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

      Abstract direct proportion

      Lesson details

      Learning outcome

      I can identify, write and solve direct proportion questions involving algebra.

      Key learning points

      1. Direct proportion equations are of the form y = kx
      2. k is the constant of proportionality and it is also the gradient of the graph.
      3. To find the gradient, k, you can use a set of coordinates (pair of values).

      Keywords

      • Direct proportion - Two variables are in direct proportion if they have a constant multiplicative relationship.

      • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.

      Common misconception

      We use the term 'multiplicative relationship' when talking about direct proportion. Pupils may need reminding that division is equivalent to multiplying by the reciprocal.

      Allow opportunities to explore division of a number and multiplication of its reciprocal. Remind pupils that any non-zero number multiplied by its reciprocal is equal to 1.

      Teacher tip

      To help overcome the misconception use mini-whiteboards. Give the class an number and ask them to write the reciprocal on their board. These can be tailored to the class, eg. stick to integers and unit fractions for lower ability and include mixed numbers, algebra and surds for higher ability.

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

      Correct Answer: constant

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

      The number of cans of drink and the number of boxes bought
      Correct answer: The time taken to fill a lorry and the number of people packing the lorry
      The number of metres run and the number of kilometres run
      The number of euros exchanged and the number of dollars
      The amount of flour needed and the number of biscuits being made

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

      $$y={{{5}\over{x}}-1}$$
      $$y={{{x}\over{5}}}$$
      Correct answer: $$y={{{5}\over{x}}}$$
      $$y={{{5}\over{x}}+1}$$

      Q4.
      A graph representing inverse proportion will appear in how many quadrants when plotted on a pair of axes?

      Correct Answer: 2, two, 2 quadrants, two quadrants

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

      Correct Answer: closer

      Q6.
      Which of the following is the graph of $$y={{{3.5}\over{x}}}$$?

      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

      6 Questions

      Q1.
      Any non-zero number multiplied by its reciprocal is equal to .

      $$-1$$
      0
      Correct answer: 1
      2

      Q2.
      Which of the following tables show direct proportion?

      An image in a quiz
      Correct answer: a
      Correct answer: b
      c
      Correct answer: d

      Q3.
      Match the numbers to their reciprocals.

      Correct Answer:5,$$1\over5$$

      $$1\over5$$

      Correct Answer:$$2\over5$$,$$5\over2$$

      $$5\over2$$

      Correct Answer:$$1\over2$$,2

      2

      Correct Answer:$$3\over4$$,$$4\over3$$

      $$4\over3$$

      Correct Answer:$$1\over4$$,4

      4

      Q4.
      Decide which of the following would share a directly proportional relationship.

      Correct answer: The time taken to mow a lawn and the size of the lawn
      The time taken to run a 5 k race and the speed at which its run
      Correct answer: The number of metres of ribbon bought and the cost of the ribbon
      The cost of hiring a coach and the cost per person

      Q5.
      $$h$$ is directly proportional to $$g$$. When $$g$$ = 12, $$h$$ = 7.2. Find $$h$$ when $$g$$ = 28.

      Correct Answer: 16.8

      Q6.
      $$g$$ is directly proportional to $$h$$. When $$g$$ = 17, $$h$$ = 93.5. Find $$g$$ when $$h$$ = 45.1.

      Correct Answer: 8.2

      To help you plan your 11 maths lesson on: Abstract direct proportion, download all teaching resources for free and adapt to suit your pupils' needs...