New
New
Year 6
Explain why there is sometimes only one solution to a problem
I can explain why there is sometimes only one solution to a problem.
New
New
Year 6
Explain why there is sometimes only one solution to a problem
I can explain why there is sometimes only one solution to a problem.
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Lesson details
Key learning points
- Some problems with two unknowns have only one solution.
- If both the sum of and difference between the two unknowns are known then there will only be one solution.
- Some problems with two unknowns have many solutions.
- Some problems with two unknowns have an infinite number of solutions.
Keywords
Sum - The sum is the total when numbers are added together.
Difference - The difference is the result of subtracting one number from another. How much one number differs from another.
Common misconception
Pupils may draw bar models which are inaccurate and do not represent the problem effectively.
These types of problems lend themselves to be drawn using bar models that are lined up one on top of the other. Model creating these bar models with the pupils and explaining how you know where the numbers sit within them.
Encourage pupils to find the structure of each problem and identify whether the sum and difference is known or whether the sum and the multiplicative relationship between the known. Broaden pupils identification of these problem types in different contexts.
Teacher tip
Equipment
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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Starter quiz
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6 Questions
Q1.
Calculate the size of a in this representation.
Q2.
Calculate the size of a in this representation.
36
36.5
37
38
Q3.
Calculate the size of c in this representation.
Q4.
Calculate the size of e in this bar model.
Q5.
Andeep and Izzy are selling 60 ice poles. Izzy sells 8 ice poles more than Andeep. How many ice poles does Izzy sell?
Q6.
Andeep and Izzy have read 348 pages altogether. Andeep has read 32 more pages than Izzy. How many pages has Andeep read?
Exit quiz
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6 Questions
Q1.
When the difference and sum of two unknown numbers is known, there are how many possible solutions?
2
3
4
Infinite
Q2.
a represents a larger number. b represents a smaller number. The sum of a and b is 60, and the difference between them is 10
What number does a represent?
30
40
45
Q3.
a represents a larger numbers and b represent a smaller number.
The sum of a and b is 205, and the difference between them is 25
What number does b represent?
80
85
95
100
Q4.
Steven is 24 years younger than his mum. The sum of their ages is 68 years. How old is Steven’s mum? years old.
Q5.
The sum of two numbers is 140
One number is three times the size of the other number. What are the two numbers?
40 and 100
30 and 110
32 and 108
Q6.
The sum of two numbers is 410
One number is one-quarter times the size of the other number. What is the value of the largest number?