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Thinking Through Mathematics

These resources, produced by The National Centre for Excellence in the Teaching of Mathematics (NCETM), have been designed to encourage distinctive ways of thinking and learning as part of the NCETM professional development package .

Analysing reasoning and solutions  sets a number of problems about proportion and percentages and gives a range of student responses to each problem. The examples provide inspiration for further discussion about student misconceptions .

Classifying  contains a number of cards each containing a different shapes. Students are asked to place the cards into categories. The task is inspiration for teachers to discuss how the teacher should proceed with the activity. The second activity, classifying using two-way tables, requires students to place the cards into a two-way table according to the shape’s properties.

Creating and solving problems  explains the ‘doing’ and ‘undoing’ processes in mathematics giving three examples of a problem poser where a closed problem is posed and the problem solver where the problem is posed in a more open format.

Evaluat i ng mathematical statements  gives a number of examples for which it has to be decided whether the statement is always true, sometimes true or never true. A further example is given in which each statement has to be categorised as true, false or unsure.

Interpreting multiple representations  contains an example of an activity in which students are asked to take it in turns to match up cards. One set of cards contain decimal numbers, one set contain diagrams of shaded squares and one set contains arrows on a number line.

As part of the NCETM course teachers were asked to make a similar activity for another area of mathematics.

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Making the most of bar modelling

Editor’s Note:

This is an updated version of a blog post published on May 15, 2019.

How do you knock a teacher’s socks off? Show them a game-changing technique that helps children solve even the trickiest mathematical problems. It’s called bar modelling and here’s why you should add it to your practice.

The first time I met the bar model method I was completely blown away by it. Since then, I’ve seen this reaction again and again with the teachers that I train. It’s a transformational technique for teachers and children alike — particularly children who struggle with maths .

What exactly is a bar model?

Essentially, the bar modelling technique is a form of visual algebra. It’s a method for visualising a maths problem where bars or rectangles represent known numbers and unknown numbers. It acts as a bridge between the word problem and the abstract maths required to solve the problem.

In 2013, the NCETM said:

“We know that when solving word problems, it is often not the calculation that children can’t do — rather they are not sure which calculation they need to do.”

This is especially true with word problems. Pupils can get bogged down in the details of a word problem, most of which has no bearing on the mathematics.

Consider the following word problem: Sarah, Amir, and Joanna all enjoyed collecting football cards, for their favourite team, Manchester United. They had 60 cards altogether. If they shared them out equally, how many would they each have.

Most of the words in this problem are totally irrelevant, but some pupils need to be taught how to extract the relevant information. One popular way of solving a problem like this is the RUCSAC method: Read, Underline, Calculate, Solve, Answer, Check .

However, this sequence of steps should be used with caution. When you look at this technique more closely, you’ll see that it emphasises process over understanding.

A lot of word problems can contain ambiguous language. Like the following:

How many more than 23 is 27? This requires the calculation 27 – 23 = 4 which is a subtraction.

But with the RUCSAC method, many children would underline ‘more than’ and think that the calculation required was addition.

What is 4 more than 23? This requires the calculation 23 + 4 = 27 which is an addition.

The language is very similar, but in this case the calculation required is different.

Enter, the bar model

The best way to help pupils with ambiguous word problems is to develop their understanding. Bar modelling helps children see the deeper structures within a maths problem and lets them construct a model of the problem that easily shows them what calculations are needed.

One of the reasons the bar model has become so popular is it’s simplicity. All you need is a pencil and paper, and it can be applied across the whole range of mathematical topics. In fact, there are only two main types of bar model: the part-part-whole model and the comparison model .

Part-part-whole model

The part-part-whole model can be used for questions involving all four operations, fractions, measure, algebra, time, ratio, proportion and much more.

In the Maths — No Problem! Primary Series the part-part-whole model is introduced like this: Here we know two parts and need to find the whole. The unknown amount is always represented with a question mark and this tells us what calculation to do. For the part-part-whole model we know two pieces of information and have to find the other. So, we may know the whole and one part and have to find the other part.

Comparison model

The comparison model is a bit different. Here we’re comparing two bars: When working with the bar model, we can draw the bars on paper or represent them with cut-out strips of paper, Cuisenaire rods , interlocking cubes or even counters.

In this example we’re looking at a before and after model. This means we need to represent the model at the start of the problem and at the end of the problem after there has been some sort of change.

