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You may also like to take a look at our I Like to Prove It! feature which gives you tasks for a similar purpose but in the context of number.
problem
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?
problem
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?
problem
School fair necklaces
Age
5 to 11
Challenge level
How many possible symmetrical necklaces can you find? How do you know you've found them all?
problem
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?
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
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?