Reasoning in the classroom
Year 7
Fraction
thinking
Support materials for teachers
Year 7 Reasoning in the classroom – Fraction thinking
These Year 7 activities encourage learners to use their understanding
of fractions to solve and create simple problems.
Fraction thinking
Learners use their understanding of fractions to solve a simple problem.
Includes:
■■ Fraction thinking question
■■ Markscheme
My fraction puzzle
They use their understanding to create puzzles for others to solve.
Includes:
■■ Explain and question – instructions for teachers
Reasoning skills required
Identify
Communicate
Review
Learners choose their own
strategies and consider
possible approaches.
They explain their thinking.
They consider their work,
reflecting on what makes a
puzzle easy or difficult to solve.
Procedural skills
Numerical language
■■ Fraction equivalence
■■ Equivalent
■■ Finding fractions of quantities
■■ Denominator
■■ Simplest form
■■ Cancel
■■ Factors
■■ Integer
Year 7 Reasoning in the classroom: Fraction thinking
Introduction
Fraction thinking
Activity 1 – Fraction thinking
or
Outline
Learners use fractional relationships to solve a simple problem.
You will need
Q
Fraction thinking question
One page for each learner
M
Markscheme
Year 7 Reasoning in the classroom: Fraction thinking
Activity 1 – Fraction thinking – Outline
Q
⅓ of a number is 18
What is ⅙ of the number?
2m
Fraction thinking
Activity 1 – Fraction thinking – Question
M
Activity 1 – Fraction thinking – Markscheme
Marks
2m
Or 1m
Answer
9
Shows 18 ÷ 2 (or half of 18)
7
Efficient method, realising that
⅙ is half of ⅓
7
Working out the number
7
Has noted the relationship
between ⅓ and ⅙ but has then
doubled rather than halved
Efficient
method
Or
Shows 54
Or
Gives the answer 36
Common
error
Note that as there is little variety in learner responses, there are no
exemplars for this item.
Year 7 Reasoning in the classroom: Fraction thinking
Activity 1 – Fraction thinking – Markscheme
My fraction puzzle
Activity 2 – My fraction puzzle
or
Outline
This Activity is designed to carry on from Activity 1 – Fraction thinking.
Learners use their knowledge and understanding of equivalent fractions to create
fraction puzzles for other groups to solve.
You will need
No resources are required.
Year 7 Reasoning in the classroom: Fraction thinking
Activity 2 – My fraction puzzle – Outline
Activity 2 – My fraction puzzle
Ask learners to work together to produce a list of (positive) fractions that are less than
1 and have denominators between 2 and 10 inclusive. The fractions should be given in
their simplest form so that ¼ is included but 24 is not (since 24 = ½ ).
Explain
For teacher reference, the fractions are:
½
17
19
⅓
27
29
⅔
37
49
¼
47
59
¾
57
79
⅕
67
89
⅖
⅛
101
⅗
⅜
103
⅘
⅝
107
⅙
⅞
109
⅚
Now ask learners to use two (or more) of these fractions to create their own fraction
puzzles for others to solve.
Easy example: ‘If ⅓ of a number is 12, what is ⅔ of the number?’
More difficult example: ‘If ⅓ of a number is 15, what is ⅗ of the number?’
Optional rule to prevent repeated use of the fraction ½ :
once you have used a fraction, it cannot be used again.
Or
Simplify by allowing the
denominators to be 2, 3, 4 or 5.
■■ How do you know when fractions are equivalent?
■■ How can factors help you decide when a fraction can be cancelled?
■■ Why do 5 and 7 have fractions that can’t be cancelled, yet 9 does? Can you tell me
Question
another denominator that has fractions that can’t be cancelled? (Any prime number.)
■■ When you choose two fractions to use for your puzzle, what makes the puzzle easy or
difficult? Did you sometimes get an answer that wasn’t an integer (whole number)?
How did you get around that problem?
Year 7 Reasoning in the classroom: Fraction thinking
Activity 2 – My fraction puzzle – Explain and question