Creating and manipulating expressions and formulae

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

What's special about the area of quadrilaterals drawn in a square?

Where should you start, if you want to finish back where you started?

Play around with the Fibonacci sequence and discover some surprising results!

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Can you make sense of these three proofs of Pythagoras' Theorem?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Can you find the hidden factors which multiply together to produce each quadratic expression?