Conjecturing and generalising

We start with one yellow cube and build around it to make a 3×3×3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

How much can you read into a T-shirt?

We usually use squares to measure area, but what if we use triangles instead?

In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Which set of numbers that add to 100 have the largest product?

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?