Patans.

Written methods

Why the second row shifts

20 minutes

Start the lesson

Before you read anything

$47 \times 23$. Cut the twenty-three the way module 5 taught you.

Write down the two pieces you would work out. Do not do either of them yet.

The cut, written down

Forty-seven threes, then forty-seven twenties. The two rows of a column multiplication are the two pieces of the cut.

Twenty-three is twenty and three. The first row is the three; the second row is the twenty.

Where the nought comes from

$47 \times 20$ is $47 \times 2$ with a nought on the end, because twenty is ten twos. So the second row ends in a nought — and that is why it looks shifted along.

Otim

learned to "put a zero there" and forgot it under pressure

A rule about typing is a rule you forget. A row you can name — this one is forty-seven twenties — cannot be written in the wrong place, because forty-seven twenties is obviously not a hundred and something.

The rectangle is still there

Module 5 cut a rectangle at the ten. Nothing has changed except that the pieces are now written under one another instead of side by side, so that they can be added.

Check yourself

Six to try

Where there are two rows, name each row before you work it out. Say it out loud: "this row is forty-seven threes".

1

$124 \times 6$

2

In $89 \times 45$ done in columns, what does the first row work out?

3

$44 \times 13$

4

Working out $64 \times 39$ in columns, the second row starts with a nought. Why?

5

$552 \times 6$

6

In $78 \times 32$ done in columns, what does the first row work out?

Away from the screen

Two rows Write beside each row what it is working out.
Two rows, page 1 Two rows, page 2

Open the PDF Save it to print

Show that you have it

Both rows, and the reason

One to work out in full, and one that asks why the second row starts where it does. They are the same fact.

1

$68 \times 35$

2

Working out $44 \times 48$ in columns, the second row starts with a nought. Why?