Compensating to Compute Larger Numbers

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Objective

SWBAT use compensation to check the addition and subtraction algorithms for accuracy.

Big Idea

Students will make numbers friendlier before computing and will compensate the answer later on.

Opening

20 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 represent their thinking using an open number line model.

Task 1: 8,200 - 800

For the first task, students subtracted parts of 800 from 8,200. For example, this student subtracted 200 to get to the landmark number, 8,000, and then she subtracted the rest of the 800: 8,200-800

 

Task 2: 92,000 - 8,000

During the next task, some students chose to decompose the 8,000 and then subtract one part at a time: 92,000-8,000. Other students showed how to Subtract Down or Add Up.

 

Task 3: 520,000 - 80,000 

For the final task, students decomposed 80,000 in a variety of ways and subtracted: 520,000-80,000. To help some students, I drew a Model on the Board to help students see the connection between 520 - 80 and 520,000 - 80,000. 

 

Teacher Demonstration

45 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. 

PowerPoint Presentation 

In order to continue providing students with compensation practice, I created a PowerPoint presentation called, Compensation Practice Day 2. This way, I could continue to provide students with a rigorous learning progression. Yesterday, students did a great job adding and subtracting 2-digit to 4-digit numbers and checking their work using compensation. Today, I wanted students to continue applying the compensation strategy to 5-digit and 6-digit numbers.

Goal & Vocabulary 

To begin, I showed the first slide, which was the Goal and reminded studentsRemember, your goal is to be able to say, "I can check the addition and subtraction algorithms using compensation." We reviewed the meaning of compensation: Compensation Meaning. Then, we took another look at the Compensation Example

Guided Instruction

We then moved on to the first problem, 61,027 + 29,985. I asked students: What could I add or subtract to make this an easier problem to solve? A student suggested, "Take away 27." I then Modeled on the Board as the student directed the calculations. Other students began coming up with their own strategies on their white boards. Here, one student is Compensating by Subtracting 1,027. Another student decided to try Adjusting Both Addends by subtracting 27 from one addend and adding 15 to the other addend. I was excited to see that this student correctly added the 27 and subtracted the 15 to adjust the solution.

At this point, we moved on to solving the rest of the problems in the same fashion: (61,027 - 29,985482,160 + 179,000, and 482,160 - 179,000).

For the last task students used multiple strategies. Here, Student Strategy 1, a student adds 840 to the first addend and 1,000 to the second addend. Later, he subtracted 1,000, then 800, and then 40. Another student, Student Strategy 2, solved this problem by subtracting 160. Then, he tried a second strategy where he subtracted 160 the minuend and added 1,000 to the subtrahend. Once students were given plenty of time to practice compensating, we then shared, discussed, and modeled student strategies as a class: Model 482,160-179,00.

Student Practice

30 minutes

For independent practice time, I created 2 practice pages by copying & pasting portions of worksheets found at Math-Aids.com. I wanted to provide students with the space necessary to check the addition and subtraction algorithms using compensation: Compensation Practice Page 2. As students finished, they compared their answers with others at the back table.

During this time, I conferenced with as many students as possible to question, encourage higher-level thinking, and to provide support.