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Find Area by Tiling and Multiplying Side Lengths

Students will tile rectangles with unit squares and count them to find area, then discover that multiplying the length by the width produces the same result. They will connect the array structure of tiled rectangles to multiplication facts.

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Find Area by Tiling and Multiplying Side Lengths

Grade 3 · Area and Multiplication · question 1 of 3

0 of 12

12 rungs. A star at the top.

ABeach square one square unit

Hana covers shape B on the classroom floor with square tiles. How many tiles does Hana need to cover shape B?

Count the squares shape B covers.

How it is taught

0:00 of 3:31

Tiling with unit squares fills the rectangle.

Multiplying the side lengths counts those squares.

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Read it: Count inside, walk around

You have a frame, three cells by four. Twelve cells sit filled inside. Then walk all the way around.

  1. Count the filled cells inside: twelve.
  2. Walk the four sides: four, three, four, three.
  3. Say twelve inside and fourteen around the edge.

Counting every filled cell from one works, but it is slow, and mixing in the edge cells double-counts corners.

The twelve inside cover the floor, while the fourteen round are only the fence.

Three rows of four make twelve inside without walking the edge at all.

Count the cells inside, then walk all the way around: two measurements of one shape.

Counting the walk around and saying fourteen cells fill the frame.

Fourteen is the edge; the fill is twelve cells inside.

A rectangle is 3 squares by 2. How many squares cover it? — 6. 3 rows of 2 squares: skip-count the rows — 2, 4, 6.

4 × 6 rectangle

Here's a rectangle. We'll find its area — the space inside.

Grade 3 · Tile a rectangle, then multiply the sides

Let's cover it with unit squares — little tiles, each one square unit.

The first row has six tiles. One, two, three, four, five, six.

And there are four rows just like it.

We could add them up: six plus six plus six plus six is twenty-four.

But there's a faster way — the tiles make a multiplication array!

The width is four — four rows tall.

The length is six — six tiles across.

So the area equals four times six.

Four times six is twenty-four square units. Same answer, much faster!

Area equals length times width. Twenty-four square units. Great work!

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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