Sam has 5 times as many marbles as Tom. If Sam gives 26 marbles to Tom, the two friends will have exactly the same amount. How many marbles do they have altogether? We can see that we’ve moved two bars so that Sam and Tom end up with equal amounts of marbles. So, two bars must represent 26, and one bar is 13. There are 6 bars in the diagram, so the total number of marbles is 78.

For this type of question, it’s useful to use rods or strips, this way pupils can physically move the bars to show the change.

One of the strengths of the bar model is that it helps children work at a higher level of maths. In the above example, without the bar model we would have to solve the problem algebraically. The solution would look a bit like this:

5x − 26 = x + 26 4x = 52 x = 13

Altogether we have 6x = 78

I’m not sure that many primary-aged children you know who could cope with that, but by using the bar model we have made this problem accessible to children from around age 8 or 9.

Access to higher-level content

In 2012, there was a question on the GCSE Maths Higher paper, that becomes very straightforward once you know how to use the bar model. I’ve tried this out with primary school children in Year 5 and 6 and they managed it with ease:

Ralph posts 40 letters, some of which are first class, and some of which are second class. He posts four times as many second-class letters as first. How many of each class of letter does he post? Try it with your class. It’s possible your pupils will take to it more easily than you do! After all, they haven’t had a lifetime of abstract algebra to contend with.

Check out this video of Maths — No Problem! founder Andy Psarianos explaining the bar model method .

Judy Hornigold

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The NCETM Maths Podcast

https://feed.podbean.com/ncetm/feed.xml

The NCETM Maths Podcast, from the National Centre for Excellence in the Teaching of Mathematics, invites teachers, maths experts and anyone with a passion for teaching maths to talk about topics that shine a light on great maths teaching. With ideas for classroom activities, inspirational stories of careers in maths, and lively debates on contemporary topics, the NCETM podcast has something for everyone. Listen wherever you get your podcasts.

Wednesday Jun 19, 2024

Oracy in the maths classroom - Part 2

In Part 2 of our episode on oracy with Jane Hawkins from the NCETM and Kathleen McBride from Voice 21, we explore the impact of the Maths Hubs’ Research and Innovation Work Groups (RIWGs), strategies for implementing oracy in both primary and secondary education, and the importance of oracy for enhancing student learning and engagement.

A transcript (PDF) of this episode is available to download.

Taking part in the discussion:

• Kathleen McBride, Senior Learning and Innovation Lead, Voice 21
• Jane Hawkins, Assistant Director for Secondary, NCETM, and Assistant Maths Hub Lead, Jurassic Maths Hub
• Julia Thomson, Communications Manager, NCETM.

Episode chapters

• 00:06 Welcome and introductions
• 00:51 Research and Innovation Work Groups (RIWGs)
• 02:28 Impact of Oracy RIWGs
• 04:41 Talk strategies
• 08:25 What does successful oracy look like?
• 10:58 The teacher’s role
• 12:18 Different types of talk
• 18:35 Oracy in secondary education
• 22:17 Ideas for teachers
• 25:44 Misconceptions about oracy
• 28:52 Resources and further reading
• 30:31 Conclusion.

Useful links

• Listen to Part 1 of this podcast episode
• All-Party Parliamentary Group Report: Speak for Change (2021)
• Voice 21 website
• Voice 21 Talk Tactics and  How to develop independent student discussion
• Voice 21 Talking Point publication (2023)
• Voice 21 Oracy Benchmarks report (2019)
• Voice 21 Impact Report (2022-23)
• NCETM Primary Curriculum Prioritisation materials
• NCETM Checkpoints for KS3
• Interthinking: Putting Talk to Work by Karen Littleton & Neil Mercer (Routledge, 2013)
• Talking Points: Discussion Activities in the Primary Classroom by Lynn Dawes (Routledge, 2012)
• Find your local Maths Hub
• Maths Hubs Research and Innovation Work Groups (RIWGs)
• Explore previous episodes of the NCETM podcast in our archive
• The NCETM Maths Podcast on Instagram.

Wednesday Jun 05, 2024

Oracy in the maths classroom - Part 1

In Part 1 of our discussion with Kathleen McBride from Voice 21 and Jane Hawkins from the NCETM’s Secondary Team and Jurassic Maths Hub, we discuss the definition of oracy, its significance for students' mathematical development, behaviour and overall well-being, and the role of Research and Innovation Work Groups (RIWGs) in exploring oracy's impact in classrooms. We also take a look at Voice 21’s Oracy Framework for schools and teachers.

