The Primary Maths Podcast

Addition is one of the first mathematical operations children meet, but that doesn’t mean it’s simple.

In this episode of AfterMaths, Jon and Becky take a closer look at what it really means to understand addition. They explore why knowing lots of different strategies matters, why column addition should be a tool rather than the destination, and why Jon has, somewhat inexplicably, developed a favourite addition calculation.

There’s also some Wordle mathematics, new research into the importance of spatial reasoning and partitioning, and a trip through the surprisingly long history of the humble + symbol.

01:16 – Can mathematics help you beat Wordle?

Researchers at Binghamton University have used Shannon entropy and information theory to develop a Wordle strategy that solved more than 99% of puzzles in simulations.

05:50 – What’s your favourite addition?

Jon nominates 8 + 7, and uses it to explore number bonds, partitioning, near doubles, compensation and the different ways children might see the same calculation.

10:58 – The structures of addition

What is the difference between aggregation and augmentation, and do children actually need to know those words?

15:00 – Column addition: servant or master?

Written algorithms are incredibly useful, but they aren’t automatically the most efficient or sophisticated strategy. Jon and Becky discuss why children need a repertoire of approaches and the freedom to choose between them.

20:54 – Research: partitioning is spatial as well as numerical

New research from Chelsea Cutting explores how spatial visualisation, spatial structuring and proportional reasoning can support young children’s understanding of partitioning and fractions.

26:33 – Where did the + symbol come from?

Becky heads down a mathematical-history rabbit hole, from ancient Egyptian walking legs to medieval shorthand and the emergence of the modern plus sign.

34:30 – Free primary maths CPD

Jon and Becky look ahead to Twinkl’s programme of free live primary maths sessions, including subtraction, problem solving, cognitive load and mathematical talk.

And next week: subtraction.

Binghamton University: researchers use maths to crack Wordle

Research paper: Solving Wordle Using Information Theory

Play Wordle

Play Nerdle

Chelsea Cutting: Exploring the critical role spatial reasoning plays in young children’s early partitioning development

Further reading:

Wilson, Myers, Edgington & Confrey: Fair Shares, Matey, or Walk the Plank

MacTutor: Earliest Uses of Symbols of Operation

Explore Twinkl’s upcoming TeachMeet events

Twinkl Primary Maths CPD collection

John Dewey, Logic: The Theory of Inquiry (1938):

The Primary Maths Podcast: AfterMaths

With Jon Cripwell and Becky Brown.

New episodes exploring the ideas, research and slightly unexpected tangents behind primary mathematics.

Why do some pupils seem to thrive in maths while others struggle to access the same lesson?

Jon and Becky discuss the latest PISA findings and the widening gap between higher and lower attainers, before exploring what that looks like in real primary classrooms. They talk about teaching for mastery, adaptive teaching, pre-teaching, the pressures of a packed timetable and why taking time to simply observe pupils can be so valuable.

With place value being taught in classrooms everywhere at this point in the year, they also look at why it can reveal so much about what children genuinely understand, rather than what they’ve simply memorised.

Plus, there’s maths in the wild involving an ultra-running teacher, a critically endangered parrot and around 70,000 pints of stolen Guinness.

How can the universe be 13.8 billion years old but the observable universe be around 93 billion light years across?

In this AfterMaths Summer Special, Jon is joined by primary science specialist Sarah Hutson to tackle some of the wonderfully ridiculous numbers involved in trying to understand the universe.

They talk solar eclipses, meteor showers, shooting stars, the speed of light, the size of the Sun and Moon, and why looking into space is really looking back in time.

There is also Sarah's highly scientific game What on Earth Have I Drawn?, a surprising rise in colander sales, the reason total solar eclipses are possible, and an attempt to explain the expansion of the universe using an ant on an elastic band.

By the end, Jon needs a lie down.

Which is probably the correct response to cosmology.

Can maths help you win at games?

