How_To_Be_Good_At_Math

CALCULATING • PARTITIONING FOR MULTIPLICATION 111

Partitioning on a grid

We can also use a grid to help us to partition for

multiplication. A grid like this is called an open array.

Partitioning practice

Try using the number line and grid

methods to work out the answers to these

multiplication calculations. Which method

do you prefer?

35 × 22 =?

17 × 14 =?

26 × 12 =?

16 × 120 =?

TRY IT OUT

First, draw a rectangle, like this

one, where each side represents

a number in the calculation. We can

draw the grid roughly, without using

a ruler or measuring the sides.

Let’s take another look at 12 × 15,

this time using a grid. As before,

we can partition 15 into 10 and 5.

We are partitioning 15 into 10

and 5, so we draw a line through

the rectangle to show that it has been

partitioned. Label the sides with 12 on

one side, and 5 and 10 on the other.

Now we multiply the sides

of each section of the grid.

First, multiply 12 by 10 to get 120.

Write 12 × 10 = 120 in the grid.

Next, multiply 12 by 5 to get 60.

Write 12 × 5 = 60 in the grid.

Finally, we just add the two

answers together: 120 + 60 = 180

So, 12 × 15 = 180

Answers on page 319

10 5

(^12) 12 × 10 = 120 12 × 5 = 60
12 × 15 = 180
12 × 15 =?
It doesn’t matter which
number in a calculation
you choose to partition –
just pick whichever is
simpler to work with.
We can also partition this calculation without
drawing a grid. We can write it like this:
12 × 15 = (12 × 10) + (12 × 5) = 120 + 60 = 180
110_111_Partitioning_for_multiplication.indd 111 29/02/2016 18:56