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      Checking and securing understanding of inverse proportion graphs

      Lesson details

      Learning outcome

      I can identify inverse proportion graphs from their features and can use the graph to create an equation to algebraically model this relationship.

      Key learning points

      1. Inverse proportion can be recognised graphically.
      2. An inverse proportion graph is always a curve that does not touch either axis.
      3. The equation is of the form y = k/x
      4. k is the constant of proportionality.

      Keywords

      • Inverse proportion - Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the reciprocal of the other

      Common misconception

      Assuming the the graph will eventually intercept the axes.

      Pupils can experiment with very large numbers. Here a spreadsheet is useful to generate numbers very quickly and show that although it gets very close to zero it never actually gets there.

      Teacher tip

      Use Desmos to explore the features of graphs representing inverse proportion.

      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.
      If two variables have a constant relationship, they are in direct proportion.

      additive
      Correct answer: multiplicative
      decreasing

      Q2.
      Which of the following tables show values of A and B in direct proportion?

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

      Q3.
      Which of the following graphs show direct proportion?

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

      Q4.
      Calculate the value of k (constant of proportionality).

      An image in a quiz
      $$3\over5$$
      $$1\over3$$
      Correct answer: $$5\over3$$
      3

      Q5.
      What is the equation of this line?

      An image in a quiz
      $$y={3\over5}$$
      Correct answer: $$y={5\over3}x$$
      $$y={5\over3}$$
      $$y={3\over5}x$$

      Q6.
      Which is the graph of $$y={1\over3}x$$?

      Correct answer: A
      B
      C
      D

      6 Questions

      Q1.
      Two variables are inversely proportional if there is a constant multiplicative relationship between one variable and the of the other.

      Correct Answer: reciprocal

      Q2.
      Which of the following is an example of inverse proportion?

      The number of euros exchanged and the number of pounds
      The number of sweets and the number of bags of sweets
      The number of kilometres travelled and the number of miles travelled
      Correct answer: The time taken to build a wall and the number of people
      The cost to fill a fuel tank and the size of the tank

      Q3.
      Which of the following is an equation representing inverse proportion?

      $$y={{{50}\over{x}}+5}$$
      Correct answer: $$y={{{50}\over{x}}}$$
      $$y={{{50}\over{x}}-5}$$
      $$y={{{x}\over{50}}}$$

      Q4.
      Which of the following are not true? A graph representing inverse proportion...

      Correct answer: will appear in all 4 quadrants.
      will not intersect the $$x$$ and $$y$$ axes.
      will appear in only 2 quadrants.
      Correct answer: will intersect the $$x$$ and $$y$$ axes.

      Q5.
      The the dividend, the closer to the origin the graph will be.

      Correct Answer: smaller

      Q6.
      Which of the following is the graph of $$y={{{2.5}\over{x}}}$$?

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

      To help you plan your 11 maths lesson on: Checking and securing understanding of inverse proportion graphs, download all teaching resources for free and adapt to suit your pupils' needs...