment Management System Journal page 0 See the itlg. Lesson 4

2 Getting Started Mental Math and Reflexes Pose fact-extension problems. Suggestions: , ,00 7 Math Message Make ballpark estimates. On a half-sheet of paper, write the number sentence you used for each estimate. Sample answers:. 4? books ? ; ? ; Home Link 7 Follow-Up Have partners share their solution strategies. On Day of this lesson, children should complete the Math Message Follow-Up, review counting up for -digit subtraction, subtract 3-digit numbers, and write equivalent names for numbers. On Day of this lesson, children should model trade-first subtraction, subtract 3-digit numbers, and play Number-Grid Difference. Subtraction Methods Make a ballpark estimate. Write a number model to show your estimate. Choose at least two problems to solve using the counting-up method and show your work. You may choose any method you wish to solve the other problems. Sample estimates given. Example: Ballpark estimate: Counting-Up Method Ballpark estimate: lunches. Ballpark estimate: Ballpark estimate: 4. Ballpark estimate:. Ballpark estimate: Teaching the Lesson Math Message Follow-Up Remind children that one way to make a ballpark estimate is to change the numbers in the problem to close-but-easier numbers that can be subtracted mentally. For example: 4 is close to 0 0, so the exact answer should be close to is close to 70 0 or 7 4, so the exact answer should be near 0 or is close to 40 0 or 0 0, so the exact answer should be near 0 or 30. NOTE There can often be more than one acceptable answer when making ballpark estimates. Reviewing the Counting-Up Method for -Digit Subtraction DISCUSSION Have children find exact answers to the Math Message problems, using the counting-up method from Second Grade Everyday Mathematics, and check them against their ballpark estimates. Children share their answers and procedures while you keep a record on the board. This is called the counting-up method because children count up from the smaller number to the larger number, using a combination of multiples of 0s and s. Math Journal, p Adding and Subtracting Whole Numbers

3 Example: 7 4 Write the problem on the board in horizontal form. Then write 4 next to the problem. Model counting up from 4 to 7. Circle each number as you count up. Remind children that they may begin with the 00s, 0s, or s in any order when adding mentally. Then model the mental addition of the circled numbers So 7 4. Ongoing Assessment: Informing Instruction Watch for children who are having difficulty using multiples of 0s and s to count up. You may want to use the number grid to model the counting-up method Subtracting 3-Digit Numbers (Math Journal, p. 47) Write the following problem on the board in horizontal format: 343 Have children solve the problem and then share their solution strategies. If no one mentions it, model the counting-up method. See the margin for other ways to record the counting-up method. Children solve the problems on the journal page. Remind them to make ballpark estimates. Provide access to the number grid and other manipulatives. Children may share their answers with a partner. If there is a disagreement, encourage them to discuss their strategies with each other and do the problem again until they agree on an answer = 343 = longs 0s 7 / 4 cubes s / Modeling the Trade-First Algorithm for -Digit Subtraction Longs and cubes to represent 7 Remind children that in Second Grade Everyday Mathematics they used the trade-first method to subtract -digit numbers. Model solving the problem using the trade-first method. Example: 7 4 Write the problem on the board in vertical format. Draw a picture on the board of 7 longs and cube to represent the number 7. Ask: Are there enough blocks to remove 4 (4 longs and cubes)? No Trade long for 0 cubes. Mark the problem to reflect this action: Draw a slash through the 7 and write ; draw a slash through the and write. Subtract 4 tens by erasing 4 longs from the picture. Subtract ones by erasing cubes from the picture. That leaves ( longs and cubes). Record this answer on the board. Trade ten for 0 ones. Subtract 4 by removing 4 tens and ones. ( tens, ones) remaining. Lesson 43

4 Subtracting 3-Digit Numbers Show 343 with 3 hundreds, 4 tens, and 3 ones. Trade hundred for 0 tens. Write this problem on the board in vertical form: 343 Ask children to solve the problem and share their solution strategies. If no one mentions it, model the trade-first method. See the margin for representations of the base-0 block trades for the solution. Try several more - and 3-digit subtraction problems as needed. Practicing Subtraction Algorithms (Math Journal, p. 0; Math Masters, p. ) Children solve the problems on the journal page. Remind them to make ballpark estimates to check answers and look for mistakes. Make sure children have access to manipulatives. Children may share their answers with a partner. If there is a disagreement, encourage them to discuss their strategies with each other and do the problem again until they agree on an answer. Use Math Masters, page to create additional practice problems as needed. Links to the Future Trade ten for 0 ones. Abundant practice with 3-digit subtraction problems will be found on Math Boxes and Home Links in future lessons. Ongoing Assessment: Recognizing Student Achievement Journal Page 0 Problems and Subtract by removing hundred, tens, and ones. ( hundred, tens, and ones) remaining. Use journal page 0, Problems and to assess children s ability to solve multidigit subtraction problems. Children are making adequate progress if they are able to solve Problems and correctly. Some children may be able to complete the remaining problems with or without manipulatives. [Operations and Computation Goal ] 3 / 3 3 4/ 3 3 / Ongoing Learning & Practice Writing Equivalent Names for Numbers (Math Journal, p. 4) Children complete name-collection boxes. Name-collection boxes were reviewed in Lesson Adding and Subtracting Whole Numbers

