Exploring and noticing

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

Are these games fair? How can you tell?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?