Conjecturing and generalising

What do you notice about the sum of two identical triangular numbers?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Explore the effect of reflecting in two parallel mirror lines.

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.