Exploring and noticing

  • Impossible triangles?
    problem

    Impossible Triangles?

    Age
    16 to 18
    Challenge level
    2 out of 3

    Which of these triangular jigsaws are impossible to finish?

  • Farey Neighbours
    problem

    Farey Neighbours

    Age
    16 to 18
    Challenge level
    2 out of 3

    Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

  • Nine Eigen
    problem

    Nine Eigen

    Age
    16 to 18
    Challenge level
    2 out of 3

    Explore how matrices can fix vectors and vector directions.

  • Inverting Rational Functions
    problem

    Inverting Rational Functions

    Age
    16 to 18
    Challenge level
    2 out of 3

    Consider these questions concerning inverting rational functions

  • Placeholder: several colourful numbers
    problem

    Integral Arranging

    Age
    16 to 18
    Challenge level
    2 out of 3

    How would you sort out these integrals?

  • How fast does it grow?
    problem

    How Fast Does It Grow?

    Age
    16 to 18
    Challenge level
    3 out of 3

    Exponential functions grow pretty quickly...

  • Making Waves
    problem

    Making Waves

    Age
    16 to 18
    Challenge level
    3 out of 3

    Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

  • Pattern Sniffing
    article

    Pattern Sniffing

    This article for primary teachers outlines how we can encourage children to create, identify, extend and explain number patterns and why being able to do so is useful.