Number Talks: Subtraction Strategies Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success February 25, 2016

Learning Intention & Success Criteria We are learning to understand how Number Talks can expand students’ understanding of subtraction. We will be successful when we can use reasoning strategies when solving subtraction problems.

Reviewing Division

No Standard Algorithm Please! Solve this problem two different ways Use an array model for one way. How are the strategies similar? 549 ÷ 8 No Standard Algorithm Please! Turn and Talk: What are the underlying skills students need to have in order to become fluent at division? This is done as a review from last time and a bit of homework practice using the array model. The big ideas from last time – division is related to multiplication because you are technically thinking about “how many groups of 8 will I need to get close to 549?” Division is then related to subtraction because you are removing equal amounts/groups in order to get as close to the dividend as possible.

Procedural Fluency from Conceptual Understanding What do we want students to be able to understand about division? Understanding the quantities Related to multiplication Subtraction of equal groups “Make sense of” the answer in relation to the problem

Thinking About Subtraction

Subtraction is Subtraction…Right? The baseball team had 84 balls in the bucket for batting practice. In the first round, there were 15 balls hit into the stands. How many balls were left for round 2 of batting practice? The temperature in Austin, TX was 84°. The temperature in Milwaukee, WI was 15°. How much cooler was it in Milwaukee than in Austin, TX?

Subtraction – Chapter 4 Read paragraph 1 and 2 on pg. 37. How does the information add to our understanding of subtraction and the need to use number talks to help students think about subtraction ideas?

What makes subtraction so hard??? Students need to understand the relationship between quantities is different than addition. (7+8=15, 15-8=7) Subtraction is often thought of as “take away” and not as a difference/distance. “Thinking backwards” is harder. We spend more time on addition than subtraction.

No Standard Algorithm Please! How would you solve? 63 – 28 Solve in two different ways. Add a name to your strategy. Add a representation if possible. No Standard Algorithm Please! Turn and share Look for people who solved the problems in a similar manner. Label 5 charts…each chart has the name of one of the strategies. We can chart the strategies - or we can sort people according to the strategies they used.

Five strategies for Subtraction p. 38 - 41 Round the subtrahend to a multiple of ten and adjust. (Use a nice number and compensate) Decompose the subtrahend. (Subtract in parts) Add instead. (Add up) Same difference. (Change to an easier equivalent number) Break apart by place. (Subtract each place)

Time to study Read pages 38 – 41. Study each strategy. Which strategies seem to be a bit more difficult to wrap your head around? 73 -28 to use just in case.

Fold your paper into four parts. You Choose! Fold your paper into four parts. Given a problem, pick a strategy. Then solve it using that strategy. WAIT . . . . . . . . . . . . . . . . . Pass your paper to another person. That person studies the work and identifies which strategy was used.

Pick a strategy. Solve it. Strategies Subtract each place Subtract the number in parts Add up from the subtracted number Use a nice number then compensate Change to an easier equivalent problem 82 – 47 = ? Exchange papers. Study the work. Name the strategy. Then repeat. You can pick the same problem, but you must pick a new strategy; or vice versa, pick a different problem but try the same strategy.

Pick a Strategy. Solve it. Strategies Subtract each place. Subtract in parts. Add up. Use a nice number then compensate. Change to an easier equivalent problem. 1.03 - .96 = ? Exchange papers. Study the work. Name the strategy. Then repeat. You can pick the same problem, but you must pick a new strategy; or vice versa, pick a different problem but try the same strategy.

Pick a Strategy. Solve it. Strategies Subtract each place. Subtract in parts. Add up. Use a nice number then compensate. Change to an easier equivalent problem. 3 1/3 – 5/6 = ? Exchange papers. Study the work. Name the strategy. Then repeat. You can pick the same problem, but you must pick a new strategy; or vice versa, pick a different problem but try the same strategy.

Pick a problem. Pick a strategy. Strategies Subtract each place. Subtract in parts. Add up. Use a nice number then compensate. Change to an easier equivalent problem. 576 – 239 = ? Exchange papers. Study the work. Name the strategy. Then repeat. You can pick the same problem, but you must pick a new strategy; or vice versa, pick a different problem but try the same strategy.

Pick a problem. Pick a strategy. 23 1/10 – 10 4/5 = ? Strategies Subtract each place. Subtract in parts. Add up. Use a nice number then compensate. Change to an easier equivalent problem. Exchange papers. Study the work. Name the strategy. Then repeat. You can pick the same problem, but you must pick a new strategy; or vice versa, pick a different problem but try the same strategy.

Learning Intention & Success Criteria We are learning to understand how Number Talks can expand students’ understanding of subtraction. We will be successful when we can use reasoning strategies when solving subtraction problems.

Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.