28/06/2026
I have used a model similar to this for just the perfect squares, but love this graphic-such a great link between area arrays and multiplication.
Have you ever looked at something familiar in a new way - and suddenly seen something completely different?
I remember my Dad showing me the picture on the right when I was about 10. What can you see?
Two Pictures in One (and a spoiler!)
For ages, every time I looked, I saw the same thing: A young woman.
Until one day, I suddenly noticed something entirely different: An old woman.
Hidden in plain sight ALL THIS TIME were two pictures!!
Here's where things get interesting...
Maths is the same.
Many students will see what they learn in one way - and in one way only. For example:
* Multiply 2 numbers and you get a written number.
* 4 x 6 gives you the 2-digit number that's written as: 24.
* Nothing more.
Here's the thing though: Maths is about more than getting to an answer using a single method. It's about more than practising skills in isolation. Maths is about connections:
* Connections to other concepts.
* Connections to other topics.
* And, yes, even connections to other subjects.
This is its power - and its beauty. ❤️
That's why the Times Table Chart on the left is so great. It uses something we take for granted, and gives it a twist. Suddenly, multiplication isn't just about getting to an answer. Instead, we can also see:
* Times tables as rectangular grids
* How multiplication and geometry are connected
* Square numbers (yes, they are square!)
* Different grids that have the same total area (i.e. composite numbers, and also the commutative property)
* The proportional relationship between numbers.
Put simply, we can see the connections that give multiplication meaning.
Just like the old lady/young lady picture, maths can be seen in different ways. This stops it from being a random set of rules and definitions. Instead, the connections we notice give maths newfound meaning.
In other words: When we look again, everything changes.
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This post comes from my latest Maths Newsletter.
I write weekly on teaching tools, tasks and strategies for the maths classroom, K-12.
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Cheers!
