Counting Stick Conjectures
Age 5 to 11
Challenge Level
How many rectangles can you see? Are they all the same size? Can you predict how many rectangles there will be in counting sticks of different lengths?
Break it Up!
Age 5 to 11
Challenge Level
In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?
Diagonally Square
Age 7 to 11
Challenge Level
Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
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.
Triangle in a Square
Age 7 to 11
Challenge Level
Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?
Unravelling Sequences
Age 7 to 11
Challenge Level
Can you describe what is happening as this program runs? Can you unpick the steps in the process?
NRICH is part of the family of activities in the Millennium Mathematics Project.