Explaining, convincing and proving

  • Mechanical Integration
    problem
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    Mechanical Integration

    Age
    16 to 18
    Challenge level
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    To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.
  • Discrete Trends
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    Discrete Trends

    Age
    16 to 18
    Challenge level
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    Find the maximum value of n to the power 1/n and prove that it is a maximum.
  • Square Mean
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    Square Mean

    Age
    14 to 16
    Challenge level
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    Is the mean of the squares of two numbers greater than, or less than, the square of their means?
  • Always, Sometimes or Never? KS1
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    Always, Sometimes or Never? KS1

    Age
    5 to 7
    Challenge level
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    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
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    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?

  • Sunrise over some tower blocks.
    problem
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    A City of Towers

    Age
    5 to 7
    Challenge level
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    In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

  • Building with Solid Shapes
    problem
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    Building With Solid Shapes

    Age
    5 to 7
    Challenge level
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    We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

  • Cuisenaire Counting
    problem
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    Cuisenaire Counting

    Age
    5 to 7
    Challenge level
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    Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

  • Domino Sorting
    problem
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    Domino Sorting

    Age
    5 to 7
    Challenge level
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    Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

  • Sizing them Up
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    Sizing Them Up

    Age
    5 to 7
    Challenge level
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    Can you put these shapes in order of size? Start with the smallest.