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      Solving simple linear equations with a multiplicative step

      Lesson details

      Learning outcome

      I can solve a linear equation requiring a single multiplicative step.

      Key learning points

      1. An equation involving an multiplicative step can be represented with a bar model.
      2. Using the bar model you can write all the arrangements of the equation with an multiplicative step.
      3. One of the arrangements will give the solution to the equation.
      4. This can be written algebraically to find the solution.

      Keywords

      • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number.

      Common misconception

      When solving equations pupils may not use the inverse operation.

      Working out should include each step then pupils can check each step using substitution.

      Teacher tip

      This is a great chance to consolidate fraction skills, including the use of reciprocals. Pupils should understand the equivalence of multiplication and division by the reciprocal and use these interchangeably to suit the question.

      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.
      Which of these equations can be written from this bar model?

      An image in a quiz
      $$x − 6.2 = 8.3$$
      Correct answer: $$x + 6.2 = 8.3$$
      $$x = 8.3 − x$$
      Correct answer: $$6.2 = 8.3 − x$$
      Correct answer: $$8.3 − 6.2 = x$$

      Q2.
      The solution to the equation $$x + 3 = 17$$ is when $$x$$ =

      Correct Answer: 14, fourteen

      Q3.
      The solution to the equation $$x − 8.6 = 10$$ is when $$x$$ =

      Correct Answer: 18.6

      Q4.
      Any non-zero number multiplied by its reciprocal is equal to

      Correct Answer: 1, one

      Q5.
      Match each number to its reciprocal.

      Correct Answer:$$1\over 5$$,$$5$$

      $$5$$

      Correct Answer:$$−{1\over 5}$$,$$-5$$

      $$-5$$

      Correct Answer:$$4\over 5$$,$$5\over 4$$

      $$5\over 4$$

      Correct Answer:$$−{4\over 5}$$,$$−{5\over 4}$$

      $$−{5\over 4}$$

      Correct Answer:$$5$$,$${1\over 5}$$

      $${1\over 5}$$

      Correct Answer:$$−5$$,$$−{1\over 5}$$

      $$−{1\over 5}$$

      Q6.
      Match each calculation to an equivalent calculation.

      Correct Answer:$$\times {2\over 7}$$,$$\div {7\over 2}$$

      $$\div {7\over 2}$$

      Correct Answer:$$\div (-{2\over 7})$$,$$\times( −{7\over 2})$$

      $$\times( −{7\over 2})$$

      Correct Answer:$$\times (−7)$$,$$\div( −{1\over 7})$$

      $$\div( −{1\over 7})$$

      Correct Answer:$$\times( −{1\over 7})$$,$$\div( −7)$$

      $$\div( −7)$$

      Correct Answer:$$\times {1\over 7}$$,$$\div 7$$

      $$\div 7$$

      Correct Answer:$$\div {1\over 7}$$,$$\times 7$$

      $$\times 7$$

      6 Questions

      Q1.
      Using this bar model, the solution to the equation $$6x = 30$$ is when $$x= $$

      An image in a quiz
      Correct Answer: 5, five

      Q2.
      Using this bar model, the solution to the equation $${1\over 4}x = 8$$ is when $$x=$$

      An image in a quiz
      Correct Answer: 32

      Q3.
      The solution to $$3x = 396$$ is when $$x=$$

      Correct Answer: 132

      Q4.
      Which of these show the correct working to isolate one positive $$x$$ for the equation $$0.5x = 3.5$$?

      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q5.
      The solution to $$-9x = 36$$ is when $$x =$$

      Correct Answer: −4, - 4, − 4, -4

      Q6.
      Which of these is the solution to $${4\over 5} x = 20$$?

      4
      5
      16
      Correct answer: 25
      28

      To help you plan your 8 maths lesson on: Solving simple linear equations with a multiplicative step, download all teaching resources for free and adapt to suit your pupils' needs...