What is the multiplicand? In this calculation -1 × 4 What is the multiplicand? What is the multiplier? So the product is -4

We know that multiplication is commutative. What about 4 × -1 We know that multiplication is commutative. The calculation is the same as -1 × 4 So the product is -4

What is the multiplicand? In this calculation -3 × 5 What is the multiplicand? What is the multiplier? So the product is -15

We know that multiplication is commutative. What about 5 × -3 We know that multiplication is commutative. The calculation is the same as -3 × 5 So the product is -15

On your whiteboards: -6 × 2 = 2 × -6 = -7 × 2 = 2 × -7 = 2 × -6 × 3 =

What is the multiplicand? What is the multiplier? In this calculation -1 × -1 What is the multiplicand? What is the multiplier? Why can’t I represent this using number cards? Most of you will say that ‘two minuses = a plus’ But why does that work?

1 + -1 = 0 -1 × 1 + -1 × -1 = -1 × 0 Some mathematical trickery… What can you tell me about these cards? 1 + -1 = 0 Let’s multiply everything by -1 -1 × 1 + -1 × -1 = -1 × 0

-1 × 1 + -1 × -1 = -1 × 0 -1 + -1 × -1 = 0 Some mathematical trickery… -1 × 1 + -1 × -1 = -1 × 0 From before, we know that this is - 1 What is this answer? Let’s rewrite the equation -1 + -1 × -1 = 0 -1 + = 0

-1 + -1 × -1 = 0 -1 × -1 = 1 Some mathematical trickery… -1 + = 0 -1 + -1 × -1 = 0 -1 + = 0 What must the box be to make the equation true? The box must equal 1 -1 × -1 = 1

This can help us find other calculations by decomposing our numbers: - 2 × - 6 = -1 × 2 × -1 × 6 = -1 × -1 × 2 × 6 = 1 × 12 = 12

Show that this works when multiplying together any two negative numbers. Choose two negative numbers. Decompose them. Rearrange and multiply. So do two negative numbers always multiply to give a positive answer?

What happens when you multiply 3 negative numbers? Or 4? Can you generalise?

If I know that -6 × 2 = -12 -12 ÷ 2 = -12 ÷ -6 =

Use what we have done today to help you fill in the multiplication and division grids. What patterns can you find? What generalisations can you make?