Area of rectangles: what children learn
In this game children work out the area of rectangles and sort them into groups with the same area. A 12 cm by 1 cm strip and a 4 cm by 3 cm rectangle look very different but both cover 12 cm², so the game shows that shapes with the same area can have very different perimeters.
Supports part of Common Core 4.MD.A.3: the area formula for rectangles. This focused game does not cover the entire standard.
Common Core connection: 4.MD.A.3. This is focused practice for part of the standard.
How to play
Sort the cards into the right groups. Tap a card, then its group. You can also drag a card, or press the number on its group. Each game has 3 rounds with no timer. Every card is checked as soon as you place it: a card in the wrong group comes back with a hint, and you get a point for each card you place right first time. For a quicker go, choose Quick quiz: 10 multiple-choice questions in 150 seconds (choose Relaxed for more time).
Step by step
- Multiply length by width. The area of a rectangle is length × width. A 6 cm by 4 cm rectangle has an area of 6 × 4 = 24 cm².
- Use square units. Area is written in square units: cm² for square centimeters, m² for square meters. Each cm² is a square 1 cm long and 1 cm wide.
- Squares too. A square is a rectangle with equal sides, so a 4 cm square has an area of 4 × 4 = 16 cm².
- Use factor pairs. All the rectangles with an area of 24 cm² use a factor pair of 24: 1 × 24, 2 × 12, 3 × 8 and 4 × 6.
Worked examples
Example 1: What is the area of a rectangle 9 cm by 4 cm?
Working: 9 × 4 = 36.
Answer: 36 cm²
Example 2: Which has the bigger area: 8 cm by 2 cm or 4 cm by 4 cm?
Working: 8 × 2 = 16 and 4 × 4 = 16.
Answer: They have the same area, 16 cm²
Example 3: A 12 cm by 1 cm and a 4 cm by 3 cm rectangle both have an area of 12 cm². Do they have the same perimeter?
Working: 12 + 1 + 12 + 1 = 26 cm and 4 + 3 + 4 + 3 = 14 cm.
Answer: No: 26 cm and 14 cm
Common mistakes and how to fix them
- Adding the sides instead of multiplying. Adding the sides gives the perimeter. Area counts the squares inside, so multiply.
- Writing the unit as cm instead of cm². Area is measured in squares, so the unit has a small 2.
- Thinking shapes with the same area have the same perimeter. Compare a long thin rectangle with a square of the same area: the thin one has a much bigger perimeter.
Activities to try at home
- Measure a tablemat or a book and work out its area.
- Draw rectangles on squared paper and count the squares, then check by multiplying.
- Plan a garden bed: how many 1 m² slabs would cover it?
Ideas for the classroom
- Students draw all the rectangles with an area of 24 cm² on squared paper and find each perimeter.
- Measure the area of the classroom floor in m².
- Estimate the area of irregular shapes by counting squares.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
How should I choose this game for my learner?
Supports part of Common Core 4.MD.A.3: the area formula for rectangles. This focused game does not cover the entire standard.
Why do some rectangles have the same area?
Different factor pairs give the same product, so different rectangles can cover the same space.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it up, then choose the group it belongs in.