Exploring and noticing

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?

Invent a scoring system for a 'guess the weight' competition.

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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?

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