Being collaborative

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.