Conjecturing and generalising

  • Isometric Areas
    problem
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    Isometric Areas

    Age
    11 to 14
    Challenge level
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    We usually use squares to measure area, but what if we use triangles instead?

  • Climbing Complexity
    problem
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    Climbing Complexity

    Age
    11 to 14
    Challenge level
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    In the 2020 Olympic Games, sport climbing was introduced for the first time, and something very interesting happened with the scoring system. Can you find out what was interesting about it?

  • Days and Dates
    problem
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    Days and Dates

    Age
    11 to 14
    Challenge level
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    Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

  • Have you got it?
    problem

    Have You Got It?

    Age
    11 to 14
    Challenge level
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    Can you explain the strategy for winning this game with any target?

  • Blue and White
    problem
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    Blue and White

    Age
    11 to 14
    Challenge level
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    Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

  • Dicing with numbers
    problem

    Dicing with Numbers

    Age
    11 to 14
    Challenge level
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    In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?

  • A green frog.
    problem
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    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?

  • Largest product
    problem
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    Largest Product

    Age
    11 to 14
    Challenge level
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    Which set of numbers that add to 100 have the largest product?

  • Picturing Triangular Numbers
    problem
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    Picturing Triangular Numbers

    Age
    11 to 14
    Challenge level
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    What do you notice about the sum of two identical triangular numbers?

  • Picturing Square Numbers
    problem
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    Picturing Square Numbers

    Age
    11 to 14
    Challenge level
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    Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?