Exploring and noticing

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?

These clocks have been reflected in a mirror. What times do they say?

How would you move the bands on the pegboard to alter these shapes?

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?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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.