Working systematically

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 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?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Can you work out the probability of winning the Mathsland National Lottery?