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Visualising Speed Problems with Graphs and Models | PSLE Math Guide
Many students struggle with speed, distance, and time calculations because they rely purely on numbers. However, using distance-time graphs and bar models can make these problems much easier to understand.
In this guide, you will learn:
- How to read and interpret distance-time graphs
- How to use bar models to solve speed problems step by step
- How to calculate average speed
- Common mistakes and how to avoid them
- PSLE-style practice questions with answers
By the end of this guide, you will be able to tackle speed-related PSLE Maths questions with confidence.
1. Understanding Speed: The Basics
Before using graphs and models, it is important to understand the key formulas:
Key Speed Formulas
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
- Distance = Speed × Time
Average Speed Formula
- Average Speed = Total Distance ÷ Total Time
Tip: Use the DST Triangle to remember these formulas. Cover the variable you need to find, and the remaining two guide your calculation!
2. Distance-Time Graphs: A Visual Approach
A distance-time graph shows how far an object has travelled over time. It helps in comparing speeds, identifying rest periods, and analysing movement patterns.
How to Read a Distance-Time Graph
- Time (x-axis): always on the horizontal axis.
- Distance (y-axis): always on the vertical axis.
- Steeper slope: Indicates a higher speed.
- Flat line: Indicates no movement (e.g., waiting/resting).
- Downward slope: Indicates returning to the starting point.
Example: A Student’s Journey to School
A student cycles 6 km to school and back home. Their journey is as follows:
|
Time Interval |
Distance (km) |
Description |
|---|---|---|
|
0 - 30 min |
6 km |
Cycles to school at a steady speed |
|
30 - 45 min |
6 km |
Stays at school (no movement) |
|
45 - 75 min |
0 km |
Returns home at a steady speed |
Plotting this journey on a distance-time graph helps visualise movement and understand speed changes.
3. Using Bar Models for Speed Problems
A bar model helps break speed problems into manageable parts, making them easier to solve step by step.
Example: A Car’s Journey
A car travels 150 km in 3 hours. Using a bar model, we can divide the journey:
- Total Distance: 150 km
- Total Time: 3 hours
- Distance per Hour: 150 ÷ 3 = 50 km/h
Seeing speed problems visually helps students break down the question logically.
4. Average Speed Calculations (PSLE Requirement)
Many PSLE questions require average speed calculations, which students often overlook.
Example: Calculating Average Speed
A cyclist travels 30 km at 15 km/h, then 20 km at 10 km/h. What is the average speed for the entire journey?
Solution:
- Total Distance = 30 km + 20 km = 50 km
- Time for First Part = 30 km ÷ 15 km/h = 2 hours
- Time for Second Part = 20 km ÷ 10 km/h = 2 hours
- Total Time = 2 hours + 2 hours = 4 hours
- Average Speed = Total Distance ÷ Total Time = 50 km ÷ 4 hours = 12.5 km/h
5. Practice Questions & Step-by-Step Solutions
Sample Question 1: Alvin’s Walk to the Park
Alvin walks 2 km to a park at 4 km/h. He rests for 30 minutes and then walks back home at 3 km/h.
- How long does Alvin take to reach the park?
- What is the total time Alvin spends on the entire trip?
Solution:
- Time to reach the park: 2 km ÷ 4 km/h = 30 minutes
- Time to return home: 2 km ÷ 3 km/h = 40 minutes
- Total time for the trip: 30 min + 30 min (rest) + 40 min = 1 hour 40 minutes
Sample Question 2: Car vs Van Speed
A van leaves Town A for Town B at 10:00 AM, travelling at 55 km/h. At 1:00 PM, a car leaves Town A for Town B, travelling at 137.5 km/h.
How long does it take the car to catch up with the van?
- Time difference: 3 hours (Van leaves at 10:00 AM, Car at 1:00 PM)
- Distance the van covered in 3 hours: 55 × 3 = 165 km
- Relative speed difference: 137.5 - 55 = 82.5 km/h
- Time for the car to catch up: 165 ÷ 82.5 = 2 hours
6. Common Mistakes to Avoid
- Forgetting to Convert Units
- Mistake: Mixing minutes and hours in calculations.
- Solution: Always convert minutes to hours by dividing by 60.
- Misinterpreting Graphs
- Mistake: confusing the axes on a distance-time graph.
- Solution: Time is always on the x-axis, and distance is always on the y-axis.
- Using the Wrong Formula
- Mistake: Multiplying speed and time when division is required.
- Solution: Memorise the DST Triangle for correct formula usage.
- Assuming Constant Speed
- Mistake: Treating problems with changing speeds as constant.
- Solution: Identify different speed sections and calculate accordingly.
- Not Reading the Question Carefully
- Mistake: Ignoring resting time or return journeys.
- Solution: Break the problem down into sections before solving.
Conclusion
Speed problems do not have to be difficult. By using graphs, bar models, and structured strategies, students can:
- Solve problems faster and more accurately
- Understand speed concepts visually
- Build confidence for PSLE success
Practising different types of speed problems and using visual tools like distance-time graphs will help students develop a deeper understanding of speed, distance, and time.
