Class: Primary 5
Term: 2nd Term
Week: 5
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Measurement
Previous Lesson: Weight, Scales, Measuring in Kg and Grams and Word Problems.
Topic: TIME
Subject Matter: Definition of average speed, using speed formula distance divided by time in km/hr, solving problems on average speed, word problems on average speed, quantitative aptitude on speed.
Specific Objectives
By the end of the lesson, pupils should be able to:
Cognitive Domain:
- Define average speed.
- State the formula for calculating average speed.
- Calculate average speed in km/hr or m/s.
- Solve problems involving average speed, distance, and time.
- Solve word problems on average speed.
- Solve quantitative aptitude problems related to speed.
Affective Domain:
- Appreciate the importance of understanding speed in daily life situations.
- Develop accuracy when calculating speed, distance, or time.
- Show interest in solving mathematical problems related to real-world scenarios.
Psychomotor Domain:
- Accurately apply the speed formula (S=D/T) to different problems.
- Correctly convert units of distance and time to solve speed problems.
- Present clear, step-by-step solutions to speed-related problems.
Social Domain:
- Work collaboratively with peers to solve speed-related word problems.
- Discuss and share different approaches to solving quantitative aptitude problems on speed.
Reference Materials
The following resources were used in planning this lesson:
- 9 Years Basic Education Curriculum (Primary 5 Mathematics)
- State Unified Scheme of Work (Primary 5 Mathematics)
- New General Mathematics for Primary Schools, Book 5.
Instructional Materials
The teacher will teach this lesson with the aid of:
- A clock
- A stopwatch
- A speedometer (picture or real)
- Charts showing quantitative aptitude problems on speed
Rationale for the Lesson
This lesson helps pupils understand how fast things move around them. It enables them to calculate speed, distance, and time, which are important skills for understanding travel and everyday activities.
Prerequisite/Previous Knowledge
Pupils should have basic knowledge of distance, time, and simple division.
Lesson Content/Board Summary
Average Speed
Definition of Average Speed
Average speed is the rate at which an object covers a certain distance over a period of time. It tells us how fast an object is moving.
Speed Formula and Units
The formula for calculating speed is:
Speed = Distance / Time
This can also be written as: S = D / T
The standard units for speed are:
- Kilometres per hour (km/hr)
- Metres per second (m/s)
Conversion of Units:
It is important to know how to convert between units of time and distance.
| Unit | Equivalent |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes |
| 1 hour | 3600 seconds |
| 1 kilometre (km) | 1000 metres (m) |
NOTE: Remember that when converting from a smaller unit to a larger unit, you divide. When converting from a larger unit to a smaller unit, you multiply.
For example, to convert km/hr to m/s:
1 km/hr = (1000 m) / (3600 s) = 5/18 m/s
To convert m/s to km/hr:
1 m/s = (1/1000 km) / (1/3600 hr) = 3600/1000 km/hr = 18/5 km/hr
Solving Problems on Average Speed
To solve problems on average speed, use the formula Speed = Distance / Time.
Example 1: A car travels a distance of 180 km in 3 hours. What is its average speed?
Solution:
Step 1: Identify the given values.
Distance (D) = 180 km
Time (T) = 3 hours
Step 2: Write down the formula for speed.
Speed (S) = Distance / Time
Step 3: Substitute the values into the formula.
S = 180 km / 3 hours
Step 4: Calculate the speed.
S = 60 km/hr
The average speed of the car is 60 km/hr.
Example 2: A cyclist covers 2000 metres in 200 seconds. Calculate the speed in m/s.
Solution:
Step 1: Identify the given values.
Distance (D) = 2000 metres
Time (T) = 200 seconds
Step 2: Write down the formula for speed.
Speed (S) = Distance / Time
Step 3: Substitute the values into the formula.
S = 2000 m / 200 s
Step 4: Calculate the speed.
S = 10 m/s
The speed of the cyclist is 10 m/s.
How to Solve for Distance or Time
The speed formula can be rearranged to find distance or time if the other two values are known.
- To find Distance: Distance = Speed × Time (D = S × T)
- To find Time: Time = Distance / Speed (T = D / S)
Example 3: A bus travels at an average speed of 70 km/hr for 4 hours. What distance did it cover?
Solution:
Step 1: Identify the given values.
Speed (S) = 70 km/hr
Time (T) = 4 hours
Step 2: Write down the formula for distance.
Distance (D) = Speed × Time
Step 3: Substitute the values into the formula.
D = 70 km/hr × 4 hours
Step 4: Calculate the distance.
D = 280 km
The bus covered a distance of 280 km.
Example 4: A train covers a distance of 300 km at an average speed of 100 km/hr. How long did the journey take?
Solution:
Step 1: Identify the given values.
Distance (D) = 300 km
Speed (S) = 100 km/hr
Step 2: Write down the formula for time.
Time (T) = Distance / Speed
Step 3: Substitute the values into the formula.
T = 300 km / 100 km/hr
Step 4: Calculate the time.
T = 3 hours
The journey took 3 hours.
Word Problems on Average Speed
Word problems require careful reading to identify the distance and time before applying the formula.
Example 5: Femi walked from his house to school, a distance of 2 km, in 20 minutes. What was his average speed in km/hr?
Solution:
Step 1: Identify the given values and check units.
Distance (D) = 2 km
Time (T) = 20 minutes
The required speed unit is km/hr, so convert minutes to hours.
20 minutes = 20 / 60 hours = 1/3 hour
Step 2: Write down the formula for speed.
