Subtraction often feels straightforward until you face a problem like 7 minus 9. Many people immediately say, "You can’t do that," because it seems impossible to take away more than you have. But this common belief limits how we understand subtraction. The truth is, 7 minus 9 equals –2, and this result makes perfect sense when we rethink subtraction beyond just "taking away." This post explores why 7 − 9 is not only possible but also a useful way to understand numbers on a br

Unitising  is the ability to treat a group of things as a single “unit” and then work with that unit as though it were one object. It’s a fundamental mathematical idea, yet often one of the least visible. When children can unitise, they can see ten ones as a single ten , two socks as one pair , or 100 centimetres as a single metre . It unlocks a huge amount of future learning. Look at the images: coins, crayons, socks, fractions, measures. They might seem unrelated at first g

In Key Stage 2, we often introduce square numbers with a familiar line: “A square number is a number multiplied by itself.” It’s well‑intentioned, but it’s also a little clumsy. Children may memorise that 6 × 6 = 36, but memorisation alone doesn’t offer depth. It doesn’t help them see the structure beneath the surface. A more meaningful explanation is that a square number is a number multiplied by the same factor . This small shift in language matters. It encourages pupils to

In the Early Years, something beautifully simple happens in maths lessons. A child places one counter on the table, then two counters next to it, and we say, “One add two makes three.”  Then, almost magically, we slide the counters around, swap their order, and show that “Two add one also makes three.” That small moment, children watching counters trade places while the total stays the same, is their first meeting with the commutative property. They don’t call it that, of cou

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Using examples in the classroom