Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
Teacher-led from the board. Pupils do not need a device, but can follow on one.
What you need:
IWB/Projector/Large Screen
Square tiles

Comparing Area and Perimeter

Explore how two shapes can cover the same area but have different perimeters. You'll measure area by counting squares and perimeter by adding side lengths, discovering that the way a shape is arranged changes the distance around its edge.

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    Shape measurer

    1 - Getting Started ~4 mins

    Here are two rectangles drawn on squared paper.

    • Rectangle A: a long thin strip, 1 square tall and 6 squares long.
    • Rectangle B: a chunky block, 2 squares tall and 3 squares long.

    Count the squares inside each one.

    Now have a think before we work anything out: if an ant walked all the way around the edge of each one, would it walk the same distance both times? Hands up for your guess.

    2 - Watch and Notice ~9 mins

    Let's look at these rectangles together. For each one, count the squares that fit inside (that is the area) and then walk right around the edge, adding every side (that is the perimeter). The first two shapes cover the same area, so watch what happens to the distance around. The third one is a bigger shape where both the area and the perimeter are different, so keep an eye on both numbers.

    3 - Draw the Two Rectangles in Your Copy ~3 mins

    COPYBOOK MOMENT

    Illustration for Draw the Two Rectangles in Your CopyIn your squared copy, draw two different rectangles that each cover 8 squares. Write the perimeter beside each one, then ring the rectangle with the longer way around.

    4 - Try It Together ~8 mins

    Now it is your turn to work out the numbers. The shape-measurer will show a rectangle, but this time it hides the area and the perimeter until you enter your answer and check it. We will work three rectangles in turn. First a 2 by 4. Then a 1 by 8. Then a 3 by 3. For each one, count the squares inside to find the area. Then add all four sides to find the perimeter. Enter your answer, press Check, and say whether the distance around is getting longer or shorter as the shape changes.

    Shape Measurer

    Pupil practice
    Module 5 · Area, Perimeter and Volume Measures
    Lesson 61 · Comparing Area and Perimeter
    Download Activity Book page (PDF)
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