New
New
Year 6

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

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

New
New
Year 6

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

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

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Lesson details

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.

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.
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2024), 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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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
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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? $$cm^2$$
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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
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Correct Answer: 1.6, 1.6 kg
Q4.
What is the value of a? a =
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Correct Answer: 120
Q5.
What is the value of b? b =
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Correct Answer: 550
Q6.
What is the value of c? c =
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Correct Answer: 80

6 Questions

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