Directed Numbers

How we teach addition & subtraction of integers

How we teach multiplication & division of integers

For multiplication, we begin with the learners' knowledge of whole numbers and build their understanding.

We know 3 x 2 = 6, and we use this to look at a pattern

(+3) x (+2) = (+2) + (+2) + (+2) = (+6)

(+3) x (+1) = (+1) + (+1) + (+1) = (+3)

(+3) x 0 = 0 + 0 + 0 = 0

What do we notice? Continuing the same pattern, we see:

(+3) x (-1) = (-1) + (-1) + (-1) = (-3)

(+3) x (-2) = (-2) + (-2) + (-2) = (-6)

(+3) x (-3) = (-3) + (-3) + (-3) = (-9)

What conclusion can we make?

If we take the last product and recognise commutative property of multiplication, we know that if

(+3) x (-3) = (-9), then

(-3) x (+3) = (-9)

(-3) x (+2) = (-6)

(-3) x (+1) = (-3)

(-3) x 0 = 0

(-3) x (-1) = (+3)

(-3) x (-2) = (+6)

(-3) x (-3) = (+9)

What do you notice?

Conclusion:

Postive x Positive = Postive

Positive x Negative = Negative

Negative x Positive = Negative

Negative x Negative = Positive

For division, we begin with what the learners are currently comfortable with, which is now multiplication of integers.

(-5) x ? = (-20)

Learners know that ? = (+4). This means that (-20) divided by (-5) must equal (+4)

We can then encourage learners to think about the division problem as a multiplication problem.