Patans.

Drawing the problem

The box you do not know yet

20 minutes

Start the lesson

Before you read anything

Draw three equal boxes in a row. Do not write any numbers in them.

Now cross the last one out and write 12 under the two that are left. You have just solved something.

One box, and what it is worth

Three equal boxes, one given away, and twelve under the two that remain. One box is six, so there were eighteen.

Nobody said what a box was worth. The picture found it anyway, because two boxes being twelve leaves only one possibility.

It has been there all along

:x nutshell-the-unknown-unit

One box, repeated, standing for an amount nobody has told you. Find what one box is worth and the problem is finished.

Module 6 asked what one share was worth. Module 9 asked it of a bar cut into fifths. This is the same question with the total hidden, and it is :the unknown unit doing the work.

What that box actually is

In three years somebody will draw this picture and write $3x = 18$.

The box is the $x$. The letters arrive as a new name for something you already do, not as a new subject.

Amina

realised she had been doing algebra all along

Where this goes next

Two bars and a gap. Before and after. One box repeated. Most of Year 7 is one of those three with harder numbers in it.

Check yourself

Six to try

These mix the two pictures on purpose. Decide which one you are drawing before you draw anything.

1

Achen has $3$ times as many exercise books as Okello. Together they have $12$. How many does Okello have?

2

Apio gives away a fifth of their mangoes and has $36$ left. How many were there to start with?

3

Amina has $4$ times as many mangoes as Otim. Together they have $70$. How many does Otim have?

4

Achen has $34$ exercise books and Okello has $20$. How many must Achen give Okello so that they have the same?

5

Achen has $5$ more exercise books than Okello, and there are $21$ altogether. Which drawing shows that?

6

Ssebba gives away a quarter of their pencils and has $21$ left. How many were there to start with?

Away from the screen

Finding one unit Boxes from module 4, divisions from module 6, and this.
Finding one unit, page 1 Finding one unit, page 2

Open the PDF Save it to print

That is the course

You started with seven as four and three.

You finish with a box that stands for a number nobody has told you, and a picture that finds it. Everything in between was the same bar.

Show that you have it

One box, whatever the story

Two last ones. Draw the boxes, find what one is worth, and answer the question that was actually asked.

1

Musa gives away a sixth of their pencils and has $30$ left. How many were there to start with?

2

Nakato has $4$ times as many sweets as Musa. Together they have $30$. How many does Musa have?