Conjecturing and generalising

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

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?

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?

How much of the square is coloured blue? How will the pattern continue?

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Engage in a little mathematical detective work to see if you can spot the fakes.