Area by Tiling
Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths
What a learner can do afterwards
- Tile a 4×6 rectangle and count 24 squares, then verify 4×6=24
- Explain why the number of rows times the number in each row gives the area
- Draw a rectangle on squared paper, tile it, and write the multiplication
1 · Read
You already know area tells you how much surface a shape covers, measured in square units. One way to find the area of a rectangle is tiling: cover it completely with unit squares, no gaps and no overlaps, then count them.
Leo tiles a rectangle that is 3 squares tall and 5 squares wide. He counts the squares in one row: 5. He has 3 rows just like that one, so the total is 3 x 5 = 15 squares, without counting one by one.
You never have to count every square. Count how many squares are in one row, count the rows, then multiply: rows times squares per row gives the area.
Tiling a rectangle with unit squares shows why its area equals rows times columns, so you can multiply instead of counting one by one.
2 · Watch
3 · Play
Tap squares to build a shape, and watch its area and perimeter change.
Take it off screen
Where it sits
This opens up
Where this leads
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.