Choose any two numbers, such as 4 and 5. One must be even and the other odd.

Try multiplying them together. How could you show this?

Lewis used a number line:

Morven used Multilink cubes:

Athol used counters:

What do you notice about the answer?

Look closely at one of these models.

Can you see anything in it that would work in exactly the same way if you used the same modelĀ with a different pair of even and odd numbers?

Can you use your one example to prove what will happen every time you multiply an even number and an odd number together?

See if you can explain this to someone else.

Are they convinced by your argument?

Once you can convince someone else, see if you can find a way to show us your argument. You might draw something or take a photo of things you have used to prove that your result is always true from your example.

Tell us about it by submitting your solution.