Subtraction Strategies

Transcription

1 Subtraction Strategies Objective To review solution strategies for subtraction of multidigit numbers. 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 up and back by 1s and 10s. [Number and Numeration Goal 1] Model multidigit numbers using base-10 blocks. [Number and Numeration Goal 2] Develop counting up and back strategies for subtraction. [Operations and Computation Goal 2] Use and explain strategies for solving multidigit subtraction problems. [Operations and Computation Goal 2] Key Activities Children solve multidigit subtraction problems using a variety of strategies. Ongoing Assessment: Informing Instruction See page Playing the Number-Grid Difference Game Math Masters, pp. 418 and 463 My Reference Book, pp. 140 and 141 per partnership: 4 each of number cards 0 9 (from the Everything Math Deck, if available), number grid, calculator, 2 pennies or counters Children use the number grid to find the difference between 2-digit numbers. Math Boxes 6 5 Math Journal 1, p. 145 Children practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 1. [Data and Chance Goal 3] READINESS Playing the Base-10 Trading Game Math Masters, p. 427 base-10 blocks (2 flats, 20 longs, 40 cubes) 2 dice Children practice subtraction using a concrete model. ENRICHMENT Analyzing a Subtraction Strategy Math Masters, p. 171 Children apply their understanding of subtraction by analyzing and explaining a subtraction strategy. Key Vocabulary trade (a base-10 long for 10 cubes) Materials Math Journal 1, p. 144 Home Link 6 4 base-10 blocks per partnership: 6 longs, 30 cubes overhead base-10 blocks (optional): 6 longs and 18 cubes number grid pennies or other counters (optional) play money (optional) Home Link 6 5 Math Masters, pp. 169 and 170 Children practice and maintain skills through Home Link activities. Advance Preparation Teacher s Reference Manual, Grades 1 3 p. 106 Lesson

2 Getting Started Mental Math and Reflexes Pose subtraction problems that feature multiples of 10. Suggestions: =? =? =? =? =? =? 132? = ? = ? = Home Link 6 4 Follow-Up Invite several children to share their stories with the class. Collect children s stories to use when you need a quick sponge or filler activity or for use during future Mental Math and Reflexes sessions. Math Message Solve the problem. Try to find the answer in two different ways. Be ready to explain how you found the answer =? 32 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS Have children share their solution strategies. For each problem, record on the board any strategies that result in the correct answer. Emphasize that there are many good ways to get correct answers to problems. You or the children might suggest the following strategies: Strategy 1 Counting Up: Start with the smaller number, 24. Model on a number grid or by quickly sketching an open number line on the board. (See margin.) Count up by ones, or 10s and ones. 34, 44, 54, 55, 56; = Number Grid Ongoing Assessment: Informing Instruction Watch for children who use the counting up strategy but include the 24 in their counts. For example, 24 (1), 25 (2), 26 (3), 27 (4) + 56 (33). This will yield an almost correct answer. This situation might be used to spark a discussion: Mahli has 33, but Harry has 32. Who s right? How did Mahli get 33? How did Harry get 32? You might also provide a penny for the children to count each move or jump Open Number Line Strategy 2 Counting Back: Start with the bigger number, 56. Model on a number grid or by quickly sketching an open number line on the board. Count back to 24 by ones, or 10s and 1s. 46, 36, 26, 25, 24 Strategy 3 Money: Think of $56 dollars. Subtract $20 and then subtract $4. Strategy 4 Manipulatives: Use manipulatives to act out the problem. Start with 56 pennies and take away 24 pennies. 402 Unit 6 Whole-Number Operations and Number Stories

