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?

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?

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Starting with two basic vector steps, which destinations can you reach on a vector walk?

This task develops knowledge of transformation of graphs. By framing and asking questions a member of the team has to find out which mathematical function they have chosen.