Explaining, convincing and proving

  • Triangles within Triangles
    problem

    Triangles Within Triangles

    Age
    14 to 16
    Challenge level
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    Can you find a rule which connects consecutive triangular numbers?

  • Honey Bees
    problem

    Honey Bees

    Age
    14 to 16
    Challenge level
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    How many bees could fly 1000 miles if they had 10 gallons of honey?

  • Hiking the Hill
    problem

    Hiking the Hill

    Age
    14 to 16
    Challenge level
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    Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?

  • The London Eye
    problem

    The London Eye

    Age
    14 to 16
    Challenge level
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    The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?

  • Peter's Primes
    problem

    Peter's Primes

    Age
    14 to 16
    Challenge level
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    Peter wrote a list of all the numbers that can be formed by changing one digit of the number 200. How many of Peter's numbers are prime?

  • Different Products
    problem

    Different Products

    Age
    14 to 16
    Challenge level
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    Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

  • Proximity
    problem

    Proximity

    Age
    14 to 16
    Challenge level
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    We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

  • Gift of Gems
    problem

    Gift of Gems

    Age
    14 to 16
    Challenge level
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    Four jewellers share their stock. Can you work out the relative values of their gems?

  • Long Short
    problem

    Long Short

    Age
    14 to 16
    Challenge level
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    What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?