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P6 Mathematics - Term II

Topic 8: Distance, Time and Speed

Lesson 6: Reading, Plotting and Interpreting Distance-Time Graphs

Duration: 45 minutes

Learning Objectives

By the end of this lesson, you will be able to:

  • Plot distance-time graphs from given data
  • Draw accurate graphs using correct scale
  • Interpret complete journeys with multiple parts
  • Calculate speed from different sections of a graph
  • Solve problems using distance-time graphs
  • Apply all knowledge of distance, time and speed

Quick Review: Graph Basics

What we learned yesterday:

  • Time on horizontal axis (x-axis)
  • Distance on vertical axis (y-axis)
  • Straight slanted line = constant speed
  • Horizontal line = rest (speed = 0)
  • Steeper line = faster speed
  • Distance never decreases

Today's Challenge: Plotting Graphs

Yesterday: We read pre-prepared graphs
Today: We create our own graphs!

The five steps:

  1. Draw and label axes
  2. Choose appropriate scale
  3. Plot points from data
  4. Join points with straight lines
  5. Interpret the graph

Example Journey Data

A cyclist's journey:

Time (hours) Distance (km)
0 0
1 10
2 20
3 20
4 35

We will plot this together step by step

Step 1: Draw and Label Axes

Distance (km)
↑
|
|
|
|____________→ Time (hours)
0

Always:

  • Draw with a ruler for straight lines
  • Label both axes clearly
  • Include units in parentheses

Step 2: Choose Appropriate Scale

Look at the data:

  • Time goes from 0 to 4 hours
  • Distance goes from 0 to 35 km

Choose scale:

  • Time axis: Each square = 1 hour (0, 1, 2, 3, 4)
  • Distance axis: Each square = 5 km (0, 5, 10, 15, 20, 25, 30, 35)

Scale must fit all data!

Step 2: Mark the Scale

Distance (km)
35 |
30 |
25 |
20 |
15 |
10 |
 5 |
 0 |___|___|___|___|___→ Time (hours)
   0   1   2   3   4   5

Mark evenly and clearly

Step 3: Plot the Points

From the data table, plot each coordinate:

  • (0, 0) - Starting point
  • (1, 10) - After 1 hour, 10 km
  • (2, 20) - After 2 hours, 20 km
  • (3, 20) - After 3 hours, still 20 km
  • (4, 35) - After 4 hours, 35 km

Mark each point with a clear dot

Step 3: Points Plotted

Distance (km)
35 |                  •
30 |
25 |
20 |          •-------•
15 |
10 |      •
 5 |
 0 |  •___|___|___|___|___→ Time (hours)
   0   1   2   3   4   5

All five points are now marked

Step 4: Join Points with Straight Lines

Use a ruler to connect consecutive points:

  • From (0,0) to (1,10)
  • From (1,10) to (2,20)
  • From (2,20) to (3,20) - horizontal!
  • From (3,20) to (4,35)

Always use a ruler for straight lines

Step 4: Complete Graph

Distance (km)
35 |                  •
30 |                 /
25 |                /
20 |          •----•
15 |         /
10 |      •
 5 |     /
 0 |  •____________→ Time (hours)
   0   1   2   3   4

The graph is complete!

Step 5: Interpret the Graph

What does this graph tell us?

Section 1 (0-2 hours): Traveling at constant speed

  • Distance: 20 km, Time: 2 hours
  • Speed = 20 ÷ 2 = 10 km/hr

Section 2 (2-3 hours): Resting

  • Distance stays at 20 km
  • Speed = 0 km/hr

Section 3 (3-4 hours): Traveling faster

  • Distance: 35 - 20 = 15 km, Time: 1 hour
  • Speed = 15 ÷ 1 = 15 km/hr

Understanding the Journey

The complete story:

  1. Cyclist travels at 10 km/hr for 2 hours (covers 20 km)
  2. Cyclist rests for 1 hour (stays at 20 km)
  3. Cyclist travels faster at 15 km/hr for 1 hour (covers 15 km more)
  4. Total distance: 35 km
  5. Total time: 4 hours

Graphs tell stories!

Your Turn: Plot This Graph

A person walking:

Time (hours) Distance (km)
0 0
1 15
2 30
3 30
4 50

Follow all five steps in your exercise book!

Checking Your Graph

Does your graph have:

✓ Labeled axes (Time and Distance with units)
✓ Appropriate scale (0-4 hours, 0-50 km)
✓ Five points plotted correctly
✓ Straight lines connecting points
✓ Horizontal line from hour 2 to 3

If yes, excellent work!

Interpreting Your Graph

Questions about your graph:

  1. What is the distance after 1 hour?
  2. What happened between 2 and 3 hours?
  3. Calculate the speed during the first 2 hours
  4. Calculate the speed between 3 and 4 hours
  5. Which section shows the fastest speed?

Write answers in your exercise book

Answers: Interpreting Your Graph

1. Distance after 1 hour = 15 km

2. The person rested (horizontal line)

3. Speed (0-2 hours) = 30 ÷ 2 = 15 km/hr

4. Speed (3-4 hours) = (50-30) ÷ 1 = 20 km/hr

5. Section 3-4 hours is fastest (20 km/hr)

The steeper line shows faster speed!

