Conjecturing and generalising

problem
More magic potting sheds

Age

11 to 16

Challenge level

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?
problem
Brush loads

Age

7 to 11

Challenge level

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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
The better choice

Age

14 to 16

Challenge level

Here are two games you can play. Which offers the better chance of winning?
problem
Cosy corner

Age

11 to 14

Challenge level

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?