Year 8 Working systematically

Can you find triangles on a 9-point circle? Can you work out their angles?

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

Can all unit fractions be written as the sum of two unit fractions?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

What are the possible areas of triangles drawn in a square?

We started drawing some quadrilaterals - can you complete them?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

What's the largest volume of box you can make from a square of paper?

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.