Patterns and Sequences: Age 11-14

This is part of our collection of favourite rich tasks arranged by topic.

If you are a teacher, you can find the whole collection on our Secondary Curriculum teacher page.
Alternatively, if you are a student, you'll find the same problems on our Secondary Curriculum student page.


  • spaces for exploration
    article

    Spaces for Exploration

    Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.

  • Days and Dates
    problem
    Favourite

    Days and Dates

    Age
    11 to 14
    Challenge level

    Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

  • Summing Consecutive Numbers
    problem
    Favourite

    Summing Consecutive Numbers

    Age
    11 to 14
    Challenge level

    15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

  • A green frog.
    problem
    Favourite

    Frogs

    Age
    11 to 14
    Challenge level

    How many moves does it take to swap over some red and blue frogs? Do you have a method?

  • Picturing Triangular Numbers
    problem
    Favourite

    Picturing Triangular Numbers

    Age
    11 to 14
    Challenge level

    What do you notice about the sum of two identical triangular numbers?

  • Picturing Square Numbers
    problem
    Favourite

    Picturing Square Numbers

    Age
    11 to 14
    Challenge level

    Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

  • Elevenses
    problem
    Favourite

    Elevenses

    Age
    11 to 14
    Challenge level

    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
    Favourite

    Shifting Times Tables

    Age
    11 to 14
    Challenge level

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

  • What numbers can we make?
    problem
    Favourite

    What Numbers Can We Make?

    Age
    11 to 14
    Challenge level

    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
    Favourite

    Odds, Evens and More Evens

    Age
    11 to 14
    Challenge level

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

  • Beach Huts
    problem
    Favourite

    Beach Huts

    Age
    11 to 14
    Challenge level

    Can you figure out how sequences of beach huts are generated?

  • Growing Surprises
    problem
    Favourite

    Growing Surprises

    Age
    11 to 14
    Challenge level

    Can you find the connections between linear and quadratic patterns?

  • 1 Step 2 Step
    problem
    Favourite

    1 Step 2 Step

    Age
    11 to 14
    Challenge level

    Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

  • Coordinate Patterns
    problem
    Favourite

    Coordinate Patterns

    Age
    11 to 14
    Challenge level

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

  • Squares in rectangles
    problem
    Favourite

    Squares in Rectangles

    Age
    11 to 14
    Challenge level

    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?

  • Triangle Numbers
    problem
    Favourite

    Triangle Numbers

    Age
    11 to 14
    Challenge level

    Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

  • The Tower of Hanoi - three wooden poles, with several coloured rings of decreasing sizes on the middle pole.
    problem
    Favourite

    Tower of Hanoi

    Age
    11 to 14
    Challenge level

    The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

  • Seven Squares
    problem
    Favourite

    Seven Squares

    Age
    11 to 14
    Challenge level

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

  • What numbers can we make now?
    problem
    Favourite

    What Numbers Can We Make Now?

    Age
    11 to 14
    Challenge level

    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

  • Train Spotters' Paradise
    article

    Train Spotters' Paradise

    Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

  • Charlie's delightful machine
    problem
    Favourite

    Charlie's Delightful Machine

    Age
    11 to 16
    Challenge level

    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Displaying 1 - 21 of 21