Patans.

Multiplying without tables

Cut it where it is easy

25 minutes

Start the lesson

Before you read anything

Lay out seven rows of fourteen stones. Or draw the rectangle — fourteen across, seven down.

Now put your finger on the line between the tenth column and the eleventh. Do not move anything yet.

The question module 4 left you with

$7 \times 14$. No table has it, no table is ever going to have it, and questions like this turn up all week.

But your finger is already on the answer.

What the line does

Seven fourteens, cut at the ten. Seven tens on one side, seven fours on the other, and ninety-eight when they go back together.

Seventy and twenty-eight. Both of those you already had.

Why the cut goes there and not somewhere else

:x nutshell-partition

Splitting a number into pieces that add back to it. Fourteen is ten and four — and it always was, before anybody drew a line.

Fourteen could be :partitioned as six and eight, or as five and nine. All of those are true. Only one of them cuts off a piece you can multiply without thinking, and that is the whole of the decision.

Musa

cut the 14 into 7 and 7

Musa is not wrong. $7 \times 7$ twice is forty-nine and forty-nine, which is ninety-eight. But he had to find $7 \times 7$ to get there, and the ten-cut asked him for nothing he did not already have.

The bar, again

Module 1 cut a bar into two parts. Module 4 made every part the same size. This is that bar with fourteen equal units in it, cut after the tenth — ten units in one hand, four in the other, and the same bar.

Play it until the cut is automatic

Cut each rectangle at the ten and read the two pieces off it. It gets faster because the cut gets faster, not because you get quicker at guessing.

The same line, drawn a hundred times.

Check yourself

Six to try

Some of these ask where you would cut. Some have the cut made already and want the piece that is left. None of them wants an answer yet.

1

$7 \times 14$ is done as $7 \times 10$ and $7 \times \square$. What goes in the box?

2

$9 \times 17$ is done as $9 \times 10$ and $9 \times \square$. What goes in the box?

3

$7 \times 17$ is done as $7 \times 10$ and $7 \times \square$. What goes in the box?

4

Where would you cut the $15$ to work out $8 \times 15$?

5

Where would you cut the $17$ to work out $6 \times 17$?

6

Where would you cut the $13$ to work out $9 \times 13$?

Away from the screen

Cut it where it is easy Write the two pieces down before you write the answer.
Cut it where it is easy, page 1 Cut it where it is easy, page 2 Cut it where it is easy, page 3

Open the PDF Save it to print

Show that you have it

Both pieces, then the whole

The first hands you both pieces already worked out; put them back together. The second hands you nothing at all — cut it yourself, and write the cut down, because that is the part being marked.

1

You know $4 \times 10 = 40$ and $4 \times 6 = 24$. What is $4 \times 16$?

2

Okello fills $3$ baskets with $19$ mangoes each. How many mangoes is that?