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# Spine 3: Fractions

Created on 04 June 2019 by ncetm_administrator
Updated on 03 September 2019 by ncetm_administrator

## Introduction

The Fractions spine is divided into 10 segments for Years 3–6, plus a preliminary segment (3.0) with guidance notes on teaching fractions in Key Stage 1. For each of these segments we have produced a detailed teacher guide, including text and images. For the 10 main segments, the images are also presented as animated PowerPoint slides, which further enhance teacher knowledge and can be used in the classroom (for best results, please view these in ‘Slideshow’ view; for some slides, supporting notes are provided in the ‘Notes’ section). These materials are not, in any way, lesson plans, but they can be used in conjunction with a high-quality mastery textbook to support planning. Click on the ‘+’ signs below to view the materials.

The following PDF offers an overview of the complete Fractions spine, including a synopsis of each segment.

## 3.0 Guidance on the teaching of fractions in Key Stage 1

Cover the Key Stage 1 statutory requirements for fractions, including recognising, finding, naming and writing one-quarter, one-third, one-half/two-quarters, and three-quarters of an object, shape or quantity.

## 3.1 Preparing for fractions: the part–whole relationship

Identify parts and wholes of areas, lengths and sets. Identify equal and unequal parts; make judgements about the relative size of a part to a whole. Find the whole when the size of a part and number of equal parts is known.

## 3.2 Unit fractions: identifying, representing and comparing

Learn to name and write unit fractions. Recognise and show unit fractions of areas, lengths and quantities. Relate numerators and denominators to parts and wholes; explore how the greater the denominators, the smaller the unit fraction.

## 3.3 Non-unit fractions: identifying, representing and comparing

Learn to name and write non-unit fractions, recognising them as multiples of unit fractions. Learn that fractions are numbers that can be positioned on a number line. Compare and order fractions with the same denominator or same numerator.

## 3.4 Adding and subtracting within one whole

Explore how to add and subtract fractions within one whole where the denominators are the same. Apply prior knowledge of the inverse relationship of addition and subtraction with whole numbers, to fractions.

Easy-download: Year 3 (All of the teacher guides and representations for segments

## 3.5 Working across one whole: improper fractions and mixed numbers

Meet mixed numbers and improper fractions, and learn to convert between them; compare, order and place them on a number line. Extend addition and subtraction from within a whole to numbers greater than one whole.

## 3.6 Multiplying whole numbers and fractions

Consider multiplication of whole numbers and proper fractions as both repeated addition and scaling. Understand that multiplication of a whole number by a proper fraction results in a smaller number.

Easy-download: Year 4 (All of the teacher guides and representations for segments

## 3.7 Finding equivalent fractions and simplifying fractions

Discover how equivalent fractions have the same proportional relationship between the numerator and denominator, and therefore have the same numerical value. Convert between equivalent fractions and simplify fractions.

## 3.8 Common denomination: more adding and subtracting

Learn to add and subtract fractions with different denominators by first finding a common denominator. Compare fractions using a range of methods, including converting to a common denominator.

Easy-download: Year 5 (All of the teacher guides and representations for segments

## 3.9 Multiplying fractions and dividing fractions by a whole number

Explore how to multiply two fractions. Learn how to divide a fraction by a whole number by first converting to an equivalent multiplication. Review how multiplying by a proper fraction makes a number smaller.

## 3.10 Linking fractions, decimals and percentages

Make connections between fractions and previous work on decimals. Learn common fraction and decimal equivalences. Understand that percentages tell us about the proportion being considered. Find percentages of quantities.

Easy-download: Year 6 (All of the teacher guides and representations for segments

## Acknowledgements

The NCETM and Maths Hubs would like to thank the following for their contribution to the materials:

• Primary mathematics specialists: Adrian Cannell, Clare Christie, Suzanne Coxon, Jonathan East, Alison Hopper, Elizabeth Lambert, Debbie Morgan, Cat Stone

• Educational consultant: Dr Alf Coles, University of Bristol

• Editorial and production: Liam Benson, Design and Define; Nicholas Bromley; Charlotte Christensen; Rachel Houghton; Jalita Jacobsen; Bill Mantovani; David Mantovani; Sam Radford; Gemma Smith; Cheryl Stirr; Yvette Sturdy, DiGiV8 Ltd; Christine Vaughan; Andrew Young

• Illustrations: Steve Evans

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27 November 2019 09:24
The Mastery PD materials focus on the overall learning trajectory of a concept rather than the content of a particular Year Group. They aim to bring greater coherence to the National Curriculum and take into account connections to other concepts.There is a note in the sequencing document in Y4 that alludes to a connection to multiplication.
22 November 2019 12:57
Please can I ask why multiplication of whole numbers and fractions is in the Y4 band when this is not a national curriculum expectation until Y5?
05 July 2019 14:28
Hi dltrinder, you'll be best to keep an eye on this page. We can't guarantee that that will get specifically announced.
05 July 2019 14:00
28 June 2019 12:53
We will produce guidance for KS1 once all the fraction segments have been published for KS2. This will draw on what is in Y3. All of the faction requirements of the primary curriculum are covered in the KS2 materials. We made the decision to focus on KS2 to address fractions in a ‘mastery way’.
28 June 2019 12:32
The NC has sections in KS1 for fractions. In year 2 I would use some areas of the Year 3 spine eg parts and whole and equal parts.