Magic Maths: Mind-Reading, Number Tricks, and Mathematical Thinking
Charlotte Lighter and Kellee Patterson
The Open University at Maths Week Wales 2025
What do you get when you mix number tricks, curious minds, and a sprinkle of mathematical magic? A room full of excited primary school pupils!
As part of Maths Week Wales 2025, we ran a public engagement session for primary children across Wales, called Magic Maths. Our session was designed to spark curiosity and mathematical thinking in young learners. The session was full of “think of a number” (THOAN) tricks – those classic puzzles where you follow a series of steps and end up with a surprising result.
Behind the magic was some serious mathematical thinking, drawn from ideas explored in our very own Open University Mathematics Education modules.
Your turn! A Magical Number Trick
Let’s start with a little magic of our own. Try this:
- Think of a number between 1 and 9
- Square it (multiply it by itself)
- Add the number you first thought of
- Divide by your original number
- Add 17
- Subtract your original number
- Divide by 6
We will using magical mind-reading to guess your answer!
Have a go before scrolling down … (No peeking!)
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Your answer is… 3!
Did it work? Try it again with a different number.
Still 3?
That’s the magic of mathematics, and it’s not just a trick. There is a powerful mathematical idea behind it: doing and undoing.
Unmasking the magic: How does it work?
Let’s look at another “think of a number” trick. This time see if you can work out what is going on and how we are able to work out your starting number.
- Think of a number
- Double it
- Add 10
- Half it
- Subtract 3
Now remember the answer!
During our live session, we asked the children to tell us their final answer, and we were then able to tell them what number they started with… magic right?
Or is it maths?
Have a go at following the steps above and see what you notice.
Try another number. Is there a pattern?
Can you generalise by describing the relationship between the starting number and the final answer?
In this example the answer is not always the same, unlike in the first trick when the last two steps always led us to 18 divided by 6… which always gave 3, in this example the answer is linked to the starting number you chose.
Have a go yourself before scrolling down.
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Did you spot that the final answer is always 2 more than the number you started with?
So, if you started with 4… the answer you got would be 6, with 5… the answer was 7 etc…
We could generalise and say if the starting value was n, the answer would always be n+2.
But why is this?
Can we look at what the trick asked us to do, and undo the steps to understand how the trick works?
When working through this with young learners, we used a numerical example to help us work through the steps. You could also use algebra.
- Think of a number 6 – our starting number is 6
- Double it 12 (2×6) – doubling this gives 2 x 6
- Add 10 22 (2×6+10) – adding 10, gives 2 x 6 + 10
Note we are recording the operations and keeping track of them. If we just write down the answers at each step (6, 12, 22) it will be very difficult to spot what is happening and how the trick works.
- Half it 11 (6+5) – halving it means we have 1 x 6 + 5
This is an important step. We had doubled six and now we are halving that, bringing us back to 6. This is an example of undoing an operation. We are using the inverse operation here. Doubling and halving (or multiplying by 2 and dividing by 2).
- Subtract 3… 8 (6+2) – subtracting 3 we have 6 + 2
- The answer is…. – our *starting number + 2
Note: We chose to keep the 6 as it is, because this was our starting number, and take 3 from the 5. This is so that we can generalise later by changing the value of 6.
To generalise we could use a box, or a letter to represent the starting number.
This might look like this:
- Think of a number n
- Double it 2n
- Add 10 2n + 10
- Half it n + 5
- Subtract 3… n + 2
- Answer is *starting number + 2
You could go back to the first maths trick and see if you can show why that always gives an answer of 3.
Doing and Undoing: The Maths Behind the Magic
In our Magic Maths session, children followed a sequence of operations (like adding, multiplying, subtracting), and then we either:
- Guessed their final answer (because it was always the same, no matter the starting number), or
- Revealed their starting number based on their final answer.
This process mirrors the mathematical idea of inverse operations: undoing what’s been done.
Exploring inverses is a powerful way to help learners understand how operations relate to each other. Doing and Undoing is a broader concept, which includes inverses, that features prominently in our OU mathematics education modules.
In ME322 (Learning and Doing Algebra) we say: In many aspects of algebra, there is a way of working forwards and working backwards; this can be thought of as doing and undoing. The doing part might be forming an equation to represent a scenario or plotting points to create a graph. Undoing is the reverse, where we try to find the way back to the starting information from the equation or graph. Sometimes this involves using inverse operations, and other times it might involve recognising a property of an algebraic object in order to work backwards. Undoing a problem often requires more creativity and insight than simply doing it.
Generalising: Make Your Own THOAN Trick
In our session, we encouraged pupils to create their own “Think of a Number” tricks using the idea of doing and undoing. This is where the concept of generalising comes in.
Generalising means spotting patterns and expressing them in a way that works for any numbers, not just the ones you try out. It’s a key part of mathematical thinking, and it’s something we explore in depth in our OU modules.
We didn’t use formal algebra with the children, but we did show that these tricks work no matter what number you start with. For example, if every time you do a trick you end up with “your number + 2,” you can start to describe that pattern more generally, maybe even write it as n + 2.
Creating your own THOAN trick is a brilliant way to explore this idea. Here are some tips we gave the pupils:
- Use at least 5 steps
- Space out inverse operations (don’t immediately undo what you just did)
- Keep the trick mysterious (don’t reveal how it works!)
- Try it with different numbers (does it always work?)
- Can you explain why?
Explore these ideas further:
If you’re studying one of our Open University Mathematics Education modules, you’ll recognise these ideas. If you’re not yet part of the OU community but this sounds exciting, here’s where you can learn more:
- ME321 Learning and Doing Geometry
This module examines how people learn geometry and the nature of geometric thinking.
- ME620 Mathematical Thinking in Schools.
This module will develop your knowledge and understanding of teaching primary and secondary school mathematics, emphasising the lower secondary school curriculum, and broaden your ideas about how people learn and use mathematics.
- ME322 Learning and Doing Algebra.
This module examines the nature of algebra and how children learn. It develops your awareness of choosing and using symbols and your ability to express general mathematical statements.
ME322 Learning and Doing Algebra
These modules are designed for anyone interested in mathematics education, whether you’re a teacher, student, or just someone who loves numbers and wants to understand how we learn to think mathematically.
Final thoughts
Magic Maths was a joyful reminder that mathematics can be playful, surprising, and deeply engaging. Whether you’re a primary school pupil or a university student, the thrill of discovering a pattern, or creating your own, is a powerful experience.
So next time you hear “Think of a number…”, don’t just follow the steps. Ask why it works. Then try making your own. Happy magic making!
If you enjoyed reading this BLOG, see our previous post on The benefits of studying mathematics in two languages (Cymraeg / Welsh and English)