• 03:03 Definition, importance and research
• 08:58 Oracy challenges and misconceptions
• 13:01 Oracy Research and Innovation Work Groups
• 14:21 Oracy’s impact on learning
• 15:54 Purposeful talk
• 17:07 The Oracy Framework
• 19:54 Oracy in the maths classroom
• 28:33 Reflecting on teaching practice
• 30:15 Conclusion.
• All-Party Parliamentary Group Report Speak for Change
• Voice 21 Impact Report 2022-2023
• Voice 21 Oracy Framework
• Maths Hubs Research and Innovation Work Groups
• Bullock Report: A Language for Life (Bullock, 1975)
• EEF Dialogic Teaching Report (2017, 2022)
• School 21 and University of Cambridge Oracy Programme Pilot (2013/14)
• Coordinating Mathematical Success: the mathematics subject report (Ofsted, 2023)
• Explore previous episodes of the NCETM podcast in our  archive

Tuesday Apr 09, 2024

The NCETM Maths Podcast: Trailer

The NCETM Maths Podcast invites teachers, maths experts and anyone with a passion for teaching maths to talk about topics that shine a light on great maths teaching. With ideas for classroom activities, inspirational stories of careers in maths, and lively debates on contemporary topics, the NCETM podcast has something for everyone. 

Most episodes are around 20 minutes long – perfect for your journey to work. So, if you like what you hear, hit subscribe to make sure you don’t miss an episode.

You can also find The NCETM Maths Podcast on Instagram: @themathspodcast . Be the first to hear about new episodes, and join in with the debate.

If there is a topic you would like to hear us discuss on the podcast, let us know at: [email protected] . 

Tuesday Apr 02, 2024

Training to teach maths with Teach First

In this episode, Early Career Teachers from primary and secondary schools talk about their experiences of training to teach with Teach First, how they have honed their maths teaching skills, and what they have learned in their first years in the classroom.

• Emily Dixon, Year 1 teacher at Tinsley Meadows Primary Academy, Sheffield
• Lauren Garrigos, maths teacher at Heartlands High School, Haringey, London
• Beth Goodliff, Senior Communications Manager, NCETM.
• 00:06 Introduction and welcome
• 00:40 Meet the guests
• 01:14 The journey to becoming a teacher: decisions and backgrounds
• 02:35 Training with Teach First
• 06:30 Overcoming challenges in the classroom
• 09:24 Celebrating successes: positive moments in teaching
• 12:12 Professional development in the first years of teaching
• 14:22 Advice.
• Teach First teacher training programme
• Specialist Knowledge for Teaching Mathematics:  Primary Early Career Teachers Programme
• Specialist Knowledge for Teaching Mathematics:  Secondary Early Career Teachers Programme
• Teaching for Mastery

Wednesday Mar 27, 2024

Early maths concepts: doubles

In this episode of the podcast, Rebecca and Sue explore the foundations of doubles in Reception and discuss how this concept is built on in KS1 and beyond. Having both been teachers in Early Years or KS1, they reflect on their own experiences and share practical tips for the classroom.

• Sue Evans, NCETM Assistant Director for Primary, and former primary teacher
• Rebecca Fisher, NCETM Communications Manager, and former Early Years teacher
• 01:28 What’s so important about doubles
• 04:01 What experiences do children need at the early stages?
• 08:28 Exploring representations in Reception
• 14:53 Doubles in continuous provision
• 19:18 What does this look like in KS1?
• 27:12 How your local Maths Hub can help and final thoughts.
• Images referred to in this episode
• The Early Years section of our website
• Mastering Number at Reception and KS1
• ‘They can see it straight away’: the impact of Mastering Number

Tuesday Feb 27, 2024

Understanding Dyscalculia

In this episode of the podcast, we speak to Cat Eadle, a teacher, dyscalculia specialist and co-founder of the Dyscalculia Network. Our conversation explores what dyscalculia is, how it differs from other maths difficulties, and how teachers can facilitate an early diagnosis. We also discuss the importance of teaching ‘maths for life’ skills, dyscalculia in the secondary maths classroom, and how teaching for mastery approaches can support dyscalculic students of all ages to do and enjoy maths.

