Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Estimating journeys from non-linear graphs

      Lesson details

      Learning outcome

      I can estimate the distance travelled for non-linear speed-time graphs.

      Key learning points

      1. For non-linear graphs, this can be estimated by considering a trapezium.
      2. The more trapezia used, the better the estimate.

      Keywords

      • Estimate - A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

      Common misconception

      When students find an area they are used to communicating the answer in units$$^2$$. The area under a speed-time graph tells us the distance travelled though.

      On the graph the base is time and the height is speed which is distance over time. Distance over time, multiplied by time, leaves just distance.

      Teacher tip

      Consider using a starter whereby students work out the area of composite shapes, considering how best to break those shapes down to be as efficient as possible. This will set up them up nicely for the skills needed in this lesson.

      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

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      An ________ is an estimate for a calculation which is greater than the exact answer.

      underestimate
      Correct answer: overestimate
      miscalculation
      approximation

      Q2.
      How far has the particle modelled in this graph travelled after $$5$$ seconds?

      An image in a quiz
      $$5$$ metres
      $$16$$ metres
      $$5\times16=80$$ metres
      Correct answer: $${1\over2}\times5\times16=40$$ metres
      $${1\over2}\times5\times20=50$$ metres

      Q3.
      Which of the below is the formula for the area of a trapezium?

      $$A=b\times{h}$$
      $$A={1\over2}\times{b}\times{h}$$
      $$A={1\over2}\times({a}\times{b})\times{h}$$
      Correct answer: $$A={1\over2}\times({a}+{b})\times{h}$$
      $$A={1\over2}\times({b}+{h})\times{h}$$

      Q4.
      How far has the particle modelled in this graph travelled after $$5$$ seconds? metres.

      An image in a quiz
      Correct Answer: 70

      Q5.
      How far has the particle modelled in this graph travelled after $$5$$ seconds? metres.

      An image in a quiz
      Correct Answer: 55

      Q6.
      How far has the particle modelled in this graph travelled after $$5$$ seconds? metres.

      An image in a quiz
      Correct Answer: 63

      6 Questions

      Q1.
      The curve models the movement of a particle. If we had scales on the axes and could find the area of the triangle it would give us __________ for the distance travelled.

      An image in a quiz
      a large number
      a small number
      a calculation
      an overestimate
      Correct answer: an underestimate

      Q2.
      Use the polygon mapped onto this graph to estimate the distance travelled by the vehicle. Distance $$\approx$$ metres.

      An image in a quiz
      Correct Answer: 76

      Q3.
      The area of the polygon will estimate the distance travelled by the vehicle modelled in this graph but this will be __________.

      An image in a quiz
      an overestimate
      Correct answer: an underestimate
      exact

      Q4.
      Which of these groups of polygons will give us the best estimate for the distance modelled by this curve?

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

      Q5.
      Use these polygons to estimate the total distance travelled by the particle modelled by this curve. Distance $$\approx$$ metres.

      An image in a quiz
      Correct Answer: 51

      Q6.
      Use these polygons to estimate the total distance travelled by the particle modelled by this curve. Distance $$\approx$$ metres.

      An image in a quiz
      Correct Answer: 48

      To help you plan your 11 maths lesson on: Estimating journeys from non-linear graphs, download all teaching resources for free and adapt to suit your pupils' needs...