Scottish Survey of Literacy &
Numeracy
Support Material
First Level – Fractions
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First Level Fractions
Did you know?…
Recent survey results have shown that more than 51% of P4 pupils have
difficulty when asked to carry out basic calculations involving fractions.
What strategies can we teach children to address this?
Consider these reflective questions then move to next section
• Think about the language used when teaching fractions.
• You may wish to make a list of key words or terms.
• Are you confident that you know and understand the
meanings of key terms such as ‘numerator’ and
‘denominator’?
• What strategies can you use to support the children’s
understanding and use of the vocabulary of fractions?
First Level Fractions
Key Points:
Pupils have difficulty with
• Finding a simple fraction of a whole
• Finding a simple fraction of a quantity, using division
Consider these reflective questions then move to next section
• The numeracy survey tells us that many children have
difficulties with finding fractions of a whole or of an
amount (using division). Do you teach children about
important relationships such as that between fractions
and division?
• What other important relationships should be
highlighted?
• Why do you believe children have these difficulties and
how can you help them avoid or overcome them?
• What other aspects of fraction work do children find
difficult?
Finding a simple fraction of a single item
Or
How can pupils be helped to tackle problems like this?
Strategies
Shade 1 out of these 4
Shade 1 out of these 4
This could be done in a number of ways, such as:
Strategies
They can then shade 1 out of each group of 3.
For example
or
Strategies
How might you work with pupils to help them understand how to shade ½ of
this regular pentagon, which has been split into unequal parts?
How would this type of problem help you assess a pupil’s understanding of
fractions?
Demonstrating that two unequal parts can make a fraction in this way will:
• Provide a good basis in developing understanding of adding fractions
• Reinforce the importance of part : part – whole relationships.
Consider these reflective questions then move to next section
• How well do you believe children understand the relationship
between ‘fraction of a whole’ and ‘fraction of an amount or
quantity’? For example:
Shade one quarter of a rectangle
Shade one quarter of 8
• How can you help children make this connection? How can you
ensure that children can do so when the number of parts is not
so friendly to work with? For example:
Shade one quarter of a rectangle
Finding a simple fraction of a single item
Strategies
Consider though not only shading 1 out of every 4 circles, such as:
Splitting into convenient
groups of 4
But also...
Shading 1 then counting and
leaving 2,3 and 4 un-shaded.
Strategies
• Consider shading 1 out of the 4 rows:
• In what other ways could you encourage pupils to look at this type of
problem?
Finding a simple fraction of a single item
Finding a simple fraction of an amount
Consider this reflective question then move to next section
• Children tend to relate fractions in terms of ‘shading’ or
identifying parts of something eg a cake or a pizza?
How do you extend their thinking of fractions as numbers
ie they lie on the number line?
Strategies
Pupils must recognise that the problem requires them to divide 66 by 3.
Strategy 1: Partitioning
Partitioning 66 into numbers that are easily divisible by 3:
66 = 60 + 6
So
66 ÷ 3 = 60 ÷ 3 + 6÷ 3
= 20 + 2
=
22
If 60 is still seen as too large a number by pupils, they could consider splitting
66 into parts which fall within the ‘normal’ range of the 3 times table
For example:
66 = 30 + 30 + 6
So
66 ÷ 3 = 30÷ 3 + 30÷ 3 + 6÷ 3
= 10 + 10 + 2
= 22
Strategies
Strategy 2: Using a number line
Many pupils are visual learners and may feel more comfortable with a visual
approach to solving a problem. Using a number line can help with this.
Consider, for example:
or
What questions might you pose to pupils to help them to find the numbers
represented by
and
?
Strategies
Strategy 3
Consider another visual approach:
Split a plate into 3 equal parts
Consider doing this with concrete
resources such as paper plates
and counters
Strategies
Split 66 equally among the 3 sections.
Pupils can ‘chunk’ 66 to do this.
For example:
Start by
putting 10
onto each
section.
This only gets
us to 30, so
repeat this:
We’re now at 60, so we
have 6 left to split among
the sections, so 2 goes
onto each section
Finding a simple fraction of an amount
What are the transferrable skills from previous knowledge?
How could pupils check their answer?
Consider these reflective questions then move to next section
Key skills
Linking number facts
Pupils should be able to make the link between finding a fraction of an
amount and dividing.
This in turn requires them to understand the link between division and
multiplication.
Work with pupils to develop their understanding of number facts…………
Key skills
Key skills
Consider this final reflective question
• How do you use word problems and contextualised
examples to develop children’s ability to apply their
fraction skills?
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