## Use a multiplication square

Teaching learners how to put a multiplication square together is also valuable. I wonder how many times we assume that because we understand what it represents, they will too?

Can they identify square numbers as a diagonal line of reflective symmetry? Are they able to explain why the same facts appear on either side of the line? (The commutative law, or switcheroos as I’ve heard them called).

### Can your learners use the distributive law to work out multiplication facts?

One of the most powerful activities I’ve done with a blank multiplication square is to show how you can use your 1, 2, 5 and 10 times tables to work out any other facts by using the distributive law.

If you know that **5 + 2 = 7**, then you also know that **(5 × 4) + (2 × 4) = 7 × 4**. You could also work this out by using **10 – 3 = 7**, so **(10 × 4) – (3 × 4) = 7 × 4**. Doubling patterns can also be used — if we know 2×, we can double this to get 4× and double it again to get 8×.

How many different ways can you and your learners work out each unknown fact from the things you do know? This activity is powerful because it gives children a way to work out a question if they can’t recall the answer. No longer are times tables either something you know or something you don’t — learners now have a way in.

### Keep revisiting the blank multiplication square

Once learners can use reasoning strategies to complete a multiplication square, you can return to the initial activity of giving them a blank one to complete. How much can they fill in now?

It will be a big confidence boost for them to see how much more they know than they realised. You might choose to repeat this activity regularly, asking learners to record the time they take to complete the square each time so they can track their progress.

I’ve had learners who are so motivated by this that they ask for blank multiplication squares to take home to practice. If they become so proficient they can complete the square in under two minutes, jumble the numbers up so they have to move beyond relying on learnt patterns.