Patans.

Written methods

One column at a time

20 minutes

Start the lesson

Before you read anything

$524 \div 4$. Five hundreds shared between four.

Say what happens to the hundred that will not share, before you do anything else.

Hundreds, then tens, then ones

Five hundreds give one each and one over. That hundred comes across as ten tens, joins the two already there, and twelve tens share exactly.

Left to right, biggest pieces first. Every column is module 6's sharing, done on one size of piece at a time.

The number that comes across

:x nutshell-carried-across

A piece too big to share, brought into the next column as ten of the smaller size so that it can be. It is not a leftover — it has not finished yet.

The hundred that would not share is not gone and it is not the answer's remainder. It is :carried across as ten tens, and those ten tens get shared with the rest.

Musa

called the leftover hundred "the remainder" and stopped

Musa stopped a column early. He answered 11, and 524 shared by 4 is a hundred and thirty-one.

Where the remainder really is

$347 \div 8$. Work down to the ones, and whatever is left when the ones are done — that, and only that, is the remainder. Module 7 then tells you what to do with it, and the answer still depends on what was being shared.

Check yourself

Six to try

Work left to right. Where a number comes across, say what it is worth before you use it — hundreds become tens, tens become ones.

1

$492 \div 4$

2

Dividing by $7$, the hundreds column leaves $6$ over and a small $6$ is written in front of the tens digit. What is it?

3

$840 \div 7$

4

$295 \div 7$. What is the remainder?

5

Amina shares $780$ bricks equally between $6$ barrows. How many bricks are in each barrow?

6

$957 \div 9$. What is the remainder?

Away from the screen

Down the columns Say what each carried number is worth as you go.
Down the columns, page 1 Down the columns, page 2

Open the PDF Save it to print

The question this leaves you with

You can now add, subtract, multiply and divide any whole numbers at all.

$7 \div 2$. Three each, and one left over — and module 7 said that leftover can sometimes be cut up instead of kept.

So cut it. What is half a thing, and how would you write it down? Nothing in these eight units has given you a way of saying it.

Show that you have it

To the end of the ones

The first wants a remainder, which means going all the way down. The second asks what the number coming across is worth — and it is never the remainder.

1

$403 \div 6$. What is the remainder?

2

Dividing by $3$, the hundreds column leaves $2$ over and a small $2$ is written in front of the tens digit. What is it?