


Days and dates

Blue and white
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?


Picturing triangular numbers

Tilted squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Parallel lines

Reflecting lines

Translating lines

Cyclic quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?


What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out?

Terminating or not


Legs eleven

1 step 2 step

Subtended angles
What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Tower of Hanoi
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?

How many miles to go?

Generating triples