Speed (S) = Distance / Time
Step 3: Substitute the values into the formula.
S = 2 km / (1/3 hour)
Step 4: Calculate the speed.
S = 2 × 3 km/hr
S = 6 km/hr
Femi’s average speed was 6 km/hr.
Quantitative Aptitude on Speed
Quantitative aptitude problems on speed often involve comparing speeds, distances, or times, or solving problems with slightly more complex scenarios.
Example 6: A tortoise moves at 5 metres per minute. A snail moves at 10 centimetres per minute. Which is faster?
Solution:
Step 1: Ensure units are consistent for comparison. Convert metres to centimetres.
Tortoise speed = 5 metres/minute = 5 × 100 centimetres/minute = 500 centimetres/minute
Snail speed = 10 centimetres/minute
Step 2: Compare the speeds.
500 cm/min (tortoise) > 10 cm/min (snail)
Step 3: Conclude.
The tortoise is faster.
Teaching Methods/Instructional Techniques
Discussion, Lecture, Demonstration, Question and Answer, Visual Aids
Instructional Procedures
Step 1: Introduction
Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them questions about how long it takes them to get to school and how far their school is from their homes. The teacher then introduces the topic “Average Speed” by explaining that speed helps us understand how quickly one covers a distance.
Pupils’ Activity: Pupils respond to the questions and listen attentively to the introduction.
Learning Point: Pupils are introduced to the concept of speed and its relevance.
Step 2: Definition of Average Speed and Formula
Time: 8 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher guides pupils to define average speed as the rate at which an object covers a distance over time. The teacher then writes the formula for speed (Speed = Distance / Time) on the board and explains its components. The teacher also introduces standard units like km/hr and m/s.
Pupils’ Activity: Pupils define average speed, copy the formula, and note the units into their notebooks.
Learning Point: Pupils define average speed and learn its basic formula and units.
Step 3: Understanding Units and Conversions
Time: 8 minutes
Teaching Skill: Demonstration/Explanation
Teacher’s Activity: The teacher presents a table of time and distance conversions (e.g., 1 hour = 60 minutes, 1 km = 1000 m). The teacher demonstrates how to convert units, especially for speed (e.g., km/hr to m/s and vice versa), explaining when to multiply or divide.
Pupils’ Activity: Pupils observe the conversion table, ask questions, and practice simple conversions as guided by the teacher.
Learning Point: Pupils understand unit conversions relevant to speed calculations.
Step 4: Solving Basic Problems on Average Speed
Time: 8 minutes
Teaching Skill: Problem Solving/Demonstration
Teacher’s Activity: The teacher works through Example 1 and Example 2 from the board summary, showing clear, step-by-step solutions for calculating average speed when distance and time are given, ensuring units are consistent.
Pupils’ Activity: Pupils follow the teacher’s examples, copy the solutions, and ask questions for clarification.
Learning Point: Pupils learn to apply the speed formula to solve direct problems.
Step 5: Solving for Distance or Time
Time: 8 minutes
Teaching Skill: Problem Solving/Guided Practice
Teacher’s Activity: The teacher explains how to rearrange the speed formula to find distance (Distance = Speed × Time) or time (Time = Distance / Speed). The teacher then guides pupils through Example 3 and Example 4, solving for distance and time respectively.
Pupils’ Activity: Pupils observe how the formula is rearranged and practice solving for distance and time under teacher guidance.
Learning Point: Pupils learn to manipulate the speed formula to find distance or time.
Step 6: Word Problems and Quantitative Aptitude
Time: 5 minutes
Teaching Skill: Application/Critical Thinking
Teacher’s Activity: The teacher presents Example 5 (word problem) and Example 6 (quantitative aptitude problem) from the board summary. The teacher guides pupils on how to extract information from word problems and how to approach comparative problems in quantitative aptitude, emphasizing unit consistency.
Pupils’ Activity: Pupils attempt to solve the problems, discuss strategies, and compare their answers.
Learning Point: Pupils apply their knowledge to solve practical word problems and quantitative aptitude questions.
Step 7: Evaluation/Review
Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:
- What is average speed?
- State the formula for calculating speed.
- A car travels 240 km in 4 hours. What is its average speed?
- If a boy walks at a speed of 5 km/hr for 2 hours, what distance did he cover?
Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.
Step 8: Conclusion
Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the main points of the lesson, reiterating the importance of speed in daily life. The teacher then assigns homework from the textbook.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils reinforce their understanding and prepare for independent practice.
Home Task: Solve three new exercises on TIME. Show each step and check each answer.
Lesson Keywords
- Average Speed – The rate at which an object covers a certain distance over a period of time.
- Distance – The total length covered by an object in motion.
- Time – The duration taken to cover a certain distance.
- Formula – A mathematical rule or relationship expressed in symbols.
- km/hr – Kilometres per hour, a unit of speed.
- m/s – Metres per second, a unit of speed.
Differentiation
For pupils who grasp concepts quickly, the teacher can provide additional complex word problems or quantitative aptitude questions involving multiple steps or different units. For pupils needing more support, the teacher will provide simpler problems with direct application of the formula and offer more guided practice, possibly using visual aids to explain the concepts of distance and time.
Note for teachers using this lesson plan
Ensure that pupils understand the concept of consistent units before attempting calculations. Emphasize the importance of showing all steps when solving problems. Encourage pupils to draw simple diagrams for word problems to visualize the scenario. Use real-life examples to make the lesson relatable and engaging.
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