Conjecturing and generalising

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Mind Reading

Age

11 to 14

Challenge level

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?
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Shape and Territory

Age

16 to 18

Challenge level

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
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Is There a Theorem?

Age

11 to 14

Challenge level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
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Sums of Pairs

Age

11 to 16

Challenge level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
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Enclosing Squares

Age

11 to 14

Challenge level

Can you find sets of sloping lines that enclose a square?
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Cubes Within Cubes Revisited

Age

11 to 14

Challenge level

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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Cunning Card Trick

Age

11 to 14

Challenge level

Delight your friends with this cunning trick! Can you explain how it works?
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Always, Sometimes or Never? KS1

Age

5 to 7

Challenge level

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
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Let's Investigate Triangles

Age

5 to 7

Challenge level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
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What's in a Name?

Age

5 to 7

Challenge level

What do you notice about these squares of numbers? What is the same? What is different?