• Maths4life booklet

This is an overall guide to some of the complexities in teaching and learning fractions, including possible misconceptions. The document also includes some suggestions for activities.

Please note, this publication was written for teachers of adult learners – lots of useful information and ideas though you will want to adapt activities.

• Fractions: difficult but crucial in mathematics learning Nunes, T. (2006) Teaching and learning research briefing, no, 13, London, The Institute of Education

This article addresses some of children’s basic ideas about fractions.

• Teaching Fractions; Education Practices series Vol:22: 2011 Fazio, L. and Siegler, R. (2011) Education Practices series; Vol:22: 2011

This research guide focuses on students’ difficulties with fractions and provides suggestions for teachers to improve fractions instruction in their own classrooms. The guide is broken up under clear subheadings that address different aspects of why fractions are difficult to teach.

• Fractional Thinking Concept Map

This concept map from a New Zealand teaching website organises and explains the different aspects of teaching fractions in a clear, visual way. It also provides definitions for vocabulary encountered when teaching fractions. There are links to some useful activities and games, although many are locked to those outside New Zealand.

• BBC Skillwise: Maths and Literacy for Adults

• Using the Singapore bar model to support the teaching and learning of fractions

An introductory guide to using the Singapore bar model, with ideas on how it can be used to support problem solving in maths, including fractions.

• Early Fraction Development by Bernard Bagnall, NRICH

A useful article in which Bernard Bagnall outlines tasks which will help young children develop the concept of fractions. It could be a good starting point for assessing pupils and has many activities involving the folding of paper.

Activity A – visualising fractions along a line

• Use counting sticks and bead strings to help children visualise fractions.

If the bead string represents one whole, then each set of ten coloured beads could represent one tenth and each individual bead could represent one hundredth.

1. Label the two ends of the bead string as 0 and 1. Give students tags to place each tenth on the bead string. You could use a 1-10 bead string instead of a 1-100 bead string.
2. Join several bead strings together to create fraction lines that extend over one. For example, five bead strings allow fractional numbers from 0 to 5. Label simultaneously in mixed numbers (2 ½) and improper fractions (5/2).
3. Ask the pupils to represent each tenth with a variety of manipulatives, for example, Numicon, Dienes (Big Base) and coins.
4. Extend pupils’ understanding to include the equivalence of fractions, decimals and percentages. For example, ½ = 0.5 = 50% or 2 2/10 = 2.2 = 220%

Activity B

• Fractional Triangles

This practical activity develops an understanding of the part and the whole,

• Understanding unit fractions: A Hungarian Approach

A series of lessons on finding fractions of amounts from Lesson 11, page 9 onwards based on an alternative, Hungarian approach, to teaching maths. 

Activity C

• Trains

An activity from New Zealand that involves using number rods to develop children’s understanding that fractions can extend beyond 1.

• Children can make number lines for display around the classroom, that demonstrate counting in different fractional steps. For example counting in steps of ½ an apple, 1/4s of pizza, 1/10 of a £1 (steps of 10p)

• Daily practice of counting forwards and backwards in 1/2s, 1/4s, 1/10s and 1/3s, including extending to below zero

Activity D – equivalent fractions

• Fractional Walls

An activity based on Cuisenaire / number rods.

• Matching Fractions

A ‘pelmanism’ style matching activity based on fractions.

• Use equivalence circles, for example pizza or cake slices in a variety of activities for pupils to explore equivalence.

Activity E – adding fractions

• Addition, subtraction and equivalent fractions

A series of activities based on deepening students’ understanding of adding and subtracting fractions with the same denominator.

• Use a variety of representations, for example, number rods, paper strips and equivalence circles to model what happens when you add or subtract fractions with the same denominator. This will help children understand why the denominator doesn’t change.

Activity F

• Fractions interactive teaching programme

(NB This resource was produced for the Primary National Strategy, which was formally discontinued in 2011. However, the resource has the potential to complement teaching in line with the new 2014 mathematics curriculum)

This ITP allows you to divide a green strip into a number of equal parts and colour the individual parts in yellow, clearly showing any comparison.

• Smartie Fractions

Use mini packets of smarties for children to find the fraction of each colour in a packet. This is useful for comparing fractions with the same denominator and for adding and subtracting fractions

More wonderful ‘Maths and Smarties’ ideas.

Activity G – solving problems

• Use the Bar Model to solve problems

Use the ‘Thinking blocks on the maths playground’ website to model word problems involving fractions and to model adding and subtracting unit fractions. There are video demonstrations, guided problems and the ability to use the blocks to solve your own problems.

• Fair Feast

Assess and develop children’s understanding of equal sharing with this picnic problem.

Useful Resources

• Mental Images for Fractions, Decimals, Percentages, Ratio and Proportion (FDPRP)

A list of models and images to support the development of children’s understanding of fractions. Includes ideas on how to use them in the classroom.

• Overcoming Barriers in Fractions

All the Overcoming Barriers materials from level 1 to level 5 linked to fractions, decimals and percentages contain useful assessment questions and a range of models and images.

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

Children should be able to:

• Use decimal notation for tenths
• Divide single digits or whole numbers by 10
• Explain how finding 1/10 is the same as dividing by 10

Here is part of a number line. Write in the numbers missing from the two empty boxes.

recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Children should be able to:

• Recognise and write unit and non-unit fractions of shapes.

Unit Fractions. Unit means one. Here are some examples of unit fractions.

Can you spot the pattern? A unit fraction is one part of a whole that is divided into equal parts.

Non-unit fractions. Unit means one, so non-unit is any number apart from one. Here are some examples of non-unit fractions.

Many (or, rather, more than one of the) parts, of an equally divided whole, is a non-unit fraction.

Taken from: BBC skillswise different types of fraction

• Understand that the number on the bottom of a fraction tells me how many pieces the whole is divided into

What fraction of this shape is shaded? How do you know? Is there another way that you can describe the fraction?

• Find fractions of amounts

Here are 21 apples. Put a ring around one third of them.

recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

Children should be able to:

• Position fractions on a number line; eg. mark fractions such as ½, 3 ½ and 2 3/10 on a number line marked from zero to 5.

A fraction of each shape is shaded. Match each fraction to the correct place on the number line. One has been done for you.

recognise and show, using diagrams, equivalent fractions with small denominators

Children should be able to:

• Identify pairs of fractions that total 1.
• Circle two fractions that have the same value.

add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

This could also be done by using drawings and in the array form:

For addition:

and for subtraction:

compare and order unit fractions, and fractions with the same denominators

Children should be able to:

• Would you rather have 1/3 of 30 sweets or 1/5 of 40 sweets? Why?

solve problems that involve all of the above

Children should be able to answer questions like:

• 15 grapes are shared equally onto five plates. What fraction of the grapes is on each plate?

• Meg has 20 pet stickers to go on this page:

1/4 of them are dog stickers
1/2 of them are cat stickers
The rest are rabbit stickers

How many rabbit stickers does she have?

• Adding and Subtracting Fractions with the same denominator

This resource hosted in the Stem Centre E-Library provides a useful overview for adding and subtracting fractions.