How to Use the Compensation Strategy for Addition

What are some of the strategies you teach your students or children to add two and three digit numbers?  Do you use compensation?  Or do you begin teaching with the standard algorithm?  Teaching students to be flexible in their strategies makes them more likely to persevere and find a solution.  One of the many strategies I have been teaching my students to use is making a ten.  The next step is teaching compensation which utilizes a number close to a ten (10, 20, 30, 40, 50, etc.).

Compensation is defined as adjusting one number when adding.  See the example below:


But hold on!  In some math textbook series, this is referred to as transformation!  So what is the difference?  In my research, the difference between compensation and transformation is that in compensation only one number at a time is adjusted, while in transformation, both numbers are adjusted simultaneously.  Though it seems like semantics, it does make a difference when teaching this strategy to second graders!

In my district, we happen to use the Go Math textbook. Though we are encouraged to NOT use it as intended but to focus on the standards, number talks, math talk and teaching students strategies I still use it for practice (students have consumables).  In Go Math, this process of adjusting numbers is referred to as compensation.


Since I have Math Their Way training, I try to start teaching a concept or a strategy at the concrete level which is defined as using manipulatives only.  Eventually, we move on to the connecting level in which numbers and symbols are now associated with the use of manipulatives, and then we move onto the symbolic level, in which students use paper and pencil.

Before I began teaching the strategy, I made some work mats that were double-sided and would help add some structure to the lesson.



Download the Compensation Strategy Work Mats here as a PDF!

In the examples below, we started learning compensation by only using manipulatives to represent numbers.  I also used a Number Talk in which I showed number models similar to the ones below and asked the students to find out how many there were.  Students shared various strategies, including counting on, making a ten, grouping tens and ones, etc.

I would give the students two numbers that they had to represent on either side of the zigzag line.  For this part, I had the students work together as partners sharing one mat since I was limited in the number of manipulatives I had for this lesson.

The students would physically move the ones over to one side to complete a ten.  Note that we did not trade the new ten for a rod (that comes later when we focus on regrouping).


Now that the students had an understanding of the concept of adjusting or compensating numbers, it was time to put manipulatives away and go to drawing models for the number as well as adding numbers and symbols for addition.

We used the boards to practice this at least 5 times before I could see that the majority could do use this strategy independently.    From there it was time to go to the symbolic level and practice in the math consumable.

Here's a video of one of my students using this strategy independently.

What other strategies do you use for teaching addition with two and three digits?  Please share below in the comments!

If you would like to make your own mats for teaching the compensation strategy, download this PDF!  Just print out on cardstock, laminate, and you're ready to go!

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