Conjecturing and generalising

  • Mind Reading
    problem
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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?
  • Is there a theorem?
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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?
  • Sums of Pairs
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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?”
  • Enclosing Squares
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    Enclosing Squares

    Age
    11 to 14
    Challenge level
    Can you find sets of sloping lines that enclose a square?
  • Cubes within Cubes revisited
    problem
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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?
  • Cunning Card Trick
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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?
  • Always, Sometimes or Never? KS1
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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?

  • Let's Investigate Triangles
    problem
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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?

  • What's in a Name?
    problem
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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?

  • Share Bears
    problem
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    Share Bears

    Age
    5 to 7
    Challenge level

    Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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