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      Reason about compound shapes using the relationship between side lengths and area and perimeter

      Lesson details

      Learning outcome

      I can reason about compound shapes using the relationship between side lengths and area and perimeter.

      Key learning points

      1. Area and perimeter are calculated from the side lengths of 2D shapes.
      2. Area and perimeter are measured in different units.
      3. Compound shapes can be decomposed and rearranged in different ways.

      Keywords

      • Compound - A compound shape is a shape created using two or more basic shapes.

      • Dimension - A dimension is a measurement of length in one direction.

      Common misconception

      The numbers used as side lengths in this lesson are generally relatively low, and based around times tables. As a result, pupils might be tempted to guess / estimate the missing side lengths.

      Remind pupils that the shapes are not to scale and encourage them to use subtraction skills instead - what is the difference between this known side length and this known side length?

      Teacher tip

      Physically cutting out the compound shapes and decomposing them that way, rather than drawing a line inside them, provides a powerful reminder that compound shapes are composed of two or more shapes. Manipulating the shapes will help to show how the missing side lengths can be calculated.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Select all of the statements that are true of this number shape.

      An image in a quiz
      Correct answer: It has a perimeter.
      Correct answer: It is a compound shape.
      Its outline forms a regular shape.
      Correct answer: It can be decomposed into two rectangles.

      Q2.
      Laura says the perimeter of this shape is 8 units. What mistakes do you think she has made?

      An image in a quiz
      Counted one side twice.
      Correct answer: Not counted all of the sides.
      Correct answer: Counted the squares inside the shape, giving the area.

      Q3.
      What is the perimeter of this rectangle? cm

      An image in a quiz
      Correct Answer: 72

      Q4.
      What is the perimeter of this shape? Remember to include the correct units.

      An image in a quiz
      Correct Answer: 206 cm

      Q5.
      What is the missing side length of this rectangle? Remember to include the correct units.

      An image in a quiz
      Correct Answer: 5 cm

      Q6.
      What is the area of this square? cm$$ ^2 $$

      An image in a quiz
      Correct Answer: 144

      6 Questions

      Q1.
      Give the missing side length. cm

      An image in a quiz
      Correct Answer: 2

      Q2.
      Give the missing side length. cm

      An image in a quiz
      Correct Answer: 5

      Q3.
      Is there enough information to calculate the perimeter of the shape?

      An image in a quiz
      Yes. Add the known side lengths together.
      Correct answer: No. Two of the side lengths are missing.
      No. One of the side lengths is missing.

      Q4.
      Calculate the perimeter of the shape. cm

      An image in a quiz
      Correct Answer: 26

      Q5.
      The area of the shape is 43 cm². Order the steps to work out the missing dimension.

      An image in a quiz
      1 - Calculate the area of one rectangle by multiplying its known side lengths.
      2 - Subtract the area of the known rectangle from the known area.
      3 - Divide the area of the other rectangle by its known side length.

      Q6.
      The area of the shape is 43 cm². What is the missing side length?

      An image in a quiz
      Correct Answer: 2 cm

      To help you plan your 6 maths lesson on: Reason about compound shapes using the relationship between side lengths and area and perimeter, download all teaching resources for free and adapt to suit your pupils' needs...