Being collaborative

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Can you find the area of a parallelogram defined by two vectors?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Your school has been left a million pounds in the will of an ex-pupil. What model of investment and spending would you use in order to ensure the best return on the money?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

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?