Five suggested number lines for use in KS3 and KS4 maths lessons
Becky Donaldson, from the NCETM's Secondary Team suggests five different number lines for use in lessons, including one appropriate for use with students aiming at the higher GSCE grades.
Show notes
Taking part in the discussion are:
Becky Donaldson, NCETM Assistant Director for Secondary Mathematics
Steve McCormack, NCETM Communications Director.
Useful links
This Espresso from Cambridge Mathematics gives more examples of number lines 
The number lines NCETM podcast discussion with examples for KS1 teaching 
Checkpoint 2 from the Arithmetic procedures including fractions PowerPoint, downloadable from our Checkpoints page, has a more structured version of the fourth number line in this discussion.
The second Key Idea PowerPoint on this page of our Secondary Mastery Professional Development Materials is devoted entirely to double number lines (the fifth example in this discussion).  
Diagram
This is the sketch Becky and Steve referred to during their conversation. Click to enlarge.

Using number lines in secondary maths

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.

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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: info@ncetm.org.uk.

The NCETM Maths Podcast: Trailer

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.
A transcript (PDF) of this episode is available to download.
Show notes
Taking part in the discussion:
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.
Episode chapters
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.
Useful links
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
Explore previous episodes of the NCETM podcast in our archive
The NCETM Maths Podcast on Instagram.

Training to teach maths with Teach First

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.
A transcript (PDF) of this episode is available to download.
Show notes
Taking part in the discussion:
Sue Evans, NCETM Assistant Director for Primary, and former primary teacher
Rebecca Fisher, NCETM Communications Manager, and former Early Years teacher
Episode chapters
00:06 Introduction and welcome
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.
Useful links
Images referred to in this episode
Find your local Maths Hub
The Early Years section of our website
Mastering Number at Reception and KS1
‘They can see it straight away’: the impact of Mastering Number
Explore previous episodes of the NCETM podcast in our archive
The NCETM Maths Podcast on Instagram.

Early maths concepts: doubles

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.
A transcript (PDF) of this episode is available to download.
Show notes
Taking part in the discussion:
Cat Eadle, The Dyscalculia Network
Julia Thomson, Communications Manager, NCETM.
Episode chapters
00:06 Introduction and welcome
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.
Useful links
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.

Understanding Dyscalculia

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

Show notes
Taking part in the discussion:
Professor Alf Coles, University of Bristol
Professor Nathalie Sinclair, Simon Fraser University, British Columbia
Julia Thomson, Communications Manager, NCETM.
Episode chapters
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
Useful links
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.

Using number lines in secondary maths

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