Concrete Learning for Subtraction with Regrouping

Provide concrete support for students when teaching subtraction with regrouping.

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

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.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

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.

11 Comments

  1. Cassidy Gibbs

    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…

    Reply
    • Donna Boucher

      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!

      Reply
  2. Nancy Penfield

    I love using base-10 blocks. It helps the student make sense of the problem. I use them as often as I can.

    Reply
    • Donna Boucher

      They are a must-have, must-use resource!

      Reply
  3. Sandra Contreras

    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

    Reply
  4. Amy

    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?

    Reply
    • Donna Boucher

      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.

      Reply
    • Amy

      Never mind I watched video. I get it thanks

      Reply
  5. Nancy

    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!

    Reply
    • Donna Boucher

      Nancy, I can email you the video for your training. Unfortunately, I don’t have one for addition.

      Reply
  6. Iris

    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.

    Reply

Submit a Comment

Your email address will not be published.

Pin It on Pinterest

Share This