Linear functions and graphs

  • Enclosing Squares
    problem
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    Enclosing Squares

    Age
    11 to 14
    Challenge level
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    Can you find sets of sloping lines that enclose a square?
  • Parallel lines
    problem
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    Parallel Lines

    Age
    11 to 14
    Challenge level
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    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
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    Reflecting Lines

    Age
    11 to 14
    Challenge level
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    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
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    Translating Lines

    Age
    11 to 14
    Challenge level
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    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
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    How Steep Is the Slope?

    Age
    11 to 14
    Challenge level
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    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?

  • Diamond Collector
    game
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    Diamond Collector

    Age
    11 to 16
    Challenge level
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    Collect as many diamonds as you can by drawing three straight lines.

  • Which is cheaper?
    problem
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    Which Is Cheaper?

    Age
    14 to 16
    Challenge level
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    When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

  • Perpendicular lines
    problem
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    Perpendicular Lines

    Age
    14 to 16
    Challenge level
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    Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

  • Negatively Triangular
    problem
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    Negatively Triangular

    Age
    14 to 16
    Challenge level
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    How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

  • problem
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    At Right Angles

    Age
    14 to 16
    Challenge level
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    Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?