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
The lesson
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.
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Where it sits
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Where this leads
8 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.