Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Perimeter of Rectangles and Regular Shapes

Learn to find the perimeter of rectangles and regular shapes by spotting equal sides and using multiplication instead of adding each side separately.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHere is a rectangle that is 5 cm along the top and 2 cm down the side. Look at it carefully. Are any of its sides the same length as each other? Which ones? Do we really need to measure all four sides to find the distance all the way around, or could we be a bit cleverer about it?

    2 - Watch and Notice ~9 mins

    The perimeter of a shape is the distance all the way around its edge, found by adding the length of every side. The space inside the shape is its area. Today we work on perimeter.

    The interactive shows three shapes in turn: a rectangle, a square and a regular pentagon. Watch how we find the perimeter of each, and look for a quicker way than adding every side one at a time.

    3 - Try It Together ~8 mins

    Here is a 6 cm by 3 cm rectangle on the board. Let's find its perimeter the smart way together. First, tell me which sides are equal. Then, instead of adding all four sides one slow side at a time, pair the equal sides: add one long side and one short side, then double it. For this rectangle that is 6 plus 3, which is 9, then double it: 9 and 9 makes 18 cm.

    Find the perimeter the smart way

    4 - Work It Two Ways in Your Copy ~5 mins

    COPYBOOK MOMENT

    In your maths copy, work out the perimeter of a 6 cm by 3 cm rectangle two ways. First add all four sides, one under the other. Then pair the equal sides: add one long side and one short side, and double your answer. Check that both ways give you exactly the same perimeter. When you have those, try the same two ways for an 8 cm by 5 cm rectangle.

    5 - Class Challenge ~9 mins

    On the board is a 4 cm by 4 cm square. Spot the equal sides first, then find its perimeter the quickest way you can. After that, I will draw three more shapes for us to work the same way: a 10 cm by 6 cm rectangle, a regular hexagon with sides of 5 cm, and a regular octagon with sides of 7 cm. For each one, name the equal sides, then find the perimeter. Read the side lengths straight from the shape tool, work each perimeter out in your copy, and we check every answer together before the next shape.

    Perimeter challenge

    6 - What Did We Notice? ~5 mins

    MATHS TALK

    Why is a regular shape's perimeter so quick to find compared with a wobbly six-sided shape where every side is a different length? What is it about a regular shape that lets us use a times-table fact instead of adding side by side?

    7 - What's Next ~3 mins

    What we learned

    • Perimeter is the distance all the way around a shape, found by adding every side.
    • When sides are equal we can be smart: pair the equal sides of a rectangle, or multiply one side by the number of sides in a regular shape.
    • Checking a perimeter two different ways tells us our answer is right.

    Coming up

    Next we move from the distance around a shape to the flat space inside it. We will start measuring area by counting the square units that cover a shape.

    Pupil practice
    Module 5 · Area, Perimeter and Volume Measures
    Lesson 58 · Perimeter of Rectangles and Regular Shapes
    Download Activity Book page (PDF)
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