Why Use Multiple Models?
By using a pictorial model alongside expanded notation, students get a visual and numeric understanding of subtraction. This helps them move beyond memorized procedures to truly grasp why and how regrouping works.
Let’s break it down step by step!
Step 1: Set Up the Problem
We’re working with 736 – 274.
- 736 is represented using pictorial models in a place value chart:
- 7 hundreds
- 3 tens
- 6 ones
- Below, we note in the corner of each place value column what we’re subtracting: 200 + 70 + 4 = 274
Step 2: Subtract Using the Pictorial Model
Subtract the Ones (6 – 4):
- Cross off 4 ones (I like to use x to represent 1s).
- That leaves 2 ones.
Regroup the Tens (30 – 70):
- Uh-oh! We don’t have enough tens to subtract 70.
- So, we regroup 100 into 10 tens (since 100 = 10 tens).
- Now, we have 13 tens total (13 tens = 130)
- We subtract 70 (or 7 tens) from 13 tens, leaving 6 tens (or 60).
Subtract the Hundreds (700 – 200):
- After regrouping, we have 600 left in the hundreds place.
- Subtracting 200 leaves us with 400.
Final Answer: 462
Step 3: Solve Using Base 10 Expanded Notation
Now, let’s represent the numbers in expanded form:
- 736 → 700 + 30 + 6
- 274 → 200 + 70 + 4
Subtracting step-by-step:
- 6 – 4 = 2
- 30 – 70 (not possible, so we regroup from the hundreds)
- Moving 100 over to the 10s place, making it 130 – 70 = 60
- 600 – 200 = 400
Final Answer: 462
The Power of Dual Modeling
Using both pictorial and expanded form models side by side helps students see:
✏️ Why we “regroup” in subtraction
✏️ How place value plays a role in regrouping
✏️ That both methods lead to the same solution, reinforcing accuracy
When students see and practice both models together, they build deeper number sense and mathematical confidence!
Try This in Your Classroom!
You can grab a free MathReps template at MathReps.com and start using this strategy with your students today!
💡 Bonus Resource: Wipebook offers workbooks with four MathReps for second grade, providing structured practice all year long. Check them out!
Nowa Techie 