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### Number and algebra

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### For younger learners

### Advanced mathematics

# Shape Your Proof

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Break it Up!

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Counting Stick Conjectures

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School Fair Necklaces

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Diagonally Square

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Brush Loads

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Triangle in a Square

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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.*

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?

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?

Age 5 to 11

Challenge Level

How many possible symmetrical necklaces can you find? How do you know you've found them all?

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?

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.

Age 7 to 11

Challenge Level

Do you agree with Badger's statements? Is Badger's reasoning watertight? Why or why not?