Explaining, convincing and proving

  • 5 by 5 Mathdokus
    problem
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    5 by 5 Mathdokus

    Age
    7 to 16
    Challenge level
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    Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

  • Xavi's T-shirt
    problem
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    Xavi's T-Shirt

    Age
    7 to 16
    Challenge level
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    How much can you read into a T-shirt?

  • Angles inside
    problem
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    Angles Inside

    Age
    11 to 14
    Challenge level
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    Draw some angles inside a rectangle. What do you notice? Can you prove it?

  • Rule of Three
    problem
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    Rule of Three

    Age
    11 to 14
    Challenge level
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    If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

  • An American flag waving in the wind.
    problem
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    American Billions

    Age
    11 to 14
    Challenge level
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    Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

  • 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?

  • Special Numbers
    problem
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    Special Numbers

    Age
    11 to 14
    Challenge level
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    My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

  • Tilted Squares
    problem
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    Tilted Squares

    Age
    11 to 14
    Challenge level
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    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Isosceles Triangles
    problem
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    Isosceles Triangles

    Age
    11 to 14
    Challenge level
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    Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

  • Triangles in circles
    problem
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    Triangles in Circles

    Age
    11 to 14
    Challenge level
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    Can you find triangles on a 9-point circle? Can you work out their angles?