Area by counting squares, step by step

The first area a child meets is not a formula — it is counting.

The question
squares

Area of an L-shape by counting

an L, not a rectangle
whole:4 × 7 =28
bite:1 × 3 =3
28 − 3 =25
first way:28 − 3 =25
strip:4 × 4 =16
upright:3 × 3 =9
16 + 9 =25 squares
  1. There is no single row that runs all the way across this one, so counting rows does not work as it stands. Cut it into pieces that ARE rectangles — and there is more than one way.
  2. First way: count the whole rectangle it would be — 4 × 7 = 28 — then take off the bite, 1 × 3 = 3. That leaves 25.
  3. Second way: two rectangles. The strip underneath is 4 × 4 = 16, the part standing on it is 3 × 3 = 9, and 16 + 9 = 25. Two ways agreeing is how you know a count is right.

How it works.

  1. 01

    There is no single row that runs all the way across this one, so counting rows does not work as it stands. Cut it into pieces that ARE rectangles — and there is more than one way.

  2. 02

    First way: count the whole rectangle it would be — 4 × 7 = 28 — then take off the bite, 1 × 3 = 3. That leaves 25.

  3. 03

    Second way: two rectangles. The strip underneath is 4 × 4 = 16, the part standing on it is 3 × 3 = 9, and 16 + 9 = 25. Two ways agreeing is how you know a count is right.