Exploring and noticing

  • Small pepper seedlings in orange pots.
    problem

    Day of the Triffids

    Age
    14 to 16
    Challenge level
    2 out of 3

    Jasmine buys three different types of plant. How many triffids did she buy?

  • Making Tracks
    problem

    Making Tracks

    Age
    14 to 16
    Challenge level
    2 out of 3

    A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

  • Small pepper seedlings in orange pots.
    problem

    Newspaper Sheets

    Age
    14 to 16
    Challenge level
    2 out of 3

    From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

  • Small pepper seedlings in orange pots.
    problem

    Collatz-Ish

    Age
    14 to 16
    Challenge level
    2 out of 3

    A sequence is generated using these rules. For which values of n is the nth term equal to n?

  • Small pepper seedlings in turquoise pots.
    problem

    Back in Time

    Age
    14 to 16
    Challenge level
    2 out of 3

    How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

  • Small pepper seedlings in orange pots.
    problem

    Oldest and Youngest

    Age
    14 to 16
    Challenge level
    2 out of 3

    Edith had 9 children at 15 month intervals. If the oldest is now six times as old as the youngest, how old is her youngest child?

  • Just rolling round
    problem

    Just Rolling Round

    Age
    14 to 16
    Challenge level
    3 out of 3

    P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

  • There's always One isn't there
    problem

    There's Always One Isn't There

    Age
    14 to 16
    Challenge level
    3 out of 3

    Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

  • Guessing the graph
    problem

    Guessing the Graph

    Age
    14 to 16
    Challenge level
    3 out of 3
    Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
  • Can you traverse it?
    problem

    Can You Traverse It?

    Age
    14 to 18
    Challenge level
    1 out of 3

    How can you decide if a graph is traversable?