Creating and manipulating expressions and formulae

Which armies can be arranged in hollow square fighting formations?

What is special about the difference between squares of numbers adjacent to multiples of three?

What's special about the area of quadrilaterals drawn in a square?

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Can you find rectangles where the value of the area is the same as the value of the perimeter?