Same Math › Grades 3–5 › Area model
What is an area model?
An area model multiplies big numbers by splitting them into tens and ones and drawing a box for each piece. Your child multiplies the small pieces, then adds the boxes together.
- Split each number by place value: 23 is 20 + 3, and 14 is 10 + 4.
- Multiply the top of each column by the side of each row: 20 × 10, 3 × 10, 20 × 4, 3 × 4.
- Add the boxes: 200 + 30 + 80 + 12 = 322
Why schools teach it
It shows where the digits come from
In the method most of us learned, you stack the numbers, carry, and add a zero on the second line without knowing why. The area model shows that the "zero" is really multiplying by 10. Kids who understand that make fewer place-value mistakes.
It comes first, not instead. Common Core expects the area model in 4th grade and the standard stacked method by 5th grade. The same picture comes back in algebra, where (x + 3)(x + 4) is drawn exactly the same way.
At the kitchen table
What to say, and what to skip
Say this
How can we split 23 into tens and ones?
Which box do you think will be the biggest? Why?
It teaches them to estimate before calculating.Did you fill in every box?
A missed box is the most common mistake.Does your answer look about right? 23 × 14 is a bit more than 20 × 14.
Skip this
Just stack them and carry the one.
The stacked method comes in 5th grade. Showing it early often mixes the two up.Ignore the zeros and stick them on at the end.
That trick hides the place value the boxes are teaching.- Insisting the boxes be drawn to size.They don't need to be. The labels matter, not the shape.
See it in action
How a 3rd or 4th grader solves 36 × 7
Split 36 into tens and ones
36 = 30 + 6Draw a box for each part and multiply each by 7
Add the boxes
210 + 42 = 252
30 × 7 is just 3 × 7 with a zero, so the hard part becomes two facts kids already know.
Free practice sheet
Make an area model sheet
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Parents also ask
Why not just teach the normal way?
They will, in 5th grade. The area model first makes sure kids know why the stacked method works, so they can catch their own mistakes.
How is this different from partial products?
It's the same math. Partial products writes the four box answers in a column (200, 30, 80, 12) and adds them. The area model draws them as boxes.
Does it work with decimals or fractions?
Yes. In grades 5 and 6, kids use the same boxes for problems like 2.5 × 4 or mixed numbers.
My child's teacher calls it the box method. Is that the same?
Yes. Box method, area model and rectangle method all mean the same picture.