Addition Strategy: Compensation

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Addition Strategies - Compensation - Upper elementary place value lesson, pictures, and resources
Let’s talk about compensation.

This is a strategy where you manipulate numbers to create friendly numbers. These friendly numbers are easier to add.


Example 1: 87 + 399

  • You take 1 from 87 and move it to 399
  • Now you have 86 + 400
  • 86 + 400 = 486

You’ve now made a simpler problem to solve.


WHY DOES THIS STRATEGY WORK?

Let’s look at some vocabulary words.

addend + addend = sum

When we took 1 away from one addend and moved it over to the other addend, we changed the expressions, but the value stayed the same.

This is a great time to take out those base 10 blocks and show students why this works.

place value concepts - addition and subtraction strategies place value concepts - addition and subtraction strategies


Example 2: 128 + 597

  • You take 3 from 128 and give it to 597
  • Now you have 125 + 600
  • 125 + 600 = 725

place value concepts - addition and subtraction strategies


WHY BOTHER WITH THIS STRATEGY?

Students sometimes make careless mistakes when faced with difficult addition problems. When students create friendly numbers, their accuracy and efficiency increases.


USE A VARIETY OF EXAMPLES

Use examples where students have to move more than 1 to make friendly numbers.

Example 3: 348 + 570

  • You take 30 away from 348 and move it to 570
  • Now you have 318 + 600
  • 318 + 600 = 918

place value concepts - addition and subtraction strategies

Use examples where students can apply the strategies to either addend.

Example 4: 286 + 135

  • You take 14 away from 135 and move it to 286
  • Now you have 300 + 121
  • 300 + 121 = 421

place value concepts - addition and subtraction strategies


ANOTHER VISUAL

You can use connecting cubes to show how the strategy of compensation works. Below is a very common way it is used. When one of the addends is 9, you can take 1 away from the other addend to make a ten.

9 + 4 = 10 + 3 = 13

place value concepts - addition and subtraction strategies  place value concepts - addition and subtraction strategies

Again, a variety of practice problems should be used. Below is another example where students take 10 away from the second addend and move it over to the first addend.

place value concepts - addition and subtraction strategies

WHAT ABOUT SUBTRACTION?

My next blog post will be about how you can use the compensation strategy in subtraction, so stay tuned!


SHOP PLACE VALUE RESOURCES


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Mrs. Santillana

Mrs. Santillana

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