Visualising and representing

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you make square numbers by adding two prime numbers together?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Try adding fractions using A4 paper.

Can you compare these bars with each other and express their lengths as fractions of the black bar?

What fraction of the black bar are the other bars? Have a go at this challenging task!

There are lots of different methods to find out what the shapes are worth - how many can you find?

Try out this number trick. What happens with different starting numbers? What do you notice?