5 EM07TLG_G3_U0_L0.qxd //0 3:4 AM Page 4 Playing Number-Grid Difference (Math Masters, pp. and 4; Student Reference Book, p. 30) Children practice finding differences by playing Number-Grid Difference. If necessary, review game directions on page 30 of the Student Reference Book. Math Boxes (Math Journal, p. 49) PARTNER Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson -. The skill in Problem previews 3 content. Writing/Reasoning Have children write an answer to the following: Explain how you figured out what the time would be in 30 minutes in Problem 3. Sample answer: Starting at the minute hand, I counted in min intervals until I added 30 min to find the new time. 00s Subtraction Methods Make a ballpark estimate. Write a number model to show your estimate. Choose at least two problems to solve using the trade-first method and show your work. You may choose any method you wish to solve the other problems. Sample estimates given. Example: Ballpark estimate: Trade-First Method s 0s dollars. Ballpark estimate:. Ballpark estimate: Ballpark estimate: 4. Ballpark estimate:. Ballpark estimate: Math Journal, p Home Link (Math Masters, p. 4) Home Connection Children solve subtraction problems. Since some of the methods children use may not be familiar to parents, you may want to send home the Student Reference Book. 3 Differentiation Options READINESS Playing Base-0 Trading Game (Math Masters, p. 4) PARTNER Min To provide experience with place-value exchanges, have children play Base-0 Trading Game. The following materials are needed per partnership: flats, 0 longs, 40 cubes; dice; and Place- Value Mats. Each partner pair needs to begin with a bank of 0 longs and 40 cubes. Each partner places flat on the Place-Value Mat. (See the next page for game directions.). Three names do not belong. Mark them with a big X fifties Name-Collection Boxes 4,0,0 0 30, ,999 9,99 3. Write at least 0 names for Write at least 0 names for Answers vary. 4. Write at least 0 names for,000.,000 4 Answers vary. Answers vary. Math Journal, p. 4 Lesson 4

6 EM07TLG_G3_U0_L0.qxd //0 3:43 AM Page 4 Math Boxes. Complete the fact extensions. 3. What time does the clock show? : What time will it be in 30 minutes? : Fill in the blanks Find the rule and complete the table. in Rule Add 0 in days out Directions: Take turns. On each turn, a player does the following:. Roll the dice and find the sum of the dice dots.. Return that number of cubes to the bank. (Whenever there are not enough individual cubes, make exchanges.) 3. The player who is not rolling the dice checks the accuracy of the transactions. 4. The first player to clear his or her Place-Value Mat wins the game. out Corey had $7. He bought a new baseball for $. How much money does he have now? $7 Number model: 7 7 Start Change End 7 7 Math Journal, p. 49. Measure the line segment to the nearest centimeter. 4 cm ENRICHMENT Making Subtraction Posters SMALL-GROUP 30 Min To further explore subtraction algorithms, have children make subtraction posters. Small groups work together to write a - or 3-digit subtraction problem. They use as many methods as they can to solve the problem. Then children create posters showing their methods. Possible methods include using the number grid, number line, base-0 blocks, counting-up, partialdifferences, trade-first, and the U.S. traditional algorithms. Children may use other methods as well. Display the posters. Home Link Master Name Teaching Aid Master Name HOME LINK Subtraction Methods 3-Digit Place-Value Mat Family Note Over the past days, your child practiced subtracting two 3-digit numbers using the counting-up method and the trade-first method. For more information, see pages 0,, and 3 in the Student Reference Book. 0 Please return this Home Link to school tomorrow. 3 Fill in the unit. Solve the problems. You may use any method you wish. Use a ballpark estimate to check that your answer makes sense. Write a number model for your estimate. On the back of this Home Link, explain how you solved one of the problems. Sample estimates given Ballpark estimate:. Ballpark estimate: 3. Ballpark estimate: Ballpark estimate:. Ballpark estimate:. Ballpark estimate: Hundreds Tens Ones Math Masters, p. 4 Math Masters, p. 4 4 Adding and Subtracting Whole Numbers

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