Conjecturing and generalising

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.
problem
Building gnomons

Age

14 to 16

Challenge level

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
problem
At right angles

Age

14 to 16

Challenge level

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
problem
Power mad!

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

Charlie has moved between countries and the average income of both has increased. How can this be so?
problem
Cuboid challenge

Age

11 to 16

Challenge level

What's the largest volume of box you can make from a square of paper?
problem
Searching for mean(ing)

Age

11 to 16

Challenge level

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
problem
Venn diagrams

Age

5 to 11

Challenge level

How will you complete these interactive Venn diagrams?
problem
Treasure hunt

Age

7 to 14

Challenge level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
problem
Magic Vs

Age

7 to 11

Challenge level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?