Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Equations from complex shapes

      Lesson details

      Learning outcome

      I can form and solve equations with more complex shapes.

      Key learning points

      1. Sometimes you are given a problem with insufficient information to reach a numerical value.
      2. Depending on the problem, it may be possible to write more than one equation.
      3. It is possible these equations can be combined to write a new, more succinct, equation.

      Keywords

      • Equation - An equation is used to show two expressions that are equal to each other.

      • Perimeter - The perimeter is the distance around a 2D shape.

      • Area - The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

      Common misconception

      Some pupils may have an equivalent algebraic expressions without noticing.

      Tell pupils to always check if their expressions can be simplified or factorised before deeming themselves incorrect.

      Teacher tip

      Provide pupils with a shape, such as a kite, with algebraic expressions for each edge and ask them to come up with as many equations as they can from the given information.

      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

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      $$3n+5=2+n$$ is an example of an .

      Correct Answer: equation

      Q2.
      The solution to $$6(2m-7)=42$$ is $$m=$$ .

      Correct Answer: 7, seven

      Q3.
      The solution to $$6y-5=2y+25$$ is $$y=$$ .

      Correct Answer: 7.5, 15/2

      Q4.
      The solution to $$8x+9=28-2x$$ is $$x=$$ .

      Correct Answer: 1.9, 19/10

      Q5.
      The solution to $$\frac{5t+12}{3}=9$$ is $$t=$$ .

      Correct Answer: 3

      Q6.
      The solution to $$6(5d+2)=3(9d-1)$$ is $$d=$$ .

      Correct Answer: -5, - 5, minus 5, negative 5

      6 Questions

      Q1.
      Given that the perimeter of this rectangle is 76 cm, then $$x=$$ .

      An image in a quiz
      Correct Answer: 5, five, 5 cm, 5cm

      Q2.
      Which of these equations are true for this square?

      An image in a quiz
      $$2(x+1)+2(3x-7)+(18-2x)=7x-18$$
      Correct answer: $$7x-18=18-2x$$
      Correct answer: $$2(3x-7)=18-2x$$
      $$2(3x-7)-(7x-18)=2(x+1)$$
      Correct answer: $$(18-2x)^2=(7x-18)(2(3x-7))$$

      Q3.
      The perimeter of this isosceles triangle is 53 cm. The length of the unmarked edge is cm.

      An image in a quiz
      Correct Answer: 7, seven

      Q4.
      Given that this is a parallelogram, complete the equation: $$5x-9=$$___________.

      An image in a quiz
      $$11y+3$$
      Correct answer: $$6y$$
      $$7(x-1)$$

      Q5.
      Given that these two shapes have equal areas, then $$x=$$ .

      An image in a quiz
      Correct Answer: 3, three, 3 cm, 3cm

      Q6.
      The area of this rectangle is 48 square centimetres. The perimeter is cm.

      An image in a quiz
      Correct Answer: 28, twenty eight, 28 cm, 28cm

      To help you plan your 10 maths lesson on: Equations from complex shapes, download all teaching resources for free and adapt to suit your pupils' needs...