• Cat Eadle, The Dyscalculia Network
• 00:18 Understanding dyscalculia and its impact
• 01:03 Cat Eadle: dyscalculia specialist
• 01:43 The birth of the Dyscalculia Network
• 03:13 Identifying dyscalculia: signs and symptoms
• 05:14 The importance of dyscalculia diagnosis
• 08:03 Supporting students with dyscalculia
• 10:40 The prevalence of dyscalculia
• 14:14 The mastery approach to teaching maths
• 16:42 The struggles of adults with dyscalculia
• 19:56 Resources, further reading and events
• 21:53 Conclusion.
• Dyscalculia Network website
• Dyscalculia Awareness Day 2024 : three separate online events for parents (23/02/24), adults (29/02/24) and educators (01/03/24)
• The Dyscalculia Show 2024 at Birmingham NEC on 15/03/24 and 16/03/24
• The Dyscalculia Assessment by Jane Emerson and Patricia Babtie (2013, Bloomsbury)
• The Dyscalculia Solution: Teaching Number Sense by Jane Emerson and Patricia Babtie (2014, Bloomsbury)
• Ronit Bird website: games for dyscalculic learners
• Steve Chinn website
• Judy Hornigold website
• The Maths and Dyscalculia Assessment by Robert Jennings and Jane Emerson (available for pre-order, published on 18/07/24, Jessica Kingsley Publishers)
• Explore previous episodes of the NCETM podcast in our archive .

Monday Jan 29, 2024

I Can't Do Maths - Part 3

In this third and final part of this podcast episode, we conclude our conversation with Professors Alf Coles and Nathalie Sinclair about the dogmas they address in their book, I Can’t Do Maths! Why children say it and how to make a difference . In this part of the conversation, we put your questions, shared with us on social media, to Alf and Nathalie, and discuss topics including maths anxiety and enjoyment in the UK compared to other nations, how to support and encourage children who struggle with maths and how to respond when children ask, ‘When will I ever need this again?’.

• Professor Alf Coles, University of Bristol
• Professor Nathalie Sinclair, Simon Fraser University, British Columbia
• 00:06 - Introduction and welcome
• 00:39 - Is maths anxiety a global issue?
• 02:31 - When will I ever need this maths?
• 09:18 - How parents can support their children
• 12:33 - The importance of learning maths
• 16:17 - Conclusion and final thoughts
• I Can’t Do Maths! Why children say it and how to make a difference by Professor Alf Coles and Professor Nathalie Sinclair (Bloomsbury, 2022)
• Vihart , maths YouTuber recommended by Nathalie Sinclair
• Maths Games with Bad Drawings by Ben Orlin (Little, Brown, 2022) recommended by Nathalie Sinclair
• Mathematics for Human Flourishing by Francis Su (Yale University Press, 2021) recommended by Nathalie Sinclair
• Learning Mathematics for an Environmentally Sustainable Future by Karl Bushnell (Association of Teachers of Maths, 2018), mentioned by Alf Coles 
• NCETM Primary Mastery Professional Development Materials
• Gattegno’s ‘numbers as lengths’ as mentioned by Alf Coles, Working with Rods and Why (Association of Teachers of Mathematics, 2017)
• I Can't Do Maths - Podcast Episode 78 - Part 1
• I Can't Do Maths - Podcast Episode 78 - Part 2
• Explore previous episodes of the NCETM podcast in our  archive .

Monday Jan 22, 2024

I Can't Do Maths - Part 2

In Part 2 of Episode 78 of the NCETM Maths Podcast, Professors Alf Coles and Nathalie Sinclair continue their discussion about the dogmas in maths teaching and learning, with host Julia Thomson. We explore the misconceptions that ‘maths is culture-free’ and that 'maths is for some people and not for others'. We also scrutinise the notion that ‘maths is hard because it is abstract’ and discuss the Concrete, Pictorial, Abstract (CPA) model within mastery and the power of representations in maths.

• 00:32 - Exploring the dogma: maths is culture-free
• 05:37 - Maths and climate change
• 07:41 - Debunking the dogma: maths is for some people and not for others
• 12:48 - The power of representations
• 17:02 - Algebra in the primary classroom
• 17:44 - Conclusion and preview for Part 3
• I Can’t Do Maths! Why children say it and how to make a difference by Professor Alf Coles and Professor Nathalie Sinclair (Bloomsbury, 2022)  
• Journeys on the Gattegno Tens Chart by Alf Coles, 2014
• Learning Mathematics for an environmentally sustainable future by Karl Bushnell (Association of Teachers of Mathematics, 2018)

Wednesday Jan 17, 2024

I Can't Do Maths - Part 1

In this episode, we talk to Professor Alf Coles and Professor Nathalie Sinclair about their book, I Can’t Do Maths! Why children say it and how to make a difference . In the book, Alf and Nathalie identify, unpick and challenge some of the most commonly-held beliefs about maths teaching and learning. In Part 1 of our conversation, we explore the background to the book and the first two dogmas, or myths, about maths education that Alf and Nathalie explore in the book.

