Time : Average speed, Distance and Duration

SUBJECT: MATHEMATICS

CLASS: BASIC FIVE / PRIMARY 5

TERM : SECOND TERM

WEEK : WEEK 11

TOPIC : Time : Average speed, Distance and Duration 

• Average speed
• Distance
• Duration
• Real life problems

Importance

• Used by travelers, motorist, tourist to plan activities and movement

Learning Objectives :

Pupils should be able to

• find the duration between one time and another
• Calculate the distance covered within a length of time
• Solve the average speed of a moving object given the total distance travelled and the time taken
• Convert the unit of Time express the hours of a 🕒 in minutes, seconds and vice versa
• Solve real live problems on distance, time and speed

Learning Activities :

• Pupils as individuals checks and says the time on a wall clock 🕒 placed at the front of the class
• Pupils work in small groups. A leader is chosen. He chooses another person from the group. A distance is 5m is set between the two pupils, a timer is required also set to record the time involved in the throwing and catching of a ball over a specific distance

This activity Embedded Core Skills

• Critical thinking and problem solving skills
• Communication and Collaboration
• Student Leadership skills and Personal Development

Learning Resources

• Flash cards
• Timer for checking time
• Ball
• Wall clock

Content

What is average speed

Average speed is a measure of how fast something is moving over a certain distance or amount of time. It is calculated by dividing the total distance traveled by the total time it took to travel that distance. For example, if a car travels 100 miles in 2 hours, its average speed would be 50 miles per hour. The unit of average speed is usually miles per hour (mph) or kilometers per hour (km/h).

1. What is average speed and how is it calculated? Average speed is a measure of how fast something is moving over a certain distance or amount of time. It is calculated by dividing the total distance traveled by the total time it took to travel that distance.
2. What are the units of average speed? The units of average speed are usually miles per hour (mph) or kilometers per hour (km/h).
3. What is the difference between average speed and instantaneous speed? Average speed is the total distance traveled over a certain period of time, while instantaneous speed is the speed at a specific point in time.
4. Can average speed change during a journey? Yes, average speed can change during a journey if the speed of the object changes. For example, a car may start off at a slow speed and then accelerate to a higher speed.
5. How does the distance traveled affect average speed? The longer the distance traveled, the longer the time it will take to travel that distance, which will make the average speed lower. Similarly, the shorter the distance traveled, the shorter the time it will take to travel that distance, which will make the average speed higher.

How to calculate average speed when distance and time are given.

1. A car travels 200 miles in 4 hours, its average speed would be 50 mph (200 miles / 4 hours = 50 mph).
2. A bicycle travels 10 miles in 30 minutes, its average speed would be 20 mph (10 miles / 0.5 hours = 20 mph).
3. A runner completes a marathon (26.2 miles) in 4 hours, its average speed would be 6.55 mph (26.2 miles / 4 hours = 6.55 mph).
4. A train travels 300 kilometers in 4 hours, its average speed would be 75 km/h (300 kilometers / 4 hours = 75 km/h).
5. A plane travels 1000 miles in 2 hours, its average speed would be 500 mph (1000 miles / 2 hours = 500 mph).

Evaluation

1. What is the formula for calculating average speed? a) distance / time b) time / distance c) speed x time d) speed / distance
2. What are the units of average speed typically measured in? a) feet per second b) meters per second c) miles per hour d) kilometers per hour
3. If a car travels 200 miles in 4 hours, what is its average speed? a) 50 mph b) 40 mph c) 60 mph d) 30 mph
4. If a bicycle travels 10 miles in 30 minutes, what is its average speed? a) 15 mph b) 20 mph c) 10 mph d) 25 mph
5. A runner completes a marathon (26.2 miles) in 4 hours, what is its average speed? a) 6.55 mph b) 5 mph c) 8 mph d) 7 mph
6. If a train travels 300 kilometers in 4 hours, what is its average speed? a) 75 km/h b) 100 km/h c) 50 km/h d) 60 km/h
7. If a plane travels 1000 miles in 2 hours, what is its average speed? a) 500 mph b) 600 mph c) 400 mph d) 700 mph
8. Can average speed change during a journey? a) Yes b) No
9. How does the distance traveled affect average speed? a) the longer the distance, the lower the average speed b) the shorter the distance, the lower the average speed c) the longer the distance, the higher the average speed d) the shorter the distance, the higher the average speed
10. If a person walks at an average speed of 3 miles/hour and distance traveled is 15 miles. What will be the time taken? a)5 hours b)4 hours c)6 hours d)3 hours

How to calculate Distance when average speed and time are given.

1. If a car is traveling at an average speed of 60 mph for 3 hours, the distance traveled can be calculated by multiplying the average speed by the time: 60 mph x 3 hours = 180 miles.
2. If a train is traveling at an average speed of 80 km/h for 4 hours, the distance traveled can be calculated by multiplying the average speed by the time: 80 km/h x 4 hours = 320 kilometers.
3. If a runner is running at an average speed of 8 mph for 2 hours, the distance traveled can be calculated by multiplying the average speed by the time: 8 mph x 2 hours = 16 miles.
4. If a bus is traveling at an average speed of 55 km/h for 5 hours, the distance traveled can be calculated by multiplying the average speed by the time: 55 km/h x 5 hours = 275 kilometers.
5. If a ship is traveling at an average speed of 20 knots for 6 hours, the distance traveled can be calculated by multiplying the average speed by the time: 20 knots x 6 hours = 120 nautical miles.

