problem Counting Cogs Age 7 to 14 Challenge level Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
problem I Like ... Age 5 to 7 Challenge level Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
problem Times Tables Shifts Age 7 to 11 Challenge level In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
problem Three Dice Age 7 to 11 Challenge level Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
problem Slick Summing Age 14 to 16 Challenge level Watch the video to see how Charlie works out the sum. Can you adapt his method?
problem Handshakes Age 11 to 14 Challenge level Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
problem Mystic Rose Age 14 to 16 Challenge level Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem Diminishing Returns Age 11 to 14 Challenge level How much of the square is coloured blue? How will the pattern continue?
problem Tower of Hanoi Age 11 to 14 Challenge level The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem Christmas chocolates Age 11 to 14 Challenge level How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?