Being collaborative

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Can you match up these equivalent algebraic expressions?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

If you know the perimeter of a right angled triangle, what can you say about the area?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.