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      Lesson details

      Learning outcome

      I can manipulate percentages of an amount with a representation.

      Key learning points

      1. Percentages of amounts can be found by combining known percentages
      2. Percentages of amounts can be represented and found using a bar model
      3. Percentages of amounts can be represented and found using double number lines
      4. Percentages of amounts can be represented and found using ratio tables

      Keywords

      • Proportion - Variables are in proportion if they have a constant multiplicative relationship.

      • Equivalent fractions - Two fractions are equivalent if they have the same value.

      Common misconception

      When finding 10% we divide by 10, so when finding 5% we divide by 5.

      Use a bar model to show the division of 10 means one tenth of the amount. When dividing by 5 it means one fifth has been found.

      Teacher tip

      Using MWB pupils must draw the same question but illustrated in different ways; ratio table, double number line or bar model. E.g show 48% of 800. They can then decide which representation they prefer. Look out for efficient approaches using subtraction where appropriate.

      Licence

      This content is © Oak National Academy Limited (2026), 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.
      Proportionality means two variables have a constant __________ relationship so the variables are in proportion to each other.

      additive
      divisive
      Correct answer: multiplicative
      subtractive

      Q2.
      40% of 440 is .

      Correct Answer: 176

      Q3.
      1% of 780 is .

      Correct Answer: 7.8

      Q4.
      Which of the following are correct strategies to find 75% of 200?

      Correct answer: $$200\div10\times7 + 10$$
      Correct answer: $$200 \div 4\times3$$
      Correct answer: $$\frac{3}{4}\times200$$
      Correct answer: $$\frac{1}{4}\times200 + 100$$
      $$75\times200$$

      Q5.
      Match each percentage question to its answer.

      Correct Answer:15% of 700,105
      Correct Answer:25% of 600,150
      Correct Answer:20% of 800,160
      Correct Answer:90% of 140,126
      Correct Answer:35% of 900,315
      Correct Answer:1% of 6000,60

      Q6.
      Starting with the calculation with the largest answer, put these percentage calculations in descending order.

      1 - 1% of 50 000
      2 - 20% of 800
      3 - 5% of 3000
      4 - 50% of 280
      5 - 100% of 90
      6 - 35% of 40

      6 Questions

      Q1.
      __________ means two variables have a constant multiplicative relationship.

      Equality
      Equivalent
      Positivity
      Correct answer: Proportionality

      Q2.
      Match each representation of proportion to its advantages.

      Correct Answer:Bar model,Good visual representation. Bars can be split in any way needed.
      Correct Answer:Double number line,Good visual representation with scaled lines.
      Correct Answer:Ratio table,Concise without visual representation and quick to construct.

      Q3.
      What percentage of 800 is represented by the calculation: 800 ÷ 2 − 8?

      40%
      Correct answer: 49%
      50%
      59%
      90%

      Q4.
      What percentage of 650 is represented by the calculation: 650 − 6.5?

      1%
      9%
      49%
      89%
      Correct answer: 99%

      Q5.
      Use the double number line to work out 45% of 700.

      An image in a quiz
      Correct Answer: 315

      Q6.
      Using the ratio table or another representation, work out 98% of 860.

      An image in a quiz
      Correct Answer: 842.8

      To help you plan your 8 maths lesson on: Securing understanding of percentages, download all teaching resources for free and adapt to suit your pupils' needs...