Creating and manipulating expressions and formulae

  • Seven Squares
    problem

    Seven squares

    Age
    11 to 14
    Challenge level
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    Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
  • Finding factors
    problem

    Finding factors

    Age
    14 to 16
    Challenge level
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    Can you find the hidden factors which multiply together to produce each quadratic expression?

  • Training schedule
    problem

    Training schedule

    Age
    14 to 16
    Challenge level
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    The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
  • Perimeter Expressions
    problem

    Perimeter expressions

    Age
    11 to 14
    Challenge level
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    Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
  • Your number was...
    problem

    Your number was...

    Age
    11 to 14
    Challenge level
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    Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
  • Packing Boxes
    problem

    Packing boxes

    Age
    14 to 16
    Challenge level
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    Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.
  • Folding in Half
    problem

    Folding in half

    Age
    14 to 16
    Challenge level
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    How does the perimeter change when we fold this isosceles triangle in half?
  • In Sum-mary
    problem

    In sum-mary

    Age
    11 to 14
    Challenge level
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    What does the sum of these three numbers tell us about their product?
  • Symbol
    problem

    Symbol

    Age
    11 to 14
    Challenge level
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    Using the new operator $\oplus$, can you solve this equation?
  • Factor List
    problem

    Factor list

    Age
    14 to 16
    Challenge level
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    Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?