Being resourceful

  • Fitted
    problem

    Fitted

    Age
    7 to 11
    Challenge level
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    Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

  • Halving
    problem

    Halving

    Age
    5 to 7
    Challenge level
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    These pictures show squares split into halves. Can you find other ways?

  • Remainders
    problem

    Remainders

    Age
    7 to 14
    Challenge level
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    I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

  • Frogs
    problem

    Frogs

    Age
    11 to 14
    Challenge level
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    How many moves does it take to swap over some red and blue frogs? Do you have a method?

  • Triangles to Tetrahedra
    problem

    Triangles to tetrahedra

    Age
    11 to 14
    Challenge level
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    Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

  • Skeleton Shapes
    problem

    Skeleton shapes

    Age
    5 to 7
    Challenge level
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    How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

  • Cubes within Cubes
    problem

    Cubes within cubes

    Age
    7 to 14
    Challenge level
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    We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

  • problem

    Two primes make one square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?

  • The Third Dimension
    problem

    The third dimension

    Age
    5 to 11
    Challenge level
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    Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?