Comparison subtraction is really tricky for kids. Part of that is lack of exposure. We typically teach subtraction as take away, and that is certainly one of the subtraction structures. But we need to move beyond that and help students understand that comparing also involves subtraction.
A common wording for comparison subtraction is how many more? There are lots of variations on that phrase: how much taller, how much more, how much faster, how many fewer, etc. Let's look at a problem:
Marla has 5 pieces of candy. Carlos has 3 pieces of candy. How many more pieces of candy does Marla have than Carlos?A very common error is to say 5. In other words, to just say the number that is bigger. I read, I think in Kathy Richardson's How Children Learn Number Concepts, that children hear how much is the number that is more? instead of how many more? I thought that was really interesting.
Another way comparison subtraction can be worded is what is the difference? So the question in our candy problem would sound like What is the difference in the pieces of candy Marla has and the pieces of candy Carlos has?
So how do we help children understand comparison subtraction. Of course it has to be concrete learning--counters, linking cubes, etc. I suggest a linear comparison, as shown in the first picture. Build each number, lining them up one on top of the other. Help students to see that up to a certain point, they had the same number (3), but Martha has 2 more. A good way to ask it is using a two-part question Who has more? How many more? To help students visualize the more part, I thought it would be helpful to cover up the part that is the same and just leave the difference showing. I made the cute little monster cards you see below, but of course you could use an index card or even your hand. Click here to grab a copy of the cards.
Graphing presents another great opportunity to highlight comparison subtraction. If you're doing a daily graphing activity, like the one shown below, the numbers are already lined up for you! Click here to read more about daily graphing.