How many each · Patans

Before you read anything

Fifteen stones, three piles. Deal them out one at a time — one here, one here, one here, and round again.

Stop when they are gone and count one pile. Say the number out loud.

Dealing, watched

Fifteen dealt one at a time into three. Five in each — and nobody knew that number until the dealing stopped.

Three was given to you. Five was not. That is the shape of this question.

What was known and what was not

Splitting a quantity into a known number of equal groups. What you are looking for is the size of one group.

Every :sharing question hands you the number of groups and hides the size. Fifteen sweets, three children — the three is in the question and the five is the answer.

The bar you already have

Module 5 cut a bar of fourteen into ten and four. This cuts a bar of fifteen into three equal parts, and equal is what makes one part worth asking about: find one, and you have found them all.

One part is worth having on its own

Nakato

found one part, then took two of them

Nakato answered a harder question with the same step. Twenty-one shared between three is seven each, so two of them have fourteen — and she never needed a second calculation.

Check yourself

Six to try

Two of these are bars and the rest are stories. Every one of them tells you how many groups there are — find what one is worth.

1

A bar of $15$ is cut into $3$ equal parts. How much is one part worth?

2

$30$ pencils shared equally between $6$ boxes. How many pencils are in each box?

3

A bar of $16$ is cut into $4$ equal parts. How much is one part worth?

4

$24$ sweets shared equally between $3$ children. How many sweets does each child get?

5

Apio has $35$ bricks and $5$ barrows, and splits the bricks equally between them. What is Apio trying to find?

6

Nakato shares $40$ sweets equally between $5$ children. How many does each child get?

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Show that you have it

One part, then more than one

Neither of these asks what one gets. Find that first anyway — it is the only step that matters, and the rest is counting.

1

$12$ exercise books are shared equally between $3$ desks. How many do $2$ of them have altogether?

2

$40$ sweets are shared equally between $8$ children. How many do $6$ of them have altogether?

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