Same Math › Grades 4–5 › Area model for division
How does the area model for division work?
The area model treats division as a missing side. You know the area (762) and one side (6). Kids build the rectangle in easy chunks, and the chunks along the top add up to the answer.
- Take a big easy chunk: 6 × 100 = 600.
- Keep going with what's left: 6 × 20 = 120, then 6 × 7 = 42.
- The top adds to the answer: 762 ÷ 6 = 127
Why schools teach it
Division becomes multiplication in reverse
Fourth graders are expected to divide using strategies based on place value and the relationship between multiplication and division, and the standard names rectangular arrays and area models as ways to show it (4.NBT.B.6).
Kids who already know the area model for multiplication see division as the same rectangle with the top missing. Each section is a multiplication fact they can check.
At the kitchen table
What to say, and what to skip
Say this
How many groups of 6 can you take in one big chunk? 100?
How much is left after that chunk?
What's the side of each box?
The numbers on top are the answer pieces.Do your boxes add up to 762?
A built-in check.
Skip this
Use long division.
The standard algorithm is a 6th-grade standard. The area model comes first.- Insisting on the biggest chunk.Smaller chunks take more boxes but are just as correct.
- Forgetting to subtract after each box.Each new box uses what's left, not the whole number.
See it in action
Solving 952 ÷ 7 with boxes
First box: 7 × 100 = 700
952 − 700 = 252 leftSecond box: 7 × 30 = 210
252 − 210 = 42 leftThird box: 7 × 6 = 42, then add the tops
100 + 30 + 6 = 136
Check: 7 × 136 = 952. The boxes make the check easy.
Free practice sheet
Make an area model division sheet
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Parents also ask
How is this different from partial quotients?
Same math, different picture. Partial quotients writes the chunks in a list; the area model draws them as boxes.
Does it work with remainders?
Yes. Whatever is left that's smaller than the divisor is the remainder.
Does it work with two-digit divisors?
Yes, that's the 5th-grade version (5.NBT.B.6).
Do the boxes need to be to scale?
No. They just need to be labeled.