Distance Time Graphs

National Curriculum References

• KS3 Mathematics Programme of Study, Number, Ratio and Algebra, and Handling Data (DfE, 2014)
• Pupils should be able to:
  • Interpret and construct tables and line graphs for given data, including distance-time and velocity-time graphs (Statistical methods 3)
  • Solve problems involving speed, distance and time (Number 3)
  • Use simple algebra to express problems mathematically and solve them (Algebra 2)

Learning Objectives

By the end of the lesson, pupils will be able to:

1. Interpret distance-time graphs and understand what different shapes on the graph represent.
2. Construct accurate distance-time graphs from given scenarios or data sets.
3. Calculate the speed from a distance-time graph.
4. Solve real-life contextual problems involving distance, time and speed using graphs.

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Success Criteria

• I can describe what flat, sloped, and curved sections of a distance-time graph represent.
• I can plot a distance-time graph from a table of values.
• I can calculate speed (distance ÷ time) for sections of the graph.
• I can explain the motion of objects through information shown on a distance-time graph.

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Lesson Structure (60 minutes)

1. Starter Activity (10 minutes)

Activity: Everyday motion brainstorm and prediction

• Show the class two images: one of a person walking steadily, one of a person standing still.
• Ask pupils to sketch a quick distance-time graph for each scenario from memory or intuition.
• Share selected predictions and briefly discuss.
• Teacher introduces how distance-time graphs represent motion at a glance.

Purpose: Activate prior knowledge and engage visualisation skills.

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2. Introduction & Teaching Input (15 minutes)

Teaching Points:

• Explain axes: horizontal axis = time; vertical axis = distance.
• Describe:
  • Flat line = stationary (distance not changing)
  • Straight sloped line = steady speed (distance increasing linearly)
  • Steeper slope = faster speed
  • Curves = changing speed (acceleration/deceleration)
• Model drawing graphs from simple data tables (e.g., distance every 1 minute).
• Demonstrate calculating speed as gradient (Δdistance / Δtime) on straight sections.

Success Criteria Addressed: Understanding the graph features, plotting points.

Interactive Element:

• Pupils complete a mini whiteboard task: judge whether a given graph shows constant speed, stationary, or acceleration.

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3. Guided Practice (15 minutes)

Activity: Constructing and interpreting graphs from data

• Provide pupils with data tables for scenarios (e.g., a jogger running with breaks, a car accelerating, a cyclist stopping).
• Pupils plot distance-time graphs in pairs on graph paper.
• Once complete, ask pairs to calculate speeds for different segments and describe the motion in their own words.
• Share a few examples with class discussion.

Teacher Role: Circulate, provide scaffolding, prompt with questions such as: “What does the flat section mean here?” or “How do you calculate speed in this section?”

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4. Independent Application (15 minutes)

Main Task: Problem solving using distance-time graphs

• Give a worksheet of 3 contextual distance-time graphs showing different journeys (e.g., a train trip with stops, a person running and resting).
• Pupils answer questions: identify sections (stationary, constant speed, acceleration), calculate speeds, explain motions.
• Challenge pupils to draw their own graph based on a written scenario (e.g., a dog walks 20m in 4 minutes, rests 2 minutes, then runs 30m in 3 minutes).

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5. Plenary & Formative Assessment (5 minutes)

• Exit ticket: each pupil writes a sentence answering: “What can a flat section on a distance-time graph tell us about an object's movement?”
• Collect responses and quickly address any misconceptions in next lesson.

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Differentiation & Extension Activities

For Lower Attaining Pupils:

• Use pre-drawn graphs and focus on interpreting rather than drawing.
• Provide number lines and step-by-step calculation prompts for speed.

For Higher Attaining Pupils (Extension):

• Introduce graphs with negative slopes (return journeys).
• Challenge: Calculate average speed over the whole journey including stops.
• Challenge: Derive algebraic expressions for distance when speed and time are variables, linking to linear graphs y = mx + c.
• Explore the difference between distance-time and velocity-time graphs briefly and discuss why they look different.

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Resources Needed

• Graph paper, ruler, pencil, eraser for each pupil
• Mini whiteboards and markers
• Printed data tables and worksheet with graphs and scenarios
• Visual aids for starter (images of walkers, runners)
• Exit ticket slips

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Notes for Teachers

• Encourage pupils to verbalise their reasoning when interpreting graphs as this deepens conceptual understanding.
• Use real-life contexts relevant to pupils’ interests to make the concept tangible (e.g., sports activities, daily travels).
• Emphasise units in calculations: distance (m or km), time (s or mins), speed (m/s or km/h).
• Use technology if available: dynamic graphing software or interactive whiteboard to plot live graphs.

By delivering this lesson, pupils will have a solid foundation to progress to more complex kinematics and graph interpretation in GCSE maths.