In this AfterMaths Summer Special, Jon and Becky explore the line between luck and strategy — and whether understanding the maths behind a game can actually give you an advantage.

They take in Rock Paper Scissors, Noughts & Crosses, chess, a deceptively simple counting game, the chessboard-and-rice problem, expected value, roulette and the mathematics hiding inside Monopoly.

Along the way: why some apparently random games aren’t quite random, why exponential growth gets ridiculous remarkably quickly, why the house tends to win at casinos, and how a little probability might improve your chances during family game night.

Maths can’t guarantee that you’ll win every game.

But it might make people considerably less keen to play Monopoly with you.

Can maths really predict the future?

We can predict the return of a comet decades in advance, but tomorrow's weather can still catch us completely by surprise. In this AfterMaths Summer Special, Jon and Becky explore why some futures are easier to calculate than others.

From probability, forecasts and projections to Halley’s Comet, the phantom planet Vulcan and Edward Lorenz's discovery of chaos theory, they ask how much mathematics can genuinely tell us about what happens next.

There's also the butterfly effect, an unexpectedly important rounding error, the difference between chaos and randomness — and the small problem that human beings refuse to behave like nice, predictable mathematical models.

Especially children.

So, can maths predict the future?

Sort of. Which is perhaps the most mathematically appropriate answer possible.

Podcast Show Notes

What makes a route the best route? The shortest distance? The quickest journey? The cheapest option? Or simply whichever one Google tells you to take?

In this AfterMaths Summer Special, Jon and Becky explore the maths of getting away — from Google Maps and traffic predictions to queues, theme parks and an 18th-century puzzle that helped create an entirely new area of mathematics.

Along the way, they discuss the Seven Bridges of Königsberg, Euler's ingenious solution and what it can teach us about problem solving: representing problems, working systematically, spotting patterns, simplifying and knowing when there might not actually be a solution at all.

Plus: why the other supermarket queue is always faster, whether you should ever switch queues, 99 smartphones causing a fake traffic jam in Berlin, and the deeply troubling emergence of people forming orderly queues at pub bars.

It's maths. It's holidays. It's considerably more Euler than your average trip to Orlando.

Who decided how long a metre should be? Why is a mile 1,760 yards? And what connects the French Revolution, an expedition from Dunkirk to Barcelona and the speed of light?

In this AfterMaths Summer Special, Jon and Becky explore the messy, surprising and occasionally bewildering history of measurement.

They begin in a world before standard units, when lengths were measured using hands, feet, cubits, spans and paces. These methods were convenient and widely understood, but rather less useful when accuracy mattered and everybody’s body produced a different answer.

From there, they investigate the historical accumulation that gave us imperial units, including the supposed connections between inches and barleycorns, feet and actual human feet, and miles and Roman paces.

The story then moves to revolutionary France, where mathematicians and astronomers attempted to create a universal decimal system based on the dimensions of the Earth. Their effort to establish the metre involved years of surveying, triangulation, political upheaval, arrests and the inconvenient discovery that neither the Earth nor their measurements were quite as perfect as hoped.

The metre was later represented by a platinum-iridium bar, then by a wavelength of light and, finally, by the distance light travels through a vacuum in a precisely defined fraction of a second.

It is a journey from body parts to universal constants, with plenty of mathematical history, questionable conversions and the inevitable disagreement about whether a pace and a “dolly step” are the same thing.

Explore The Primary Maths Podcast and more from Twinkl:

https://www.twinkl.co.uk/resources/twinkl-podcasts/primary-maths-education-podcast-twinkl-podcasts

We always love hearing from listeners. Send your questions, episode ideas and examples of maths hiding in everyday life to:

[email protected]

Subscribe to the podcast newsletter on Substack:

https://primarymathspodcast.substack.com/

Connect with Jon on LinkedIn:

https://www.linkedin.com/in/joncripwell/

If you enjoyed the episode, please follow the podcast, leave a rating or review, or share it with a colleague. It really helps more teachers discover the show.

