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Maths

Interpreting Real-Life Graphs

Overview

Students practise extracting information from complex real-life graphs, identifying key features and calculating values including speed from distance-time graphs.

Learning Objective
Students read and interpret real-life graphs including distance-time graphs, recognising what different gradients and horizontal sections represent.

Resources needed

  • Printed or displayed graphs
  • Ruler
  • Calculator

Lesson stages

0 / 7 done
  1. 1 Display a simple distance-time graph. Ask: 'What are the axes? What are the units? What does the title tell us?' Recap: gradient = steepness, horizontal section = no change, steeper = faster change.
  2. 2 In a distance-time graph: gradient = speed. Steeper line = faster speed. Horizontal = stationary (not moving). Negative gradient = travelling back. Students match sections of a graph to descriptions.
  3. 3 On a distance-time graph: speed = distance ÷ time = gradient. Read two points from the line (e.g. (0,0) and (3,12)): speed = 12km ÷ 3h = 4km/h. Students calculate speed for three different sections of the same graph.
  4. 4 Display a complex distance-time graph. Students write a narrative: 'The person walked for 2 hours, then stopped for 30 minutes, then returned home more quickly.' Compare stories in pairs.
  5. 5 Students draw their own distance-time graph from a story: 'Mia cycled 12km in 1 hour, rested for 30 minutes, then cycled 6km further in 45 minutes.' Mark all sections and label axes.
  6. 6 Show a conversion graph (pounds to kg), a depth-over-time graph (filling a bath), a temperature graph. Students extract values, describe trends, and identify rates of change.
  7. 7 Two people set off from different points walking towards each other. Show both on the same graph. When and where do they meet? (The intersection.)

Tap a step to mark it as done.

Variations

  • Introduce speed-time graphs and the concept of acceleration
  • Use journey graphs with multiple travellers on the same axes
  • Link to equation of a line for proportional sections
More information

Display: gradient, rate of change, stationary, horizontal, axes, title, units. Teach: 'The gradient of this section is ___, which means the speed is ___ km/h.'

Provide graphs with key points pre-labelled. Simplify to one-section graphs before multi-section ones. Provide sentence starters for the narrative task.

Do students read coordinates accurately? Do they calculate gradient using (change in y) ÷ (change in x)? Do they correctly interpret horizontal sections as 'stationary'?

All graphs can be drawn on plain paper. Distance-time graph problems can be given verbally for students to sketch rather than using printed axes.

Students may think a steeper section means 'further away' rather than 'faster'. Reinforce: the steepness shows the rate of change of distance over time — i.e. speed.

Activity details
Secondary Medium 40 minutes 5 minutes prep Solo, Pairs Indoor
Topics
Graphs Interpretation Distance-time Graphs Speed