• 00:05 - Introduction to part 1
• 01:02 - Meet Professors Alf Coles and Nathalie Sinclair
• 02:06 - Unpacking the concept of ‘dogmas’ in maths education
• 05:52 - Exploring the first dogma: maths is a building-block subject
• 11:51 - Challenging the second dogma: maths is always right or wrong
• 16:58 - Conclusion and preview of Part 2.
• NCETM Curriculum Prioritisation in Primary Maths

Thursday Nov 16, 2023

Maths games - Part 2

In Part 2 of our discussion with Dr Ems Lord and Liz Woodham from NRICH and Grace Coker from the EEF, we explore how games can facilitate collaborative problem-solving, encourage parental engagement and make homework more enjoyable.

• Ems Lord, Director of NRICH, University of Cambridge
• Liz Woodham, Primary Coordinator, NRICH, University of Cambridge
• Grace Coker, Maths Content Specialist, Education Endowment Foundation (EEF)
• 00:05 - Introduction
• 00:59 - Exploring the importance of collaboration in maths
• 03:20 - Introducing maths games: NIM-7 and Got It
• 05:53 - More game suggestions and utilising classroom resources
• 07:51 - Encouraging parental involvement in maths practice
• 10:08 - Solving Together: a homework project for secondary schools
• 16:58 - Opportunities for new learning through games
• 17:56 - Top tips for using games in the classroom
• 19:54 - Conclusion
• EEF Improving Mathematics in the Early Years and Key Stage 1
• EEF Working with Parents to Support Children’s Learning
• Making Maths Visual and Tactile by Judy Hornigold (SEN Books, 2016)
• NRICH games mentioned in podcast: Got It and Nim-7
• Number Hive , mentioned by Grace Coker
• NRICH Secondary parental engagement project: Solving Together
• NRICH Primary games
• NRICH Secondary games

• What is a Maths Hub?
• Strategic Board
• Meet the Team
• Teaching for Mastery

Mastering Number

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Since 2014, the NCETM and Maths Hubs have been working together to develop approaches to teaching for mastery within primary maths. Thousands of schools have benefited. The Mastering Number Programme has been running since 2021 and is wholly consistent with teaching for mastery.

Please find below the details of our Mastering Number Work Groups and Community. 

Multiplication and Division

Spine 2 of the Primary Mastery Professional Development Materials

Introduction

The Multiplication and Division spine is divided into 30 segments. For each of these segments we have produced a detailed teacher guide, including text and images.

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. 

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

Spine 2 Overview

Counting, unitising and coins

Spine 2: Multiplication and Division – Topic 2.1

Structures: multiplication representing equal groups

Spine 2: Multiplication and Division – Topic 2.2

Times tables: groups of 2 and commutativity (part 1)

