SWBAT use compatible numbers to check for reasonableness when subtracting multi-digit numbers.

Students will round the subtrahend and minuend to numbers that work well together to determine if an answer is reasonable.

15 minutes

**Today's Number Talk**

For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to use their knowledge of decomposing to subtract.

**Tasks 1: 89 - 56**

For the first task, students were able to successfully decompose to solve: 89-56 Student Example A. This student surprisingly checked for reasonableness: 89-56 Student Example B. However, here's the student that surprised me the most: 89-56 Student Example C. I loved how he came up with: 89-56 = (40-20) + (40-30) + (5-3) + (4-3). Others were so inspired that they immediately tried using his strategy!

**Tasks 2:** **689 - 56**

During the next task, students decomposed in a variety of ways: 689-356 Student Example A. I really enjoyed watching this student replicate another student's strategy: 689-356 Student Example B!

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40 minutes

**Reasoning for Teaching Multiple Strategies**

During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively. I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility.

**Goal**

I began today's lesson by explaining the goal written on the board: *I can use compatible numbers to check for reasonableness when subtracting multi-digit numbers. *I explained: *Compatible numbers are numbers that work well together. *I wrote an example problem on the board: 21 +28 on the board and continued: *For example, if I had the problem 21 + 28, I could think of the 21 as being close to 25 and the 28 as close to 25 too. If I add 25 + 25, I'll know that a reasonable answer should be around 50. Now, what is the exact solution to 21 + 28? *Students responded quickly, "49!" *Is 49 close to 50? *"Yes!" *Then this tells me that my answer is... *Students piped in, "Reasonable!"

**Vocabulary**

We then moved on to vocabulary development. I first began by reviewing key vocabulary from yesterday's lesson (addend, sum, algorithm, and checking for reasonableness). Then, I moved on the today's key vocabulary: *Today, I want to continue using high-level math vocabulary when you are turning and talking about the reasonableness of answers.* By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments).

I then taught students the terms, difference, minuend, and subtrahend using the Subtraction Vocabulary Poster. After teaching new vocabulary, I always give students time to absorb the new information by turning and talking: *Tell someone next to you what the minuend is!*

**Finding Compatible Numbers**

I explained: *Remember, today we are going to be finding compatible numbers (numbers that work well together) to check for reasonableness. Let's practice this together! *Using the Checking for Reasonableness Poster, we discussed how to make sure answers are not too high and not too low.

**Guided Practice**

I continued: *As I model each problem on the board, please use your white boards to practice finding compatible numbers with me! *Prior to the lesson, I created a list of problems (with increasing complexity) on the board prior to the lesson:

- 92-52
- 112-48
- 156-49
- 124-26
- 572-53
- 1291-48

Pointing to the first problem, I asked students: *What compatible numbers could we use to check the solution to this problem? *Hands shot up quickly, almost as if it was a game! One student said, "92 is close to 100." Another offered, "52 is close to 50." I wrote the the "approximately equal to sign" (below) followed by 100 - 50. *Okay, everyone, what it is 100 - 50? *"50!" *Is this the exact answer? *"No" *What is the exact answer? *"40!" *Is 40 close to 50? *There were mixed views on this question. Some students felt that 40 and 50 were not close at all! So then I asked, *Well, what if we had gotten 124 as a solution. Would we know that our answer is reasonable or unreasonable? *We continued in this same fashion, solving each problem on the list: Compatible Numbers Practice.

Then, I asked:* Do you think you are ready to practice this on your own? *The room filled with excitement!

45 minutes

To help students meet today's goal, I wanted them to practice solving the algorithm and checking their answers by finding compatible numbers so I choose the following practice page from the Grade 4 Module 1 Engage New York Unit found online:

Practice Page: Subtraction Algorithm Practice

**Algorithm Practice**

At first, I asked students to solve each problem using the standard algorithm. To make sure all students remembered the steps of subtraction, we solved the first row altogether, step-by-step. Then, I asked students to continue on with group members.

During this time, I conferenced with students and checked for understanding. Some students needed extra support with borrowing across zero, remembering to subtract instead of add, and/or subtracting down instead of subtracting up.

Once finished, I asked students to check their work with a partner. I do this specifically to support Math Practice 3 (Construct Viable Arguments) and to provide students with opportunities to discuss possible mistakes when they have arrived at two different answers.

**Practice Finding Compatible Numbers to Check for Reasonableness **

Next, I modeled (Teacher Model) how to Use Compatible Numbers to check each problem in the first row for reasonableness. Thereafter, students got right to work!

During work time, I asked guiding questions, such as: *How do you know your answer is reasonable? *Here's an example of a student conference during this time: Finding Compatible Numbers.

The most challenging part of completing this page was the last problem. Since I hadn't taught my students how to use a tape diagram (bar diagram) yet, I chose to model this on the board: Teacher Support with Last Problem. Then, students were able to find success: Student Example of Last Problem.

Again, as students finished checking each problem for reasonableness, they checked their answers with a partner. Most students were able to reach the goal: Student Practice Page Example.