Thanks for listening, and as ever, keep doing the maths.

Probability often feels as though it should be intuitive, right up until the mathematics tells us that our instincts are completely wrong.

In this AfterMaths Summer Special, Jon and Becky explore the strange mathematics of chance. From rainy-day board games and rolling two dice to coin-toss streaks, lottery numbers and casino myths, they investigate why humans are so determined to find patterns in genuinely random events.

Why is seven the most likely total when rolling two dice? How can just 23 people produce a better-than-even chance of two sharing a birthday? Are 1, 2, 3, 4, 5 and 6 genuinely bad lottery numbers? And after choosing between three mysterious doors, why should you abandon your original choice?

The episode concludes with the famously counterintuitive Monty Hall problem: three doors, two goats, one car and a very good mathematical reason to switch.

Expect hidden maths, questionable gambling strategies and several probability problems capable of making your brain hurt.

Explore The Primary Maths Podcast and more from Twinkl:

https://www.twinkl.co.uk/resources/twinkl-podcasts/primary-maths-education-podcast-twinkl-podcasts

We always love hearing from listeners. Send your questions, episode ideas and examples of maths hiding in everyday life to:

[email protected]

Subscribe to the podcast newsletter on Substack:

https://primarymathspodcast.substack.com/

Connect with Jon on LinkedIn:

https://www.linkedin.com/in/joncripwell/

If you enjoyed the episode, please follow the podcast, leave a rating or review, or share it with a colleague. It really helps more teachers discover the show.

Thanks for listening, and as ever, keep doing the maths.

Why did the six-week summer holiday feel endless when we were children, yet now seems to disappear almost as soon as it begins?

In the first of the 2026 Aftermaths Summer Specials, Jon and Becky explore the strange relationship between time, age and memory. They consider the popular proportional theory of time, the role of novelty in creating richer memories and the “return-trip effect”, which can make the journey home feel shorter even when the distance is the same.

The conversation also takes in unusually long post-GCSE summers, children’s television, World Cup statistics and the role of the railways in creating standardised time across Britain.

Before that, Jon and Becky discuss Andy Burnham’s arrival in Downing Street and Lucy Powell’s appointment as education secretary. What might the change mean for schools—and can the sector retain some much-needed continuity around SEND, curriculum reform, funding, recruitment and retention?

Why Teaching Time Is So Hard and What We Can Do About It:

https://www.twinkl.co.uk/l/1abmzu

Explore PlanIt Maths Year 2 time resources:

https://www.twinkl.co.uk/l/t9r41

Listen to our earlier Summer Special, Making Sense of Time:

https://www.twinkl.co.uk/l/1n860n

Read the return-trip effect research:

https://pubmed.ncbi.nlm.nih.gov/21861201/

Subscribe to The Primary Maths Podcast Substack:

https://theprimarymathspodcast.substack.com/

Get in touch with Jon and Becky at [email protected].

Subscribe to The Primary Maths Podcast so you don’t miss the next Summer Special: What Are the Chances of That?

What do this year’s KS2 SATs results really tell us about primary maths—and what might they be hiding?

Jon and Becky examine the newly released national data, including the rise in maths attainment, the return of greater-depth results to pre-pandemic levels and the growing number of pupils working below the level of the tests. They discuss why a single score can never tell the whole story, why missing the expected standard does not mean a child “can’t do maths”, and whether the improving headline figures may be masking a widening gap between different groups of pupils.

They also explore new research into pupils’ use of AI for mathematical word problems. Homework accuracy increased and answers were completed in seconds—but performance fell when pupils had to work independently under supervision. Are pupils using AI as a helpful learning tool, or simply outsourcing the thinking that helps learning happen?

Read Jon’s blog on using AI tools to support maths learning:

https://www.twinkl.co.uk/l/ecwcw

Explore the newly updated PlanIt Maths scheme:

https://www.twinkl.co.uk/l/ndlp8