Exploring and noticing

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?

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

Can all unit fractions be written as the sum of two unit fractions?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Can you find a way to identify times tables after they have been shifted up or down?