Evaluation

1. What is the formula for calculating distance when average speed and time are given? a) distance = speed x time b) distance = time / speed c) speed = distance / time d) time = distance / speed
2. If a car is traveling at an average speed of 60 mph for 3 hours, how far has it traveled? a) 120 miles b) 180 miles c) 100 miles d) 160 miles
3. If a train is traveling at an average speed of 80 km/h for 4 hours, how far has it traveled? a) 320 kilometers b) 280 kilometers c) 240 kilometers d) 360 kilometers
4. If a runner is running at an average speed of 8 mph for 2 hours, how far has it traveled? a) 12 miles b) 16 miles c) 14 miles d) 18 miles
5. If a bus is traveling at an average speed of 55 km/h for 5 hours, how far has it traveled? a) 275 kilometers b) 250 kilometers c) 225 kilometers d) 300 kilometers
6. If a ship is traveling at an average speed of 20 knots for 6 hours, how far has it traveled? a) 120 nautical miles b) 100 nautical miles c) 140 nautical miles d) 160 nautical miles
7. If a bike is traveling at an average speed of 15 km/h for 3 hours, how far has it traveled? a) 45 kilometers b) 35 kilometers c) 25 kilometers d) 55 kilometers
8. If a car is traveling at an average speed of 70 mph for 4 hours, how far has it traveled? a) 280 miles b) 260 miles c) 240 miles d) 300 miles

How to calculate time when average speed and distance are given

1. If a car is traveling at an average speed of 60 mph and the distance traveled is 180 miles, the time can be calculated by dividing the distance by the average speed: 180 miles / 60 mph = 3 hours.
2. If a train is traveling at an average speed of 80 km/h and the distance traveled is 320 kilometers, the time can be calculated by dividing the distance by the average speed: 320 kilometers / 80 km/h = 4 hours.
3. If a runner is running at an average speed of 8 mph and the distance traveled is 16 miles, the time can be calculated by dividing the distance by the average speed: 16 miles / 8 mph = 2 hours.
4. If a bus is traveling at an average speed of 55 km/h and the distance traveled is 275 kilometers, the time can be calculated by dividing the distance by the average speed: 275 kilometers / 55 km/h = 5 hours.
5. If a ship is traveling at an average speed of 20 knots and the distance traveled is 120 nautical miles, the time can be calculated by dividing the distance by the average speed: 120 nautical miles / 20 knots = 6 hours.

Evaluation

1. Given an average speed of 60 miles per hour and a distance of 120 miles, how long would it take to travel that distance? a. 2 hours b. 3 hours c. 4 hours d. 5 hours
2. If an average speed of 50 kilometers per hour and a distance of 200 kilometers is given, how long would it take to travel that distance? a. 4 hours b. 3.5 hours c. 3 hours d. 2.5 hours
3. Given an average speed of 30 miles per hour and a distance of 90 miles, what is the time taken for the journey? a. 2 hours b. 3 hours c. 4 hours d. 5 hours
4. If an average speed of 80 kilometers per hour and a distance of 320 kilometers is given, how long would it take to travel that distance? a. 4 hours b. 3 hours c. 2.5 hours d. 2 hours
5. Given an average speed of 70 miles per hour and a distance of 140 miles, how long would it take to travel that distance? a. 2 hours b. 2.5 hours c. 3 hours d. 3.5 hours
6. If an average speed of 100 kilometers per hour and a distance of 500 kilometers is given, how long would it take to travel that distance? a. 5 hours b. 4.5 hours c. 4 hours d. 3.5 hours
7. Given an average speed of 40 miles per hour and a distance of 80 miles, how long would it take to travel that distance? a. 2 hours b. 2.5 hours c. 3 hours d. 3.5 hours
8. If an average speed of 60 kilometers per hour and a distance of 240 kilometers is given, how long would it take to travel that distance? a. 4 hours b. 3.5 hours c. 3 hours d. 2.5 hours
9. Given an average speed of 90 miles per hour and a distance of 180 miles, how long would it take to travel that distance? a. 2 hours b. 2.5 hours c. 3 hours d. 3.5 hours
10. If an average speed of 120 kilometers per hour and a distance of 600 kilometers is given, how long would it take to travel that distance? a. 5 hours b. 4.5 hours c. 4 hours d. 3.5 hours

Lesson Presentation

Introduction (10 minutes):

• Begin by asking students if they have ever heard of the term “average speed” before.
• Explain that average speed is a measure of how fast an object is moving over a certain distance.
• Provide examples of real-world scenarios where average speed is important, such as determining the fuel efficiency of a car or the pace of a runner in a marathon.

Direct Instruction (20 minutes):

• Write the formula for average speed on the board: (total distance traveled) / (total time taken)
• Use a series of example problems to demonstrate how to calculate average speed using the formula.
• Have students work through practice problems on their own or with a partner.
• Circulate the room to assist students as needed.

Guided Practice (20 minutes):

• Provide a few more examples of real-world scenarios where average speed is relevant.
• Ask students to work through these examples and calculate the average speed.
• Have students share their answers and reasoning with the class.

Independent Practice (20 minutes):

• Assign a set of practice problems for students to complete on their own.
• Provide time for students to work on the problems, and circulate the room to assist students as needed.

Closure (10 minutes):

• Review the key takeaways from the lesson, including the formula for average speed and its significance in real-world scenarios.
• Ask students to share one thing they learned during the lesson.
• Collect the independent practice assignments and provide feedback.

Assessment:

• Observe students as they work through the practice problems during the guided and independent practice portions of the lesson.
• Collect and grade the independent practice assignments for accuracy and completeness