Exploring and noticing

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Amy's mum gave her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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.