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      Problem solving with real-life graphs

      Lesson details

      Learning outcome

      I can use my knowledge of interpreting real-life graphs to solve problems.

      Key learning points

      1. Real life graphs present a visual model of a situation.
      2. Linear graphs are not always the best representation.
      3. The different parts of the graph describe different parts of the whole situation.

      Keywords

      • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

      • Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the $$y$$-direction with respect to the positive $$x$$-direction.

      Common misconception

      When matching, or sketching, distance-time and speed-time graphs pupils may think these have a similar shape.

      Questioning helps. Ask pupils to explain what is happening on a variety of graphs. For example, "A diagonal line with positive gradient on a speed-time graph. What is happening?" "A horizontal line on distance-time graph. What is happening?"

      Teacher tip

      There is a great opportunity here to get pupils physically active. Take the pupils outside and ask one pupil to model a journey. "I'd like you to go slow for ten metres, fast for ten metres, stop a short time, then go slow for ten metres". Then, ask the rest of the class to sketch the graphs.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      A linear graph like this shows __________ between $$x$$ and $$y$$.

      An image in a quiz
      no relationship
      Correct answer: a constant rate of change
      indirect proportion

      Q2.
      A constant rate of change on a distance-time graph shows __________.

      An image in a quiz
      Correct answer: constant speed
      increasing speed
      acceleration
      a stop

      Q3.
      This distance-time graph shows the journey of a cyclist. When were they travelling fastest?

      An image in a quiz
      Correct answer: a
      b
      c

      Q4.
      This distance-time graph shows the journey of a cyclist. When did the cyclist stop?

      An image in a quiz
      a
      Correct answer: b
      c

      Q5.
      A horizontal line on this graph represents __________.

      An image in a quiz
      Correct answer: a constant speed
      a stop
      acceleration
      deceleration

      Q6.
      This speed-time graph shows the journey of a car. When is it travelling fastest?

      An image in a quiz
      a
      b
      c
      Correct answer: d

      6 Questions

      Q1.
      This graph shows __________ rate of change between speed and time.

      An image in a quiz
      a decreasing
      an increasing
      a fast
      Correct answer: a constant

      Q2.
      Which speed-time graph matches this distance-time graph?

      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz

      Q3.
      Which distance-time graph matches this speed-time graph?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      Q4.
      Match these descriptions to the graph of this car journey.

      An image in a quiz
      Correct Answer:Fastest constant speed,d
      Correct Answer:Acceleration,c
      Correct Answer:Deceleration,a
      Correct Answer:Slowest constant speed,b

      Q5.
      Which moment represents the longest stop on this displacement-time graph?

      An image in a quiz
      a
      Correct answer: b
      c
      d
      e

      Q6.
      Which section shows the fastest speed?

      An image in a quiz
      Correct answer: a
      b
      c
      d
      e

      To help you plan your 11 maths lesson on: Problem solving with real-life graphs, download all teaching resources for free and adapt to suit your pupils' needs...