Transforming lives through learning

Scottish Survey of Literacy & Numeracy

Support Material

First Level – Fractions

Produced by Education Scotland

Transforming lives through learning

222222

First Level FractionsDid 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?

• 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?

Consider these reflective questions -then move to next section

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 4Shade 1 out of these 4

This could be done in a number of ways, such as:

They can then shade 1 out of each group of 3. For example

or

Strategies

StrategiesHow 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.

• 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

Consider these reflective questions -then move to next section

Finding a simple fraction of a single item

Consider though not only shading 1 out of every 4 circles, such as:

Strategies

Splitting into convenient groups of 4

Shading 1 then counting and leaving 2,3 and 4 un-shaded.

But also...

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

• 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?

Consider this reflective question -then move to next section

Pupils must recognise that the problem requires them to divide 66 by 3.

Strategy 1: PartitioningPartitioning 66 into numbers that are easily divisible by 3:66 = 60 + 6So 66 ÷ 3 = 60 ÷ 3 + 6÷ 3 = 20 + 2 = 22If 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 + 6So66 ÷ 3 = 30÷ 3 + 30÷ 3 + 6÷ 3 = 10 + 10 + 2 = 22

Strategies

Strategies

Strategy 2: Using a number lineMany 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 ?

StrategiesStrategy 3Consider another visual approach:Split a plate into 3 equal parts

Consider doing this with concrete resources such as paper plates and counters

StrategiesSplit 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

How could pupils check their answer?

What are the transferrable skills from previous knowledge?

Consider these reflective questions -then move to next section

Key skillsLinking 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

• How do you use word problems and contextualised examples to develop children’s ability to apply their fraction skills?

Consider this final reflective question

www.educationscotland.gov.uk