When teaching multi-digit addition and subtraction with regrouping, it can be tempting to jump straight to the standard algorithm. But when students simply memorize steps without understanding why place values shift, procedural errors quickly multiply.
To build lasting mathematical capacity, we need to honor the CRA (Concrete-Representational-Abstract) learning model.
In my latest video demonstration using MathReps 3.2 on Wipebooks, I break down how pairing physical place value disks with expanded form addition helps students bridge the gap between concrete reasoning and abstract algorithms.
Why This Bridge Matters
Physically counting, bundling, and trading number disks alongside written expanded form gives students a visual and tactile anchor for place value. They aren’t just “carrying a 1”, they are physically exchanging 10 tens for 1 hundred.
By using dry-erase Wipebooks, students can move, erase, and manipulate numbers in a low-risk environment before transitioning into traditional symbolic math.
Check out the full video walkthrough here, and grab ready-to-use templates on MathReps.com!
How do you help your students visualize regrouping in place value? Do you use number disks, base-ten blocks, or expanded form? Let’s discuss in the comments!
Lisa, the disks would be handy for 402 − 178, where the zero can make the first trade hard to see. On the place-value mat, trade one hundred for ten tens, then one of those tens for ten ones. Have students record the two trades as 400 + 2 = 300 + 100 + 2 = 300 + 90 + 12 before subtracting. A quick partner check could be, ‘What changed on the mat, and what stayed the same?’ That gives them a reason for the 9 tens and 12 ones they’re about to use.
Exactly! Love partner checks.