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Year 6

Solve problems with two unknowns with one, several and infinite solutions

I can systematically solve problems with two unknowns with one, several and infinite solutions.

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New
New
Year 6

Solve problems with two unknowns with one, several and infinite solutions

I can systematically solve problems with two unknowns with one, several and infinite solutions.

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Lesson details

Key learning points

  1. Problems can be represented using bar models.
  2. Problems can be solved using trial and improvement.
  3. Different strategies work for different problems.

Keywords

  • Precise - If something is precise, it is exact, accurate and careful about the details.

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

Common misconception

Pupils resort to trial and improvement each time to solve every problem.

Pupils should look to apply what they know from previous learning and explore the structure of each problem to help them identify how best to solve it. You could come up with a checklist as a class for how best to explore a new problem each time.


To help you plan your year 6 maths lesson on: Solve problems with two unknowns with one, several and infinite solutions, download all teaching resources for free and adapt to suit your pupils' needs...

There is no set criteria to identify whether a problem has one, multiple or an infinite number of solutions. However, similarities can be found between problems. Encourage pupils to reason each time why they think a problem has one, multiple or infinite solutions.
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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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6 Questions

Q1.
In this problem, the difference between the known addends is 15 Match the expressions correctly.
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Correct Answer:When a = 20,the second addend = 35
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the second addend = 35

Correct Answer:When a = 35,the second addend = 50
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the second addend = 50

Correct Answer:When a = 52,the second addend = 67
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the second addend = 67

Correct Answer:When a = 61,the second addend = 76
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the second addend = 76

Q2.
If we call the first missing addend a, match the expressions correctly.
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Correct Answer:When a = 15,the second addend = 28
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the second addend = 28

Correct Answer:When a = 24,the second addend = 37
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the second addend = 37

Correct Answer:When a = 48,the second addend = 61
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the second addend = 61

Correct Answer:When a = 60,the second addend = 73
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the second addend = 73

Q3.
If we call the first missing addend a, what is the second addend when a = 10?
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Correct Answer: -10, negative 10, minus 10
Q4.
Match the value of the first missing number with the correct value of the second missing number.
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Correct Answer:When the first missing value is 70,the second missing value is 45
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the second missing value is 45

Correct Answer:When the first missing value is 85,the second missing value is 60
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the second missing value is 60

Correct Answer:When the first missing value is 92,the second missing value is 67
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the second missing value is 67

Correct Answer:When the first missing value is 88,the second missing value is 63
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the second missing value is 63

Q5.
Match the value of the second missing number with the correct value of the first missing number.
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Correct Answer:When the second missing value is 75 ,the first missing value is 57
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the first missing value is 57

Correct Answer:When the second missing value is 90,the first missing value is 72
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the first missing value is 72

Correct Answer:When the second missing value is 85,the first missing value is 67
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the first missing value is 67

Correct Answer:When the second missing value is 89,the first missing value is 71
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the first missing value is 71

Q6.
If the value of the first missing number is a, what is the value of the second missing number when a = 77?
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Correct Answer: 60

6 Questions

Q1.
How many solutions do you think this problem has?
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One solution
Multiple solutions
Correct answer: Infinite solutions
Q2.
What are the possible values of c if c is an integer? 4c < 13
4
Correct answer: 3
Correct answer: 2
Correct answer: 1
Correct answer: 0
Q3.
c and d are integer values. What is the value of c? You will need to find the value of d to help you. c =
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Correct Answer: 14
Q4.
A baker is packing cakes into boxes to take to a shop. He has 72 cakes. A small box can hold 6 cakes and a large box can hold 8 cakes. Correctly match the numbers of small and large boxes.
Correct Answer:4 small boxes ,6 large boxes
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6 large boxes

Correct Answer:9 small boxes ,2 large boxes
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2 large boxes

Correct Answer:8 small boxes ,3 large boxes
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3 large boxes

Q5.
Which of the solutions are correct?
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44 = 8t + 5s
44 = 5t + 8s
44 = 6t + 9s
44 = 9t + 5s
Q6.
Look at this isosceles triangle. What are the sizes of the remaining two angles? °
An image in a quiz
Correct Answer: 76