Spine 2: Multiplication and Division – Topic 2.3

Times tables: groups of 10 and of 5, and factors of 0 and 1

Spine 2: Multiplication and Division – Topic 2.4

Commutativity (part 2), doubling and halving

Spine 2: Multiplication and Division – Topic 2.5

Structures: quotitive and partitive division

Spine 2: Multiplication and Division – Topic 2.6

Times tables: 2, 4 and 8, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.7

Times tables: 3, 6 and 9, and the relationship between them

Spine 2: Multiplication and Division – Topic 2.8

Times tables: 7 and patterns within/across times tables

Spine 2: Multiplication and Division – Topic 2.9

Connecting multiplication and division, and the distributive law

Spine 2: Multiplication and Division – Topic 2.10

Times tables: 11 and 12

Spine 2: Multiplication and Division – Topic 2.11

Division with remainders

Spine 2: Multiplication and Division – Topic 2.12

Calculation: multiplying and dividing by 10 or 100

Spine 2: Multiplication and Division – Topic 2.13

Multiplication: partitioning leading to short multiplication

Spine 2: Multiplication and Division – Topic 2.14

Division: partitioning leading to short division

Spine 2: Multiplication and Division – Topic 2.15

Multiplicative contexts: area and perimeter 1

Spine 2: Multiplication and Division – Topic 2.16

Structures: using measures and comparison to understand scaling

Spine 2: Multiplication and Division – Topic 2.17

Using equivalence to calculate

Spine 2: Multiplication and Division – Topic 2.18

Calculation: ×/÷ decimal fractions by whole numbers

Spine 2: Multiplication and Division – Topic 2.19

Multiplication with three factors and volume

Spine 2: Multiplication and Division – Topic 2.20

Factors, multiples, prime numbers and composite numbers

Spine 2: Multiplication and Division – Topic 2.21

Combining multiplication with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.22

Multiplication strategies for larger numbers and long multiplication

Spine 2: Multiplication and Division – Topic 2.23

Division: dividing by two-digit divisors

Spine 2: Multiplication and Division – Topic 2.24

Using compensation to calculate

Spine 2: Multiplication and Division – Topic 2.25

Mean average and equal shares

Spine 2: Multiplication and Division – Topic 2.26

Scale factors, ratio and proportional reasoning

Spine 2: Multiplication and Division – Topic 2.27

Combining division with addition and subtraction

Spine 2: Multiplication and Division – Topic 2.28

Decimal place-value knowledge, multiplication and division

Spine 2: Multiplication and Division – Topic 2.29

Multiplicative contexts: area and perimeter 2

Spine 2: Multiplication and Division – Topic 2.30

Acknowledgements

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

• Primary mathematics specialists : Joanna Caisová, Adrian Cannell, Clare Christie, Katie Crozier, Jonathan East, Claire Gerrard, Rebecca Holland, Alison Hopper, Elizabeth Lambert, Conor Loughney, Suzanne Mathews, Debbie Morgan, Sally O'Brien, Alexandra Parry, Georgia Ryan, Cat Stone, Debbie Weible, Andrew Whitehead  
• Educational consultant : Dr Alf Coles, University of Bristol  
• Editorial and production : Liam Benson, Design and Define; Nicholas Bromley; Charlotte Christensen; Tracey Cowell, Passion for Publishing; Rachel Houghton; Jalita Jacobsen; Bill Mantovani; David Mantovani; Sam Radford; Rosie Stewart, Swales & Willis; Cheryl Stirr; Yvette Sturdy, DiGiV8 Ltd; Rachel Trolove, Trolove Engineering Solutions Ltd; Andrew Young  
• Illustrations : Steve Evans; Alphablocks Ltd

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NCETM inspired Y4 Maths Unit - Fractions

Subject: Mathematics

Age range: 7-11

Resource type: Unit of work

Last updated

28 March 2024

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This unit of work is based off of the NCETM lesson spines and is aimed at Year 4. Some tasks have been taken from White Rose to meet the learning objectives from the NCETM. There are two parts to this planning unit.

PART 1: REVIEW OF FRACTIONS Lesson 1: Identify the whole and the parts Lesson 2: Identify equal and unequal parts Lesson 3: Construct the whole from one part

PART 2: FRACTIONS Lesson 1: Write mixed numbers Lesson 2: Add and subtract mixed numbers from a part-whole model Lesson 3: Add and subtract mixed numbers Lesson 4: Label fractions on a number line Lesson 5: Identify how many fractional parts make a whole Lesson 6: Compare and order fractions on a number line Lesson 7: Compare and order fractions Lesson 8: Compare and order fractions with the same numerator Lesson 9: Add fractions with the same denominator Lesson 10: Subtract fractions with the same denominator Lesson 11: Add and subtract fractions Lesson 12: Identify equivalent fractions Lesson 13: Identify equivalent fractions

Some of these lessons are intended to be purely practical, working with whiteboards and physical resources/manipulatives. This is stated on the first page of each lesson on the PowerPoint.

Lessons that are designed to be in books have tasks that are easily written into books by childen or come with a ‘Fluency, Problem-solving, Reasoning’ sheet to show clear progression. These lessons are provided with a ‘next step’ to move children on even further in their learning.

Each PowerPoint follows the structure of: Revisit, Address Misconceptions, Vocabulary, Focus, Guided Practice, Talk Task, Deepen, Independent Practise, Next Steps.

#ncetm #year4 #fractions #year4fractions #ks2 #ks2fractions #maths #mathsmastery #diagnosticquestions #stemsentences #mastery #progression #numerator #denominator #mixednumbers

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