Exploring and noticing

  • Standard Index Form Matching
    problem
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    Standard Index Form Matching

    Age
    14 to 16
    Challenge level
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    Can you match these calculations in Standard Index Form with their answers?

  • Triangle midpoints
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    Triangle Midpoints

    Age
    14 to 16
    Challenge level
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    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

  • Two Ladders
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    Two Ladders

    Age
    14 to 16
    Challenge level
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    Two ladders are propped up against facing walls. At what height do the ladders cross?

  • Plus Minus
    problem
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    Plus Minus

    Age
    14 to 16
    Challenge level
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    Can you explain the surprising results Jo found when she calculated the difference between square numbers?

  • Sitting Pretty
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    Sitting Pretty

    Age
    14 to 16
    Challenge level
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    A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

  • Of all the areas
    problem
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    Of All the Areas

    Age
    14 to 16
    Challenge level
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    Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

  • Fair Shares?
    problem
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    Fair Shares?

    Age
    14 to 16
    Challenge level
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    A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

  • What's Possible?
    problem
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    What's Possible?

    Age
    14 to 16
    Challenge level
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    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

  • Tree tops
    problem
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    Tree Tops

    Age
    14 to 16
    Challenge level
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    Can you make sense of information about trees in order to maximise the profits of a forestry company?

  • Tiny Nines
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    Tiny Nines

    Age
    14 to 16
    Challenge level
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    What do you notice about these families of recurring decimals?