Functions and Graphs: 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.


  • A rolled up old-fashioned treasure map.
    problem
    Favourite

    Treasure Hunt

    Age
    7 to 14
    Challenge level

    Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

  • How far does it move?
    problem
    Favourite

    How Far Does It Move?

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

  • Parallel lines
    problem
    Favourite

    Parallel Lines

    Age
    11 to 14
    Challenge level

    How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

  • Reflecting Lines
    problem
    Favourite

    Reflecting Lines

    Age
    11 to 14
    Challenge level

    Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.

  • Translating Lines
    problem
    Favourite

    Translating Lines

    Age
    11 to 14
    Challenge level

    Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.

  • How steep is the slope?
    problem
    Favourite

    How Steep Is the Slope?

    Age
    11 to 14
    Challenge level

    On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

  • Speeding up, slowing down
    problem
    Favourite

    Speeding Up, Slowing Down

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.

  • Route to infinity
    problem
    Favourite

    Route to Infinity

    Age
    11 to 14
    Challenge level

    Can you describe this route to infinity? Where will the arrows take you next?

  • Fill Me Up
    problem
    Favourite

    Fill Me Up

    Age
    11 to 14
    Challenge level

    Can you sketch graphs to show how the height of water changes in different containers as they are filled?

  • Up and across
    problem
    Favourite

    Up and Across

    Age
    11 to 14
    Challenge level

    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

  • Diamond Collector
    game
    Favourite

    Diamond Collector

    Age
    11 to 16
    Challenge level

    Collect as many diamonds as you can by drawing three straight lines.

  • Dotty grids in the classroom
    article

    Dotty Grids in the Classroom

    This article suggests ways in which a dotty grid can be used in the classroom as an environment for rich exploration

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