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Lesson 8 of 8

    Problem solving with ratios

    I can use my knowledge of ratio to solve problems.

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    Lesson 8 of 8
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      Problem solving with ratios

      I can use my knowledge of ratio to solve problems.

      Download all

      These resources were made for remote use during the pandemic, not classroom teaching.

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      Lesson details

      Key learning points

      1. It is important to preserve the relationship between the parts of a ratio.
      2. Changing this relationship would change the ratio.
      3. Painting, cooking and traveling all involve ratios.

      Keywords

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

      • Coordinates - Coordinates are a set of values that show an exact position.

      • Expression - An expression contains one or more terms, where each term is separated by an operator.

      • Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

      Common misconception

      Procedural understanding of sharing in a ratio where pupils add the parts, divide the amount by this and then multiply by each part without considering the information in the question

      In the lesson encourage pupils to look for keywords in the question which indicate if the amount given is the total, one part or the difference. The use of a bar model to display the information can also be used to help pupils.

      When working with ratios in geometry a sketch can be really important. Being able to plot the coordinates accurately in relation to each other without having to have a complete coordinate grid will be key to success. Mini-whiteboards could help.
      Teacher tip

      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

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      6 Questions

      Q1.
      Which are of the following are expressions?

      Correct answer: $$4x+5y$$
      $$4x$$
      Correct answer: $$4x + 5$$
      $$4x=5y$$
      Correct answer: $$4(2x +5)$$

      Q2.
      What is the length of AB?

      An image in a quiz
      Correct Answer: 9, nine

      Q3.
      Which of the following are equivalent ratios to 3 : 9?

      Correct answer: 27 : 81
      Correct answer: 1 : 3
      Correct answer: 1.5 : 4.5
      Correct answer: 12 : 36
      36 : 117

      Q4.
      Point A and B are on a straight line. The coordinates of point A are (2, 3). Point B is 2 to the right and 4 below point A. What are the coordinates of point B?

      $$(0, -1)$$
      Correct answer: $$(4, -1)$$
      $$(0, 7)$$
      $$(4, 7)$$

      Q5.
      There are 42 cars and vans in a car park in the ratio of 5 : 2. How many vans are there?

      Correct Answer: 12, 12 vans, twelve, twelve vans

      Q6.
      Bag A contains $$b$$ beads, bag B contains two more than bag A and bag C contains twice as many as bag B. Which of the following is the correct expression for the number of beads in bag C?

      $$b+2$$
      $$b-2$$
      $$2b+2$$
      Correct answer: $$2(b+2)$$

      Assessment exit quiz

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      6 Questions

      Q1.
      Which are of the following are expressions?

      $$2y=3x$$
      Correct answer: $$2y - 3x$$
      Correct answer: $$2(y + 3)$$
      $$2y$$
      Correct answer: $$2y-3$$

      Q2.
      The points A, B, C and D are in order on a straight line. AB : BD = 2 : 7, AC : CD = 15 : 3. Find the ratio of AB : BC : CD

      Correct Answer: 4 : 11 : 3, 4:11:3

      Q3.
      The points A, B and C are on a straight line. The coordinates of A are (6, 2). The coordinates of B are (8, 5). Given that AB : BC = 1 : 2. Find the $$x$$ coordinate of C.

      Correct Answer: 12, twelve, x=12, x = 12

      Q4.
      3 bags contain 38 beads between them. Bag A contains 2 more than bag B. Bag C contains 3 times the number in bag A. Find the ratio of marbles in bag A : bag B : bag C in its simplest form.

      Correct Answer: 4 : 3 : 12, 4:3:12

      Q5.
      The ratio of red to yellow sweets in a bag is 2 : 3. The ratio of hearts to stars in the bag is 3 : 1. What is the probability of picking out a red heart? (Give your answer as a decimal)

      Correct Answer: 0.3

      Q6.
      The ratio of gravel to water in this fish tank is 1 : 5. What volume of water is in the tank?

      An image in a quiz
      $$5000 cm^3$$
      $$6 000 cm^3$$
      $$24 000 cm^3$$
      Correct answer: $$25 000 cm^3$$

      Lesson appears in

      UnitMaths / Ratio

      Maths

      Show Foundation unit