Being resourceful

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Can you replace the letters with numbers? Is there only one solution in each case?

A Deca Tree has 10 trunks, and on each trunk are 10 branches, and on each branch are 10 twigs...

Can you find out where all the numbers on this clock face are using the ten statements?

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Using the picture of the fraction wall, can you find equivalent fractions?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.