Today, we’re diving into second-grade math with a MathRep that focuses on addition with regrouping.
In our previous posts, we explored using MathReps for addition and subtraction without regrouping. Now, we’re taking it a step further and tackling regrouping, helping students make the jump from pictorial models to expanded notation and the base 10 system.
So, buckle in—let’s get started!
Step-by-Step Guide: Regrouping with MathReps
Set Up the Numbers
For this example, we’re adding 682 + 234, and we’ll use a pictorial model to visually represent the numbers before transitioning into the expanded form.
Solve Using a Pictorial Model
1️⃣ Start with the Ones Place:
- 2 + 4 = 6
- No regrouping needed here, so we write 6 in the ones place.
2️⃣ Move to the Tens Place:
- We add 8 tens + 3 tens = 11 tens, which equals 110.
- Since 10 tens = 100, we regroup by circling ten tens and moving them into the hundreds place.
- This leaves 1 ten (10) in the tens place.
3️⃣ Move to the Hundreds Place:
- We now have 6 hundreds + 2 hundreds + 1 regrouped hundred = 9 hundreds.
Bringing it all together:
916
Transition to the Base 10 Model (Expanded Notation)
Now, let’s break it down using expanded form:
- 682 → 600 + 80 + 2
- 234 → 200 + 30 + 4
Adding the place values:
- Ones: 2 + 4 = 6
- Tens: 80 + 30 = 110 → Regroup into 100 + 10
- Hundreds: 600 + 200 + 100 = 900
Total: 916
Alternative Thinking: Flexible Number Sense
Instead of regrouping immediately, students can leave the tens as 110 and think of the sum as:
800 + 110 + 6 = 916
This approach challenges students to see numbers flexibly before applying the standard algorithm, deepening their conceptual understanding.
Why This Works
MathReps provide a structured, visual approach that helps students bridge the gap between pictorial models and formal mathematical notation. By working through regrouping in different ways, students develop number flexibility and problem-solving confidence.
Get Your Free MathReps!
Want to try this in your classroom? Download your free MathRep template at MathReps.com and explore even more math resources.
💡 Bonus Resource: Check out Wipebook for workbooks featuring MathReps—each workbook includes four MathReps to last the entire year!
Nowa Techie 