Conjecturing and generalising

problem
Nice or nasty

Age

7 to 11

Challenge level

There are nasty versions of this dice game but we'll start with the nice ones...
problem
Strike it out

Age

5 to 11

Challenge level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
problem
Vector walk

Age

14 to 18

Challenge level

Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Keep it simple

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
problem
Circles in quadrilaterals

Age

14 to 16

Challenge level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
problem
Holes

Age

5 to 11

Challenge level

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
problem
Speeding boats

Age

14 to 16

Challenge level

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
problem
Tangled trig graphs

Age

16 to 18

Challenge level

Can you work out the equations of the trig graphs I used to make my pattern?
problem
Reflecting lines

Age

11 to 14

Challenge level

Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.