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Maths

Area by Counting Squares

Overview

Students explore the concept of area through drawing, covering shapes with squares, and comparing areas of different shapes.

Learning Objective
Students understand area as the amount of space a shape covers and calculate it by counting unit squares, including partial squares.

Resources needed

  • Centimetre squared paper
  • Coloured pencils
  • Ruler (optional)

Lesson stages

0 / 7 done
  1. 1 Draw two shapes on the board — a tall thin rectangle and a short wide one. 'Which is bigger?' Take a vote. 'How could we prove it?' Lead students towards the idea of counting squares.
  2. 2 Draw a simple shape on squared paper. 'Area tells us how much space a flat shape covers. We measure it in squares.' Count the squares inside the shape together. 'This shape has an area of ___ squares.'
  3. 3 Draw three different shapes on squared paper — all with the same area (e.g. all have area 12). Students count and notice they look different but have the same area. 'Shape and size are different things.'
  4. 4 Draw a shape with diagonal edges. 'What about this half square? We count two halves as one whole.' Model how to deal with partial squares — colour one colour, count halves in pairs.
  5. 5 Students design a shape with exactly 16 squares area on squared paper. They colour it, label the area, and swap with a partner who checks by counting.
  6. 6 Students draw three different shapes and order them from smallest to largest area. 'How did you know which was largest?'
  7. 7 Provide a shape on squared paper. Students count the area and write it with units: '___ square centimetres.'

Tap a step to mark it as done.

Variations

  • Introduce the formula for rectangles (length × width) as a shortcut
  • Use 1cm square sticky notes to physically cover shapes
  • Compare area to perimeter: two shapes with same area can have different perimeters
More information

Introduce: area, unit, square centimetre (cm²). Use sentence frames: 'The area of this shape is ___ cm².' 'This shape is bigger/smaller because it has more/fewer squares.'

Provide shapes with squares already marked inside to reduce counting errors. Limit partial squares for those finding this challenging.

Do students count squares accurately without missing or double-counting? Do they include units? Can they explain why two differently shaped figures can have the same area?

Draw squared grids on plain paper by hand. Students draw their own shapes using the grid.

Students may confuse area (space inside) with perimeter (distance around). Use different colours to mark the inside vs the outside boundary.

Activity details
Primary Medium 30 minutes 10 minutes prep Solo, Pairs Indoor
Topics
Area Measurement Squares Shapes