### 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?

# Paw Prints

##### Age 7 to 11Challenge Level

We had some good solutions sent in and here are just some of them. Many pupils from Bradon Forest in the U.K. sent in solutions. Hannah produced a Powerpoint presentation for the solutions she found. Well done Hannah - here are her slides.

Georgia, also from Bradon, sent in a Word document with pictures to show the solutions. Here is what she wrote.

In the case with the three obstacles, the dog starts at the kennel and walks on the path that leads to the signpost.
When he gets to the signpost, he goes down the path straight ahead (the one with the arrow pointing at the tree).
He then goes down the path with the arrow pointing towards the kennel, and then goes down the path pointing at the tree.
Finally, he goes down the only remaining path that he hadn't previously walked on, arriving at the signpost.

In the second case, you start at the kennel and proceed to the tree.
Next, you carry on until you reach the signpost.
Next take the path pointing at the lamppost, until you reach the lamp.
Turn and head back to the signpost.
Then, you take the path round to the kennel and, when you reach it, go down the path to the lamppost, then turn and reach your final destination, the tree.

In the third case you start at the big tree, and go to the small tree.
Then, you continue on the path to the kennel.
Once you reach the kennel, you go to the signpost.
Then, back to the big tree and take the last path going away from the tree.
You then go on the unused path to the kennel, and loop back to the small tree.
To finish off, you go from the little tree directly to the lamppost.

Lastly Krystof's dad emailed us his son's solutions to four of the problems and here's his solution for this activity.