Conjecturing and generalising

Zias have 3 legs and Zepts have 7 legs. If there were 52 legs, how many of each were there?

Abundant numbers are less than the sum of their factors (excluding themselves). Can you find some?

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?

These rows of children are holding cards with numbers on them. Can you work out the missing numbers?

Using the picture of the fraction wall, can you find equivalent fractions?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.