Creating and manipulating expressions and formulae

  • Fibonacci Surprises
    problem
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    Fibonacci Surprises

    Age
    11 to 14
    Challenge level
    2 out of 3

    Play around with the Fibonacci sequence and discover some surprising results!

  • Fibs
    problem
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    Fibs

    Age
    11 to 14
    Challenge level
    3 out of 3
    The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
  • How Many Miles To Go?
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    How Many Miles to Go?

    Age
    11 to 14
    Challenge level
    3 out of 3

    How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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    Marbles in a Box

    Age
    11 to 16
    Challenge level
    2 out of 3

    How many winning lines can you make in a three-dimensional version of noughts and crosses?

  • Pythagoras Proofs
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    Pythagoras Proofs

    Age
    11 to 16
    Challenge level
    2 out of 3

    Can you make sense of these three proofs of Pythagoras' Theorem?

  • Pair Products
    problem
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    Pair Products

    Age
    14 to 16
    Challenge level
    1 out of 3

    Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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    Salinon

    Age
    14 to 16
    Challenge level
    1 out of 3

    This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

  • Finding factors
    problem
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    Finding Factors

    Age
    14 to 16
    Challenge level
    1 out of 3

    Can you find the hidden factors which multiply together to produce each quadratic expression?

  • Generating Triples
    problem
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    Generating Triples

    Age
    14 to 16
    Challenge level
    1 out of 3

    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

  • Steel Cables
    problem
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    Steel Cables

    Age
    14 to 16
    Challenge level
    1 out of 3

    Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?