Visualising and representing

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?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Try out these calculations. Are you surprised by the results?