Before, and after

Before you read anything

Achen has 16 sweets and Okello has 8. Achen gives Okello some, and they end up with the same number.

How many did she hand over? Most people say eight. Say your answer, then count what each of them would have.

Two moments, one picture

Sixteen and eight before; twelve and twelve after. Four moved, not eight — and the total across the two bars never changed.

Four. Every sweet that leaves one bar arrives in the other, so the gap closes twice as fast as the amount handed over.

What held still

:x nutshell-before-and-after

Two rows of bars: how things were, and how they ended up. What decides the method is which amount stayed the same.

In a giving problem the total holds still. In a spending problem nothing does. In a problem where everybody gets the same extra, the difference holds still.

That is visible in a :before-and-after drawing and completely invisible in the numbers.

The question module 11 left you

A third given away, and 12 left. Draw three equal boxes, cross one out, and the twelve is sitting under two boxes.

One box is six. Three of them is eighteen — and nobody had to be told a method.

Nakato

drew both rows before writing anything down

Check yourself

Six to try

Draw two rows every time — before on top, after underneath. Then say which amount is the same in both rows.

1

Amina spends $15$ shillings and has $12$ left. How many shillings were there before?

2

Nakato has $20$ sweets and Musa has $16$. How many must Nakato give Musa so that they have the same?

3

Nakato gives away a quarter of their pencils and has $9$ left. How many were there to start with?

4

Apio gives Wasswa some pencils until they have the same amount. What stayed the same the whole time?

5

Apio has $23$ pencils and Wasswa has $7$. How many must Apio give Wasswa so that they have the same?

6

Wasswa gives away a fifth of their sweets and has $12$ left. How many were there to start with?

Before, and after · page 1 of 2 Print it

Before, and after · page 2 of 2 Print it

Show that you have it

What stayed the same

The first asks outright what held still. The second is the giving-away question, and the drawing answers it before the arithmetic starts.

1

Amina gives Otim some mangoes until they have the same amount. What stayed the same the whole time?

2

Apio gives away a third of their sweets and has $26$ left. How many were there to start with?

Next: The box you do not know yet The whole thing on one page