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Shape Your Proof

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In this feature for Primary students, we offer geometrical tasks which give you the chance to notice patterns and make conjectures. Can you create a mathematical argument that would convince a mathematician that your conjecture is always true?

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.

Counting Stick Conjectures
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Counting Stick Conjectures

Age
5 to 11
Challenge level
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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!
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Favourite

Break it up!

Age
5 to 11
Challenge level
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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?

School fair necklaces
problem
Favourite

School fair necklaces

Age
5 to 11
Challenge level
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How many possible symmetrical necklaces can you find? How do you know you've found them all?
Diagonally Square
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Diagonally Square

Age
7 to 11
Challenge level
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Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?
Brush Loads
problem
Favourite

Brush Loads

Age
7 to 11
Challenge level
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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
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Triangle in a Square

Age
7 to 11
Challenge level
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Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?