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How Many More? Comparison Subtraction

Comparison subtraction is really tricky for kids. Part of that is a 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.

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A common way to phrase comparison subtraction problems 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, they 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 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. Consider 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.

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  1. My firsties always struggle with this too. I also do concrete examples with manipulatives or draw pictures when I can’t. I have them line up the two groups and I rephrase the question at first to “How many extras are there?” I teach my students to take the partners away. That shows how many extras are left and then I restate the original question as intended and they give me the answer. We go over this several times and then I slowly stop rephrasing the questions to where they knwo what I’m asking when I say “How many more ____ does ______ have than ______?” We also switch it to how many fewer (or at least our program does- we use Scott Foresman). Is this okay? What do you think? I love your cards too!!

    1. All AWESOME ideas! You do a great job of scaffolding a tough skill. I especially like the “How many extras?”. Isn’t virtual collaboration great?!

    2. Donna,
      I was wondering, what do you think is the best way to keep our first graders from confusing how many more with some more or 2 more . My group thinks when they see more they add just because they have seen it so much already, and it was add in those situations. Any suggestions for explicit language to separate the 2 problem types? Thanks ahead of time
      Amy Terry

    3. I think exposure to it is a big factor. One way I like to word it is a two part question: “Who has more? How many more?” That seems to help.

  2. Donna-this is just what I was looking for! We have been trying several different ways to understand the wording of these types of story problems and your strategy and cards are perfect! THANK YOU!

  3. Donna, this is perfect for what I am working on with the child I am tutoring. How would you suggest how to teach her to write a number sentence with these comparison story problems?

    1. Since this is referring to comparison subtraction, it would be a subtraction number sentence. So for the first picture in the post, the number sentence would be 5-3=2 to show that 5 is 2 more than 3.

  4. This was SO helpful. I work with 3-5th special education, and had never encountered this problem before. I had already done the manipulatives, and they still weren’t getting it. The card over the same units will be my next try. I had honestly RUN OUT of ideas! Thank you so much.

  5. I find that Cuisenaire rods are an excellent tool for showing this as well. We line them up with one on top so you can see the number that is larger and then we find the rod that makes the difference. For those firsties ready for it, we bridge the ten to help by figuring out the distance from each to ten and add those two distances together. So 14-8 becomes 4+2 for a total of six.

  6. I found that when they first are doing these I add the question, โ€œhow many more does โ€”- need to have the same amount. That helps them understand what they need to look for. It is a very hard concept in first!

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