Arithmetic sequences

  • Elevenses
    problem

    Elevenses

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

  • Shifting Times Tables
    problem

    Shifting times tables

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you find a way to identify times tables after they have been shifted up or down?

  • What numbers can we make?
    problem

    What numbers can we make?

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

  • Odds, Evens and More Evens
    problem

    Odds, evens and more evens

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

  • Growing Surprises
    problem

    Growing surprises

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Can you find the connections between linear and quadratic patterns?

  • More Number Pyramids
    problem

    More number pyramids

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

  • Seven Squares - Group-worthy Task
    problem

    Seven squares - group-worthy task

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
  • Coordinate Patterns
    problem

    Coordinate patterns

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

  • Squares in rectangles
    problem

    Squares in rectangles

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

  • Seven Squares
    problem

    Seven squares

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?