We all love to teach our children new things and we all want to protect our children when they are struggling. With maths it’s easy for many of us to show children how to solve problems but we often miss out the stage where they discover and solve problems themselves and work out why the method is valid. Children who solve problems themselves are unsurprisingly more able to remember how to solve similar problems in the future.

At monster maths we love to see children solve problems themselves. Let’s take times tables for example. Times tables is the perfect opportunity for children to learn the commutative property of multiplication, although we don’t need to call it that! That’s the property that means 7 x 8 = 8 x 7 for example. Now many children are told that you can swap the order of the numbers you multiply in times tables. They rarely discover why for themselves. Now why is this important? It may be obvious to you and me that 13 x 20 = 20 x 13 even though it’s not in the times tables but it’s not obvious to many children. They’ve been taught that this works for times tables but not beyond. An extension of this lack of realisation is that when they start algebra they don’t realise that a x b = b x a. This is a fundamental algebra principle that they will certainly need at GCSE. So how to we help children to learn this generalisation of the times tables fact? We start with the times tables themselves. We set children problems and let them discover themselves, using blocks in a rectangle for example, that this commutative property works and why it works. Then they can extend, with encouragement if needed, to bigger numbers. It’s this path of discovery and asking “why” that sets the foundations for maths at GCSE and beyond.