Count the squares

About this video

Two friends each need a rug for their bedroom floor: one floor is long and thin, the other short and wide. Who needs the bigger rug? Walking round the edge won't answer that, because the question is about the floor inside. This animation covers each floor with equal squares and counts them as they land: both take 12. The amount of flat surface a shape covers is its area, and these two shapes have the same area even though they look quite different.

Why squares? Circles, like coins, leave gaps between them, and squares that overlap get counted twice. Equal squares laid edge to edge cover a shape with no gaps and no overlaps, so counting them measures the surface exactly. The squares everyone agrees on are built from units of length: a square with sides of 1 centimetre is one square centimetre, written 1 cm², about the size of a fingernail; a square with sides of 1 metre is one square metre, 1 m², big enough for a young child to sit in.

Last, the video keeps area apart from perimeter. A long ribbon of 12 squares has an area of 12 cm², but the way round its edge is 26 cm. To keep the two apart, ask: am I walking round it, or covering it? This video goes with the lesson Area: Counting Squares of Geometry Level 1 on Knaph.

Transcript

1. 0:00Two bedroom floors, one long and thin, one short and wide. Who needs the bigger rug?
2. 0:06Walking round the edge won't tell you. The question is about the floor inside.
3. 0:12Cover the floor with equal squares, and count them. Twelve.
4. 0:19The other floor. Twelve again.
5. 0:25The same area, even though the shapes look different.
6. 0:30Why squares? Circles leave gaps.
7. 0:34Squares that overlap are counted twice.
8. 0:38Squares edge to edge. No gaps, no overlaps.
9. 0:42A square one centimetre on each side is one square centimetre.
10. 0:48A square one metre on each side is one square metre. A child can sit in it.
11. 0:56A ribbon of twelve squares. Its area is twelve, but twenty-six round the edge.
12. 1:02So ask, am I walking round it, or covering it?
13. 1:08Area is the surface inside. Cover it with squares and count them.