Conjecturing and generalising

Generalise this inequality involving integrals.

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

Can you find the area of a parallelogram defined by two vectors?

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

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

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

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?

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