This KS3 simultaneous equations lesson plan uses area to introduce simultaneous equations. Students will move from informal to formal solutions effortlessly.

NCETM departmental workshops inspired this lesson plan. You’ll find two NCETM documents included in the download.

KS3 simultaneous equations video

Begin the lesson by watching this BBC video about solving simultaneous equations using plums and peaches in China.

Initial questions

• Draw a shape with an area of 2x
• Draw a shape with an area of 4y
• Draw a shape with an area of x – y

Main activity

Work individually or in groups to answer these questions:

• Which shape has half the area of H?
• What’s the difference in area between A and B? B and C?
• If you know that B has an area of 9cm² and C has an area of 21cm² what other areas can you work
  out?
• Shape P’s area is written 3x + 2y and shape Q’s area is written 3x – 2y. Which is the bigger shape and by how much?
• If shape P has an area of 7cm² and shape Q has an area of 5cm² what’s the area of shape x
  and shape y?

Zeb Friedman is a maths teacher. Follow her on Twitter at @zebfriedman. Browse more simultaneous equations questions.

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