### Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

### Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

# Stairs

##### Stage: 1 and 2 Challenge Level:

Here is a solution to STAIRS, which we very happily received from Hannah of West Flegg Middle School, Norfolk. She writes:

Numbers 1, 5, 8, 11, 12, 13, 14, 15, 16, 17 start with one up then two across. Only number 10 starts with 2 up at the beginning. Number 18 and Number 2 have one up and then 3 across.
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Biggest and smallest:-

This is my biggest

This is my smallest

Then:-

14 on the first sheet - No 19.
15 on the sheet - Nos. 14, 2, 3, 6.
16 on the sheet - No. 9.
17 on the sheet - Nos. 8, 13, 18.
18 on the sheet - Nos. 4, 11.
19 on the sheet - Nos. 1, 12, 13, 16.

22 on the sheet - No. 10.
23 on the sheet - No. 17.

And so on... you can just add one to the last square, up the top if you like. I added them up at the top of the last three.

She went on to extend the challenge! WELL DONE

I wonder what would happen if it were 5 along and four up?

The amount would be smaller all the time but the method would be the same.

She also looked at 5 by 6 and 6 by 5. She finishes by saying:

I wonder what would happen if you could have two sets of steps?

e.g.,

Bernard says "Well done, a good approach. I liked the way you had a go, then sorted them into an order, put in the missing ones, and saw how it was just going to go on. Then you asked a further question, and explored it a little. And you finished with a brand new question. Keep up this good work all of you!''