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Concrete Learning for Subtraction with Regrouping

Earlier in the week, I wrote about the importance of following the concrete, representational, abstract (CRA) sequence for math instruction. One thing I failed to mention is that the types of learning should overlap. It’s not all concrete, then all representational, and finally all abstract. You have to connect the abstract to the concrete or representational or the symbols remain abstract. In this post, I’ll show you what I mean using subtraction with regrouping as an example.

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In this video, you see a student modeling subtraction with regrouping over zeros using base-10 blocks (concrete), but also recording her work using the standard algorithm (abstract), so you see the connection between concrete and abstract learning.

Using the manipulatives builds understanding for the abstract process! While it might seem like it takes more time to use manipulatives, it actually saves time in the long run. Don’t skip that step! If a student doesn’t understand the place value concepts behind subtraction with regrouping, spending additional time practicing the algorithm at the abstract level, with no concrete support, won’t build understanding. It’s difficult to memorize procedures that you don’t understand. Using base-10 blocks alongside the algorithm helps to reinforce the understanding of the part place value plays in subtraction with regrouping.

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  1. Will you have a lesson on TPT similar to this but more geared for 4th grade? I see that the one listed is for 2nd grade…

    1. I have a number of products for 4th grade, Cassidy, but not one exactly like the one shown. I try to incorporate CRA into all of my products!

  2. I am a firm believer we should incorporate manipulatives with our daily lessons. Math is such an abstract subject that children need to see concrete representations of what it is they are working out and like you mentioned it should be a combination of concrete, representational and abstract. Great Post

  3. Do you lace the first number out like 32 and subtract the other group by putting out like 25 and then showing how you subtract it?

    1. No, for subtraction, you only build the number you are starting with. So you would build 32 and then take 25 out of that. Since you can’t take 5 ones away from the original number (because there are only 2 ones), you have to trade a ten for ten ones. Then you have 32 built as 2 tens and 12 ones, so you can take out the 25.

  4. I love your stuff Donna! I would love to use this video in a professional development. I was just going to make my own but I can use yours now! Wish I could save the video but I can’t figure out how.

    Do you have a video similar to this on using addition and an open number line to subtract? I always have a large group of students at my school who refuse to start with the ones so I wanted to offer my teachers the counting on with an open number line as a strategy for those kids instead of trying to make them think like us.

    As a math specialist, I am working really hard to help my teachers understand that we must balance procedures with conceptual understanding.

    Thank you for getting good math out there!

  5. I have done this for years, usually starting with just the blocks, then evntually moving to recording on paper. Unfortunately, teachers at mly school only give the blocks a brief time in favor of digging into the algorithm alone. I don’t know if the idea of not having enough one, tens,etc. , to subtract even comes up. Students are just taught to look for the “big” number and go from there.

  6. Would you be able to share this video with me for a professional development day with early elementary level teachers? I LOVE all of your materials and feel it would be more beneficial for them to hear you say it than me:)

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