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Use the Distributive Property to Find Area

Students will use tiling to show that the area of a rectangle with side lengths a and (b + c) equals the sum of (a × b) and (a × c). This models the distributive property visually and connects area to algebraic reasoning.

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Use the Distributive Property to Find Area

Grade 3 · Area and Multiplication · question 1 of 3

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12 rungs. A star at the top.

ABCeach square one square centimeter

Sam is making a sticker mat from grid shapes. He adds up the squares in shape B to see how big it is. What is its area?

Shape B can be cut into two rectangles. Add their areas.

How it is taught

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A split rectangle still has the same area.

Multiply the shared side by each part, then add.

Read it: Cut it, then add the parts

A 3 by 5 rectangle. Cut 5 into 3 + 2. 3 × 3 = 9 and 3 × 2 = 6, so 9 + 6 = 15.

  1. Cut the shape into rectangles along a line.
  2. Find the area of each part.
  3. Add the parts: 9 + 6 = 15.

Cutting does not add or take away a square, so the parts make the whole.

3 × 5 is the same as 3 × 3 and 3 × 2 put together.

An L-shape is 2 rectangles too, so cut it and add the parts.

To find an area, cut the shape into rectangles and add their areas.

Adding the side lengths, 3 + 5, instead of the squares.

Area counts the squares inside: 3 × 5 = 15, not 3 + 5.

A rectangle is 7 by 7. Split 7 into 4 + 3. What is its area? — 49. 7 × 4 = 28 and 7 × 3 = 21; 28 + 21 = 49.

4 × 6 by splitting into 4 × 4 and 4 × 2

Today we'll find the area of a rectangle by splitting it into two easier pieces — that's the distributive property!

Here's a rectangle. It's four squares tall and six squares wide.

Grade 3 · Splitting rectangles to make multiplication easier

To find the area, we multiply: four times six.

But what if we split the rectangle into two smaller pieces? It might be easier!

Let's split the six into four plus two. Now we have a four-by-four piece and a four-by-two piece.

The left piece is four times four — that's sixteen squares.

The right piece is four times two — that's eight squares.

Add the two pieces together: sixteen plus eight equals twenty-four.

So four times six is twenty-four. Splitting the rectangle made the multiplication easier!

Now you try. Find the area of this rectangle. What is the area?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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