Lesson 7 of 17
Covering a floor with no gaps
Show on a big screenA footpath is laid in grey blocks. Not one gap anywhere.
No gaps, no overlaps
A tiling covers a flat area with shapes. There are no gaps. Nothing overlaps: no shape lies on another.
A 2 × 1 tile is two squares joined, like a domino.
Example: a 4 × 5 grid. Count the squares first: 4 × 5 = 20.
Each 2 × 1 tile covers 2 squares. So 20 ÷ 2 = 10 tiles cover it. An odd count cannot be covered by 2 × 1 tiles.
| Grid | Squares | Can 2 × 1 tiles cover it? |
|---|---|---|
| 4 × 5 | 20 | Yes |
| 3 × 8 | 24 | Yes |
| 5 × 5 | 25 | No. 25 is odd |
Watch out!
An even count is not enough. Shade a 4 × 4 grid like a chessboard. Remove two opposite corner squares. Now 6 squares are one colour and 8 are the other. Each tile covers one square of each colour. So these 14 squares cannot be covered.
Tap the grid to lay tiles. Then ask the lab.
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Try the lab to finish this lesson.