3 If no one suggests it, point out that they may use base-10 blocks to solve 2-digit subtraction problems as well. Adjusting the Activity ELL Use play money to illustrate Strategy 3. Put five $10 bills and six $1 bills in one stack. Take out two $10 bills and four $1 bills. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L NOTE Everyday Mathematics students solve subtraction problems using many different strategies even though they have not been introduced to a standard algorithm. These experiences help children understand the concept and prepare them for more formal work with subtraction algorithms in Unit 11. If children suggest a standard paper-and-pencil algorithm, record it on the board, but do not take the time to teach it. Formal subtraction methods are addressed in Unit 11. Using Base-10 Blocks to Model Subtraction PROBLEM SOLVING WHOLE-CLASS Write the following problem on the board: Ask partners to represent the top number (the minuend) with the least number of blocks. Then ask them to subtract the bottom number (the subtrahend) by removing the correct combination of blocks. Invite children to demonstrate and explain what they did. Have the class gather around a table as children demonstrate with actual blocks. You might want to use base-10 blocks for the overhead if you have them. Refer to the longs alternately as longs and as 10s; refer to the cubes alternately as cubes and as 1s. Example: Model =? as follows: 1. Count out three longs and six cubes to represent 36. Lay these on the table, with the longs to the left of the cubes. 2. Ask: Are there enough longs and cubes on the table so I can remove 14 (1 long and 4 cubes)? yes 3. Remove 1 long and 4 cubes. 4. Count the remaining blocks and record the answer (the difference) on the board Take away 1 long and 4 cubes. } 2 longs and 2 cubes are left. Lesson

4 Write the following problem on the board: Date LESSON 6 5 Subtraction Time Use base-10 blocks to help you subtract. 1. Longs Cubes 2. Longs Cubes Student Page Longs Cubes 4. Flats Longs Cubes Ask partners to represent the top number (the minuend) with the fewest blocks. Then ask them to subtract the bottom number (the subtrahend) in any way they can. Children cannot solve these problems by simply removing some of the blocks shown. Invite them to come up with strategies. For example: Subtract 38 in two stages. First, remove 3 longs and 3 cubes, leaving 2 longs. Then cover up 5 cubes on one of the longs. That leaves one long (10 cubes), plus 5 cubes showing on the second long, for a total of 15. Trade one of the longs for 10 separate cubes so 53 is represented by 4 longs and 13 cubes. Then remove 8 cubes and 3 longs, leaving 1 long and 5 cubes, or 15. To support English language learners, discuss the everyday meaning of trade as well as its meaning in this context. Have the class gather around a table as children demonstrate with actual blocks. You might want to use base-10 blocks for the overhead if you have them. Show 53 Trade a long for 10 cubes. Take 38 away. Example: Model =? as follows: 1. Count out five 10s and three 1s to represent 53. Lay these on the table, with longs to the left of the cubes. 2. Ask: Are there enough longs and cubes on the table so I can remove exactly 38 (3 longs and 8 cubes)? No. There are only 3 cubes on the table, so it s not possible to remove 8 cubes. 3. Trade a long for cubes: Remove one of the longs that is used to represent 53 and replace it with 10 cubes. 53 is now represented by 4 longs and 13 cubes. 4. Remove 38 (3 longs and 8 cubes) from the table. 5. Record the answer (difference) on the board. 15 Repeat the steps as needed. Model problems that involve 2- and 3-digit numbers. Use any strategy to solve Solving Subtraction Problems (Math Journal 1, p. 144) PARTNER Math Journal 1, p Partners work together to solve the subtraction problems. For Problems 1 4, children are expected to continue using base-10 blocks; many will actually trade 1 long for 10 cubes. Some children might simply move one of the longs next to the pile of cubes and answer the problem without actually exchanging the long for cubes. 404 Unit 6 Whole-Number Operations and Number Stories

