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

2. 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

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

4. 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

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

6. 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?

7. 1 + -1 = 0 -1 × 1 + -1 × -1 = -1 × 0 Some mathematical trickery…
What can you tell me about these cards?
= 0
Let’s multiply everything by -1
-1 × × -1 = -1 × 0

8. -1 × 1 + -1 × -1 = -1 × 0 -1 + -1 × -1 = 0 Some mathematical trickery…
-1 × × -1 = -1 × 0
From before, we know that this is - 1
What is this answer?
Let’s rewrite the equation
× -1 = 0
= 0

9. -1 + -1 × -1 = 0 -1 × -1 = 1 Some mathematical trickery… -1 + = 0
× -1 = 0
= 0
What must the box be to make the equation true?
The box must equal 1
-1 × -1 = 1

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

11. 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?

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

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

14. 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?