One box, and what it is worth

Before you read anything

Lay fifteen stones out as three rows of five. Do not count them again.

Read the rows out loud. Then walk round and read the columns.

One picture, both questions

Three rows of five is fifteen shared between three. Five columns of three is fifteen grouped in threes. The fifteen never changes.

Neither reading is the true one. The rectangle is what is true, and the two divisions are two ways of looking at it.

The fact underneath both

:x nutshell-one-unit

The amount one box stands for. Almost every problem in this course is that question wearing different clothes — find one, and the rest is counting.

$3 \times 5 = 15$. That single fact answers fifteen between three and fifteen in threes, and module 4 built it. Both questions want :one unit — so division is not a new thing to learn, it is that fact asked from a side you have not stood on.

You have been doing this since module 4

Musa

saw that $\square \times 7 = 56$ was a division

The box was always the unknown unit. A missing factor, a share, a count of groups — three questions, one box, and finding what it is worth answers all of them.

Play until finding one unit is automatic

Unit Rush — Sharing and grouping, mixed on purpose.

Check yourself

Six to try

These alternate between the two kinds without saying which. Before each one, say whether you are being told the number of groups or the size.

1

A bar of $9$ is cut into $3$ equal parts. How much is one part worth?

2

How many $4$s are there in $12$?

3

Okello has $24$ bricks and $4$ barrows, and splits the bricks equally between them. What is Okello trying to find?

4

Achen has $45$ exercise books and puts $5$ on each desk. What is Achen trying to find?

5

A bar of $36$ is cut into $6$ equal parts. How much is one part worth?

6

$108$ bricks, with $12$ in every barrow. How many barrows is that?

One box, and what it is worth · page 1 of 2 Print it

One box, and what it is worth · page 2 of 2 Print it

The question this leaves you with

Sixteen sweets, three children. Deal them out.

You get five each and there is one left in your hand. It will not go, and cutting it is not always allowed.

So what happens to it? The answer is not a rule — it depends entirely on what was being shared.

Show that you have it

Which question is it

Neither of these wants an answer. Both want you to say what is being looked for, and the two are not the same.

1

Musa has $32$ pencils and puts $8$ in each box. What is Musa trying to find?

2

Apio has $72$ sweets and $9$ children, and splits the sweets equally between them. What is Apio trying to find?

Check what stuck The whole thing on one page