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:
COMPENSATION OR TRANSFORMATION?
But hold on! Some math textbook series call it transformation! So what is the difference? The research states compensation only adjusts one number at a time while transformation adjusts both numbers 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. The district encourages the teachers to NOT use it as intended. Instead, the district encourages teachers to focus on the standards, number talks, math talk, and strategies. However, I still use the math for practice (students have consumables). In Go Math, this process of adjusting numbers is referred to as compensation.
TEACHING THE STRATEGY
Many years ago, I trained in Math Their Way®. Because of this training, I teach a concept or a strategy at the concrete level. At the concrete level, students use manipulatives only. The next level is the connecting level. The connecting level associates numbers and symbols with the manipulatives or models the students have made. 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.
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).
SWITCHING TO THE CONNECTING LEVEL
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!