Conjecturing and generalising

problem
Tables without tens

Age

7 to 11

Challenge level

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
problem
Areas of parallelograms

Age

14 to 16

Challenge level

Can you find the area of a parallelogram defined by two vectors?
problem
Litov's mean value theorem

Age

11 to 14

Challenge level

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
problem
Mixing more paints

Age

14 to 16

Challenge level

Can you find an efficent way to mix paints in any ratio?
problem
Harmonic triangle

Age

14 to 16

Challenge level

Can you see how to build a harmonic triangle? Can you work out the next two rows?
problem
Fractional wall

Age

7 to 11

Challenge level

Using the picture of the fraction wall, can you find equivalent fractions?
problem
Bishop's paradise

Age

11 to 14

Challenge level

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?
problem
Board block challenge

Age

7 to 11

Challenge level

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
problem
Triangle pin-down

Age

7 to 11

Challenge level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
problem
Right angles

Age

11 to 14

Challenge level

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