Working systematically

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?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Can you work out the fraction of the original triangle that is covered by the inner triangle?

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?

There is a particular value of x, and a value of y to go with it, which make all these five expressions equal in value. Can you find that x, y pair?

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?