### Cubes

Investigate the number of faces you can see when you arrange three cubes in different ways.

### I'm Eight

Find a great variety of ways of asking questions which make 8.

### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

# Doing and Undoing

## Doing and Undoing

Maybe you are used to making knots and sometimes you undo them!

Let's look at undoing some maths that's been done.

Suppose we have a starting number and then we doubled it.
That's the bit we'll call "doing".
To "undo" the maths we start with just the answer and see if we can get back to our starting number.
When I  doubled my starting number, I got $6$. What do I have to do, to "undo" the $6$ and get back to my starting number?
Suppose that I did it again with a new starting number so I doubled and got to $16$. What would you have to do to "undo" and get back to my new starting number?

Can you think what you would have to do to "undo" these three children's maths?

Danesh says
"I took $4$ away, what should I do to get back to my starting number?"
Meg says
" I added $8$, what should I do to get back to my starting number?"
Chris says
"I halved, what should I do to get back to my starting number?"

Now, if they all finished with a $12$ what were their starting numbers?

Photograph acknowledgements;

http://www.instructables.com/image/FPRA3T8FZ8J4A39/How-to-tie-various
-knots.jpg
http://2.bp.blogspot.com/-Jg0te1K_F5g/TpFcEY8xT6I/AAAAAAAAHy4/vgkke
-0QQ98/s1600/knot.jpg
http://www.instructables.com/image/F0PMDJ8FZ8J4A36/Figure-8-Knot.jpg

### Why do this problem?

This activity possibly presents a new way for many pupils to think about the arithmetic they do. The idea of inverse operations is core mathematical concept and this activity offers opportunities to explore them in a meaningful way.

### Possible approach

One way would be to start by saying "Here's the number $4$  I'll double it",  inviting the pupils then to say what the answer is and then how to get back to the $4$.
You could try some different numbers and repeat the process with doubling each time as the operation.
The operation can then be changed to an addition or subtraction one.
This can now lead to the bigger question about whether same inverse operation works for every starting number.
If your pupils are secure then use the same rule but choose a different, and this time mystery, starting number and tell them the finishing number.  Invite them to think about what calculation they'd do to get back to your mystery starting number.

### Key questions

What number do you get?
If you 'undo' the operation what do you get?
What do you have to do to 'undo' adding $6$?
What do you have to do to 'undo' doubling?