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      Explain how you know you have found all the possible solutions to a problem with two unknowns

      Lesson details

      Learning outcome

      I can explain how you know you have found all the possible solutions to a problem with two unknowns.

      Key learning points

      1. A trial and improvement approach can be used if a model can't easily be drawn.
      2. A table can be used to record and check all possible solutions have been found.
      3. Some problems with two unknowns have an infinite number of solutions.

      Keywords

      • Systematically - To work systematically means to work in an organised way, often according to a fixed plan or system.

      • Infinite - Infinite means without an end. If something is unlimited, you could say it has an infinite number of things.

      Common misconception

      Pupils attempt to represent the problems with bar models rather than take a systematic, trial and improvement approach.

      Encourage pupils to represent each problem how they would like. Pupils should take time to notice why it is that the bar model if not appropriate to help solve these problems and identify these clues within the questions.

      Teacher tip

      Ensure pupils experience a wide range of problems with either one solution or many solutions. In doing this, pupils can begin to generalise the features of problems where there is only one or many solutions, drawing upon this when solving future problems of a similar nature.

      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.
      1 eraser (a) and 4 pencils (4b) cost £3; 3 erasers (3a) and 4 pencils (4b) cost £3.80; Find the cost of one eraser. p

      An image in a quiz
      Correct Answer: 40, 40 p, 40 pence

      Q2.
      Two different designs are made with the same square and triangular tiles. The area of the whole design is given. What is the area of one square tile? $$cm^2$$

      An image in a quiz
      Correct Answer: 26

      Q3.
      The masses of some groups of large and small bags of potatoes are shown here. What is the mass of the small bag? kg

      An image in a quiz
      Correct Answer: 1.6, 1.6 kg

      Q4.
      What is the value of a? a =

      An image in a quiz
      Correct Answer: 120

      Q5.
      What is the value of b? b =

      An image in a quiz
      Correct Answer: 550

      Q6.
      What is the value of c? c =

      An image in a quiz
      Correct Answer: 80

      6 Questions

      Q1.
      Match the pairs of missing unknown numbers to find possible solutions.

      An image in a quiz
      Correct Answer:5,20

      20

      Correct Answer:1,16

      16

      Correct Answer:3,18

      18

      Correct Answer:2,17

      17

      Correct Answer:4,19

      19

      Q2.
      If one of the unknowns is 50, what would the other unknown be?

      An image in a quiz
      Correct Answer: 65, 35

      Q3.
      Laura has some triangles and pentagons. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 35 How many of each shape could she have?

      An image in a quiz
      Correct answer: 5 triangles and 4 pentagons
      4 triangles and 5 pentagons
      10 triangles and 2 pentagons
      Correct answer: 10 triangles and 1 pentagon

      Q4.
      Laura has some squares and pentagons. She chooses some of the shapes and when she counts the number of sides, she finds that the total is 52 How many of each shape could she have?

      An image in a quiz
      Correct answer: 8 squares and 4 pentagons
      8 pentagons and 4 squares
      Correct answer: 8 pentagons and 3 squares
      3 pentagons and 9 squares

      Q5.
      I use two different lengths of wood to make a fence 10.4 m long. One length of wood is 80 cm and the other is 1.20 m. If four 80 cm planks were used, how many of length 1.20 m were used? planks

      An image in a quiz
      Correct Answer: 6

      Q6.
      In one month, Jun spends 9.5 hours in maths and science lessons. One Maths lesson is 50 minutes and one science lesson is 70 minutes. Jun had 3 maths lessons, how many science lessons did he have?

      Correct Answer: 6

      To help you plan your 6 maths lesson on: Explain how you know you have found all the possible solutions to a problem with two unknowns, download all teaching resources for free and adapt to suit your pupils' needs...