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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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New
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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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Share activities with pupils
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Lesson details

Key learning points

  1. Some problems with two unknowns have only one solution.
  2. If both the sum of and difference between the two unknowns are known then there will only be one solution.
  3. Some problems with two unknowns have many solutions.
  4. 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 (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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Starter quiz

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6 Questions

Q1.
Calculate the size of a in this representation.
An image in a quiz
Correct Answer: 35
Q2.
Calculate the size of a in this representation.
An image in a quiz
36
36.5
37
Correct answer: 37.5
38
Q3.
Calculate the size of c in this representation.
An image in a quiz
Correct Answer: 175
Q4.
Calculate the size of e in this bar model.
An image in a quiz
Correct Answer: 75
Q5.
Andeep and Izzy are selling 60 ice poles. Izzy sells 8 ice poles more than Andeep. How many ice poles does Izzy sell?
Correct Answer: 34
Q6.
Andeep and Izzy have read 348 pages altogether. Andeep has read 32 more pages than Izzy. How many pages has Andeep read?
Correct Answer: 190, 190 pages

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?
Correct answer: 1
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
Correct answer: 35
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
Correct answer: 90
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.
Correct Answer: 46
Q5.
The sum of two numbers is 140 One number is three times the size of the other number. What are the two numbers?
Correct answer: 35 and 105
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?
Correct Answer: 328