Move a two across

Before you read anything

Sixteen fives. Lay them out — sixteen columns with five in each, or draw the rectangle.

Cut it down the middle and stand one half under the other. Count what you have before you read on.

Nothing was added

Sixteen fives cut in half, and the half moved underneath instead of beside. Eight tens. The eighty at the top never changes.

Eighty either way, and not because of a rule. The same eighty squares are on screen throughout — only standing somewhere else.

What actually moved

A two came off the sixteen and went onto the five: eight and ten. One side gave, the other took — which is why the tray keeps its size.

Nakato

halved the 16 and doubled the 5

Musa

halved the 16 and left the 5 alone

Musa has half a tray. Halving is one end of the move, and the doubling is what pays for it.

Three moves

Three ways to do a multiplication that is in no table:

Cut at the ten. $7 \times 14 = 7 \times 10 + 7 \times 4$.
Go too far, come back. $9 \times 6 = 10 \times 6 - 6$.
Move a two across. $16 \times 5 = 8 \times 10$.

Which one, and when

Choosing is the lesson. Look for a ten first — one to cut at, one to overshoot, or one you can make by halving an even side. If there is no ten anywhere near, the fact is small enough to know.

Check yourself

Six to try

Before each one, say which of the three moves you are about to make. Say it even when the answer arrives first.

1

Which of these is the same size as $12 \times 5$?

2

Which of these is the same size as $14 \times 5$?

3

$9 \times 7$. Ten lots of $7$ is $70$. How much do you take off?

4

Where would you cut the $13$ to work out $4 \times 13$?

5

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

6

You know $3 \times 10 = 30$ and $3 \times 3 = 9$. What is $3 \times 13$?

Which move, and why · page 1 of 3 Print it

Which move, and why · page 2 of 3 Print it

Which move, and why · page 3 of 3 Print it

The question this leaves you with

You have worked out that $6 \times 14 = 84$.

Now somebody hands you eighty-four mangoes and asks for fourteen in each basket. How many baskets?

You need no new fact for that. You have the one you need already, standing the wrong way round.

Show that you have it

The move, chosen

Neither of these wants an answer. Both want the decision you would make, and the reason for it.

1

Otim cuts at the ten every time. Which one does that not help him with?

2

Where would you cut the $15$ to work out $5 \times 15$?

Check what stuck The whole thing on one page