Conjecturing and generalising

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

How many different shaped boxes can you design for these sweets?

There are six numbers written in five different scripts. Can you sort out which is which?

On the planet Vuv there are two sorts of creatures. The Zias have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zias and how many Zepts were there?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Norrie sees two lights flash at the same time. How many times do they flash together during a whole minute?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?