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      Problem solving with fractions and ratios

      Lesson details

      Learning outcome

      I can use my knowledge of fractions and ratios to solve problems.

      Key learning points

      1. Any fraction can be turned into a ratio.
      2. Moving between fractions and ratios can make a problem easier.
      3. There can be lots of information, it is important to think about what is required to solve the problem.

      Keywords

      • Proportion - Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

      • Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

      Common misconception

      Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'.

      Offer opportunities to match problems to bar models ensure the same numbers are used to highlight the differences.

      Teacher tip

      As a recap of ratio, ask the pupils to come up with their ratios based on their own lives and the multiplicative relationship between them. E.g. The ratio of pets to people in their house, the ratio of matches their favourite team has won to lost.

      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.
      In this list of common metric units of length which one is missing? millimetre, centimetre, metre, .

      Correct Answer: kilometre, km, kilometres, kilometer, kilometers

      Q2.
      1 km = 1000 m, 1 m = 100 cm. What is 5 400 000 cm in kilometres?

      5400 km
      540 km
      Correct answer: 54 km
      5.4 km
      0.54 km

      Q3.
      The scale on a map is 1:5 000 000. The distance between two places on the map is 5 cm. What is the distance in real life in kilometres?

      2.5 km
      25 km
      Correct answer: 250 km
      2500 km
      25 000 km

      Q4.
      The scale on a map is 1:500 000. The distance between two places is 86 km. What is the distance on the map?

      Correct answer: 17.2 cm
      172 cm
      17.2 km
      172 m

      Q5.
      The length of a pencil is 2.5 inches. Convert this into centimetres given that 1 inch = 2.54 cm.

      Correct Answer: 6.35 cm, 6.35cm, 6.35, 6.35 centimetres, 6.35centimetres

      Q6.
      The distance between London and Manchester is 200 miles. Convert this into kilometres given that 5 miles = 8 km.

      Correct Answer: 320 km, 320, 320km, 320 kilometres

      6 Questions

      Q1.
      Fill in the missing word: Variables are in proportion if they have a multiplicative relationship.

      Correct Answer: constant

      Q2.
      Select the bar model that is correctly labelled to solve this problem: Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

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

      Q3.
      Sam and Jacob share some stickers in the ratio of 3 : 7. Sam get 168 less than Jacob. How many stickers does Sam get?

      Correct Answer: 126, 126 stickers

      Q4.
      The ratio of children to adults in a club is 2 : 3. If there are 26 children, how many are in the club in total?

      Correct Answer: 65, 65 people, sixty-five, sixty five, sixtyfive

      Q5.
      A bag contains red, green and yellow sweets. $$1\over4$$ of them are red. The rest of the sweets are either green or yellow, in the ratio 4 : 5. There are 72 sweets in the bag. How many are yellow?

      Correct Answer: 30, 30 yellow , 30 yellow sweets, thirty

      Q6.
      Andeep’s older sister Belle is 3 times his age. His brother Charlie is $$5\over6$$ of Belle's age. The total of Andeep’s and Belle’s ages is 48. How old is Charlie?

      Correct Answer: 30, 30 years old, thirty, thirty years old

      To help you plan your 7 maths lesson on: Problem solving with fractions and ratios, download all teaching resources for free and adapt to suit your pupils' needs...