5 2 Ongoing Learning & Practice Playing the Number-Grid Difference Game (Math Masters, pp. 418 and 463; My Reference Book, pp. 140 and 141) PARTNER Children practice subtraction skills by playing the Number-Grid Difference Game. Children will find directions on page 140 of My Reference Book. Math Boxes 6 5 (Math Journal 1, p. 145) INDEPENDENT Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 6-1 and 6-3. The skills in Problems 5 and 6 preview Unit 7 content. Home Link 6 5 (Math Masters, pp. 169 and 170) INDEPENDENT Home Connection Children subtract by crossing out cubes. Before sending this Home Link with the children, go over the example and make sure they understand that each long shows 10 connected cubes. Date LESSON 6 5 Math Boxes 1. Circle the one that is likely to happen. It is likely that... you will do a Math Box today. you will fly like a bird. an elephant will visit the classroom. 3. Kurtis scored 13 points in the first half of the game and a total of 24 points by the end. How many points did Kurtis score in the second half? 11 points Which number occurs most often? Choose the best answer. 8, 17, 9, 8, Student Page or Time Math Journal 1, p Measure the line segment. about about 6. Use your calculator. Count by 9s. Start at in. cm 4. How many dots are in this 7-by-9 array? ,,,, 112, 121 What pattern do you see? Sample answer: The number in the ones place goes down by one. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 1 Use Math Boxes, Problem 1 to assess children s knowledge of probability language. Children are making adequate progress if they circle the correct answer. [Data and Chance Goal 3] Home Link Master HOME LINK 6 5 Subtracting with Base-10 Blocks Home Link Master HOME LINK 6 5 Subtracting with Blocks continued Family Note In this lesson, your child found the answers to subtraction problems by using longs and cubes to represent tens and ones, respectively This will help your child understand the concept of subtraction before he or she learns to subtract using a step-by-step procedure, or algorithm, with paper and pencil. When you see the problems on this Home Link, you may be eager to teach your child to subtract the way you were taught. Please wait the introduction of a formal algorithm for subtraction will be taught later in second grade. Please return this Home Link to school tomorrow. Show subtraction by crossing out cubes. Example: long cube are shown in all? cubes. How are shown in all? cubes. How are shown as separate cubes and as part of the longs? 23 cubes. How are shown in all? cubes. How are shown in all? cubes. How are shown in all? cubes. How Math Masters, p. 169 Math Masters, p. 170 Lesson

6 Teaching Aid Master Place-Value Mat hundreds tens ones Math Masters, p Differentiation Options READINESS Playing the Base-10 Trading Game (Math Masters, p. 427) PARTNER Min To provide experience with subtraction using a concrete model, have children play the Base-10 Trading Game. Begin with a bank that has 20 longs and 40 cubes. Each partner begins with 1 flat on their Place-Value Mat. Rules: Take turns. On each turn, a player does the following: 1. Roll the dice and find the sum of the dice. 2. Return that number of cubes to the bank. (When there are not enough individual cubes, make exchanges.) 3. The player not rolling the dice checks on the accuracy of the transactions. 4. The first player to clear their Place-Value Mat wins the game. ENRICHMENT SMALL-GROUP Analyzing a Subtraction Strategy (Math Masters, p. 171) Min LESSON 6 5 Meredith uses an interesting strategy for solving subtraction problems when you have to trade. Try to figure out how it works On my first step, I get 12. On my second step I get is my final answer On my first step, I get 14. On my second step I get is my final answer First Step: Second Step: Final Answer: Teaching Master A Subtraction Strategy To apply children s understanding of subtraction, have them analyze a subtraction strategy. When children have figured out the strategy and applied it to solving a new problem, have volunteers share explanations of the strategy and how they figured it out. Sample answer: I noticed a pattern that in the first step, only the tens place changed. Then I figured out you add back the difference between your second number and a multiple of ten. Ask: What is easy about Meredith s strategy? Sample answer: You always subtract a multiple of 10 and then add some back on. Ask: What is hard about Meredith s strategy? Sample answer: Sometimes it s hard to remember what to add back on. Try This First Step: Second Step: Final Step: 45 Math Masters, p Unit 6 Whole-Number Operations and Number Stories