Mathematics
Intermediate
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+80 XP
What you need:
IWB/Projector/Large Screen

Perimeter of Rectangles and Simple Shapes

Learn how rectangles have two pairs of equal sides, use this to find missing measurements, then add all four sides to calculate perimeter. Apply this to rectangles and simple composite shapes.

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    1 - Getting Started ~4 mins

    Key point

    Look at the rectangle on the board. Only two sides have numbers: the top is 6 cm and one side is 3 cm. The other two sides are blank.

    Have a think: what must the bottom side be? And the other side? How could you be so sure without measuring them?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Watch four shapes on the board. For each rectangle, notice which two sides match, so we can fill in the sides that have no number before we add. The last one is an L-shape, so look carefully at how many sides it really has.

    Shape Measurer

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~10 mins

    How we work

    A pupil takes a turn at the board while the rest of us work out the perimeter aloud first, then that pupil types in our answer. We fill in the sides we were not given, then add all four.

    Our shapes:

    • 4 cm by 3 cm rectangle
    • 6 cm by 2 cm rectangle
    • 5 cm by 5 cm square — all sides match
    • 8 cm by 3 cm rectangle — don't miss the two threes
    • L-shape — count all six sides carefully before you add

    Find the missing sides, then the perimeter

    +15 XP

    4 - Draw the Rectangle in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, draw a 5 cm by 3 cm rectangle using your ruler. Write the length on all four sides, so both 5 cm sides and both 3 cm sides have a number. Then write the perimeter sentence underneath with its total, like this: 5 + 3 + 5 + 3 = ___ cm.

    +10 XP

    5 - Class Challenge ~8 mins

    Now we work these out on the board together, filling in any missing sides first. Draw each shape as we go so we can trace right around its edge.

    Our shapes:

    • 4 cm by 4 cm square
    • 6 cm by 3 cm rectangle
    • 7 cm by 4 cm rectangle
    • L-shape from two rectangles — count the six sides carefully
    Example

    For the L-shape, the six sides going around are 5 cm, 2 cm, 3 cm, 4 cm, 2 cm and 2 cm.

    Work out the perimeter of each shape. Fill in any missing sides first, then add every side once. For the L-shape, use the labelled figure drawn on the board.

    For each rectangle, fill in the two missing opposite sides, then add all four. For the L-shape, use the labelled board figure: count and check every side, then add them one at a time.

    1. A 4 cm by 4 cm square flag. What is the distance all the way around its edge?
    2. A 6 cm by 3 cm garden bed. What is its perimeter?
    3. A 7 cm by 4 cm noticeboard. What is its perimeter?
    4. The L-shape drawn on the board, with sides 5 cm, 2 cm, 3 cm, 4 cm, 2 cm and 2 cm going around. What is the distance all the way around?

    Ways to start:

    • Read out the two sides you were given, then say what the two matching sides must be.
    • On the L-shape drawn on the board, trace one full trip around the edge with your finger, saying each side length as you touch it.

    Stretch:

    • On the L-shape drawn on the board, how do you know you have counted every side and none of them twice?
    Answers & strategies (teacher)
    1. A 4 cm by 4 cm square flag. What is the distance all the way around its edge? — 16 cm
    2. A 6 cm by 3 cm garden bed. What is its perimeter? — 18 cm
    3. A 7 cm by 4 cm noticeboard. What is its perimeter? — 22 cm
    4. The L-shape drawn on the board, with sides 5 cm, 2 cm, 3 cm, 4 cm, 2 cm and 2 cm going around. What is the distance all the way around? — 18 cm
    +15 XP

    6 - What Did We Notice? ~3 mins

    MATHS TALK

    If you know the long side and the short side of a rectangle, why do you not need to measure the other two sides at all?

    +10 XP

    7 - What's Next ~2 mins

    What we learned today

    • A rectangle has two pairs of equal sides, so once you know two sides you already know the other two.
    • To find the perimeter, fill in any missing sides first, then add every side once.
    • An L-shape has more than four sides, so you count and add each one carefully.

    Coming up

    Next time we look at two shapes that cover the same amount of space but have very different distances around, and we start to see that area and perimeter are not the same thing.

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