Explaining, convincing and proving

  • School fair necklaces
    problem
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    School Fair Necklaces

    Age
    5 to 11
    Challenge level
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    How many possible symmetrical necklaces can you find? How do you know you've found them all?

  • Shadow Play
    problem
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    Shadow Play

    Age
    5 to 11
    Challenge level
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    Here are shadows of some 3D shapes. What shapes could have made them?

  • Odd times Even
    problem
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    Odd Times Even

    Age
    5 to 11
    Challenge level
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    This problem looks at how one example of your choice can show something about the general structure of multiplication.

  • Four playing cards on top of each other. Each card shows a different ace.
    problem
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    Statement Snap

    Age
    7 to 11
    Challenge level
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    You'll need to know your number properties to win a game of Statement Snap...

  • problem
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    Rectangle Tangle

    Age
    7 to 11
    Challenge level
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    The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

  • Square Corners
    problem
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    Square Corners

    Age
    7 to 11
    Challenge level
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    What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

  • Odd Squares
    problem
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    Odd Squares

    Age
    7 to 11
    Challenge level
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    Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

  • What Do you Need?
    problem
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    What Do You Need?

    Age
    7 to 11
    Challenge level
    filled star empty star empty star

    Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?