Area (age 8+)

Activities to try

1. 1

   Tile and count an L-shaped garden

   Why it works: Area is the count of unit squares that cover the inside of a shape — notches and all — and is about the surface inside, not the fence or distance running around the edge.

   1. Cover an L-shaped figure's whole interior with unit squares so there are no gaps and no overlaps, including the awkward squares inside the notch of the L.
   2. Count the covering squares systematically — row by row, or by splitting the L into two rectangles and counting each — marking each square as you count it so none is missed or double-counted.
   3. State the result in square units, e.g. '18 square cm' or in square metres, not just a bare number.
   4. Repeat with a plain rectangle and then compare two shapes side by side, deciding which covers more by comparing their counts.
2. 2

   Tile a real surface before squared paper

   Why it works: Measuring area means physically covering a surface with equal square units and counting them; the squared-paper diagram is a picture of that same covering.

   1. Lay square-centimetre tiles across a small real surface such as a book cover, filling it with no gaps or overlaps; if strips narrower than a tile are left at the edges, note them informally as part-squares rather than counting them as whole tiles.
   2. Count the tiles and say the area in square centimetres.
   3. Then move to a squared-paper diagram of the same shape drawn at the same size (one paper square for each tile) and count the covering squares there.
3. 3

   Compare and check with quick counting questions

   Why it works: Comparing areas means comparing counts of all the covering squares, edge squares included; counting only the border squares does not give the area, and the distance around the outline (perimeter) is a different thing from the area inside.

   1. Given two shapes on squared paper, decide which covers more area by counting each one's squares.
   2. Answer a short set of count-the-squares questions using whole-square figures — a plain rectangle and an L-shape, each with a definite count — then separately look at one shape with part-squares at the edge and discuss (rather than score) how to handle the part-squares informally.
   3. Watch for a tempting wrong answer that comes from counting only the border squares (or the unit lengths around the outline) instead of all the squares covering the inside, and explain why it is wrong.