A More Complex Problem

A matatu journey from Kampala:

Time (hours) Distance (km)
0 0
1 50
2 100
3 100
4 140

What's different about this journey?

Questions About the Matatu

Answer these:

  1. What was the matatu's speed in the first hour?
  2. What was the speed from hour 1 to 2?
  3. When did the matatu stop? For how long?
  4. What was the speed from hour 3 to 4?
  5. Calculate the average speed for the entire journey

Think about each question carefully

Answers: Matatu Questions

1. Speed (hour 1) = 50 ÷ 1 = 50 km/hr

2. Speed (1-2 hours) = (100-50) ÷ 1 = 50 km/hr

3. Stopped between 2 and 3 hours, for 1 hour

4. Speed (3-4 hours) = (140-100) ÷ 1 = 40 km/hr

5. Average speed = Total distance ÷ Total time
   = 140 ÷ 4 = 35 km/hr

Understanding Average Speed

Important concept:

Average speed ≠ mean of all speeds

Correct way:

Average Speed = Total Distance ÷ Total Time
              = 140 ÷ 4 = 35 km/hr

Not: (50 + 50 + 0 + 40) ÷ 4

Always use total distance and total time!

Comparing Two Journeys on One Graph

We can show two journeys on the same graph:

  • Person A: slower speed (gentle slope)
  • Person B: faster speed (steeper slope)

Useful for comparing speeds visually!

Real-Life Application Problem

Planning a trip:

You need to travel 120 km. You can:

  • Walk at 4 km/hr
  • Bicycle at 20 km/hr
  • Matatu at 60 km/hr

Calculate time for each. Which is best?

Solution: Planning a Trip

Using T = D ÷ S:

Walking: T = 120 ÷ 4 = 30 hours (too long!)
Bicycle: T = 120 ÷ 20 = 6 hours (possible)
Matatu:  T = 120 ÷ 60 = 2 hours (fastest!)

Matatu is fastest, but consider cost too!

Summary: All Six Lessons

What we learned in this topic:

Lesson 1: Time units and conversions
Lesson 2: Distance and speed units
Lesson 3: Speed = Distance ÷ Time
Lesson 4: All three formulae (S, D, T)
Lesson 5: Reading distance-time graphs
Lesson 6: Plotting and interpreting graphs

A complete journey through distance, time and speed!

The Three Formulae (Revision)

Remember these always:

S = D ÷ T  (Speed = Distance ÷ Time)
D = S × T  (Distance = Speed × Time)
T = D ÷ S  (Time = Distance ÷ Speed)

And the triangle:

      D
     ___
    |   |
    | S | T
    |___|

Key Graph Skills

You can now:

✓ Draw and label axes correctly
✓ Choose appropriate scales
✓ Plot points accurately
✓ Join points with straight lines
✓ Interpret constant speed (slanted lines)
✓ Identify rest periods (horizontal lines)
✓ Calculate speeds from graph sections

Why This Topic Matters

Distance, time and speed knowledge helps you:

  • Plan real journeys and estimate times
  • Understand vehicle speeds and safety
  • Read timetables and schedules
  • Solve everyday transport problems
  • Build foundation for physics in secondary school
  • Think mathematically about motion

Common Mistakes to Avoid

Graph mistakes:

❌ Forgetting to label axes
❌ Using wrong scale (data doesn't fit)
❌ Drawing freehand lines (use ruler!)
❌ Putting distance on x-axis

Formula mistakes:

❌ Using wrong formula
❌ Forgetting units
❌ Not showing working

Homework: Final Challenge

Assignment:

  1. Plot a distance-time graph for this journey:

    Time (hours):  0   0.5   1   1.5   2
Distance (km): 0    2    4    4    7

  2. Answer about your graph:
    a) What is the distance after 0.5 hours?
    b) What happened between 1 and 1.5 hours?
    c) Calculate speed during first hour
    d) Calculate speed between 1.5 and 2 hours

  3. Real-life problem: Think about a journey you made recently. Estimate the distance and time. Calculate your approximate speed. Draw a simple distance-time graph for your journey.

Expected time: 30-35 minutes

Congratulations!

You have completed Topic 8: Distance, Time and Speed!

You now understand:

  • Time, distance, and speed units
  • All three formulae
  • How to solve problems
  • How to plot and interpret graphs

Well done! This knowledge will serve you well.

Looking Ahead

In future mathematics topics, you will:

  • Use these formulae in algebra (Term III, Topic 12)
  • Apply graphs in other contexts
  • Study more complex motion in secondary school
  • Use these skills in science and physics
  • Apply this knowledge in everyday life

This is just the beginning!

Credits

Created: January 11, 2026
Based on: NCDC P6 Mathematics Curriculum - Topic 8: Distance, Time and Speed

Source: National Curriculum Development Centre (NCDC), Uganda

Thank you for your hard work and dedication throughout this topic!