Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate elapsed time.
• Convert between units of time and temperature.
• Calculate and interpret rates like speed and cost.
• Solve problems involving temperature changes.
• Apply these skills to real-world scenarios.

Lesson summary

This week, we delve into the vital topic of measurement, specifically focusing on time, temperature, and rates. Measurement isn't just an abstract mathematical concept; it's a fundamental skill we use every day in countless situations. From managing our time effectively to understanding weather patterns and calculating costs, measurement is crucial for navigating our daily lives successfully. In the South African context, understanding these measurements is particularly important for tasks like managing public transport schedules, monitoring electricity usage (especially with load shedding), and understanding financial rates like interest on loans.

Lesson notes

2.1 Time Units of Time: The standard units of time are seconds (s), minutes (min), hours (h), days, weeks, months, and years. It's crucial to understand the relationships between these units: 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 month ≈ 30 days (approximation, varies by month) 1 year = 365 days (366 in a leap year)

Elapsed Time: This is the amount of time that passes between a start time and an end time. To calculate elapsed time, subtract the start time from the end time. 24-hour vs. 12-hour Time: 12-hour time: Uses am (ante meridiem - before noon) and pm (post meridiem - after noon).

It goes from 1:00 am to 12:00 noon, and then 1:00 pm to 12:00 midnight. 24-hour time: Uses numbers from 00:00 to 23:

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9. This format avoids confusion between am and pm. To convert from 12-hour time to 24-hour time, add 12 to the hours for pm times (except for 12:00 pm, which remains 12:00).

AM times remain the same (except for 12:00 am, which becomes 00:00).

Example: 3:00 pm = 15:00; 9:00 am = 09:00; 12:00 am = 00:00; 12:00 pm = 12:

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0. Example 1: Thando starts working at 8:30 am and finishes at 5:00 pm. How long did she work?

Solution: Convert 5:00 pm to 24-hour time: 5:00 pm + 12 hours = 17:00 Subtract the start time from the end time: 17:00 - 08:30 = 8 hours and 30 minutes. She worked for 8 hours and 30 minutes.

Example 2: A bus leaves Johannesburg at 14:45 and arrives in Durban at 06:15 the next day. How long was the bus journey?

Solution: Calculate the time from 14:45 to midnight (00:00): 24:00 - 14:45 = 9 hours and 15 minutes.

Calculate the time from midnight to 06:15: 6 hours and 15 minutes.

Add the two times together: 9 hours 15 minutes + 6 hours 15 minutes = 15 hours and 30 minutes. The bus journey was 15 hours and 30 minutes. 2.2 Temperature Units of Temperature: The two main units of temperature are Celsius (°C) and Fahrenheit (°F). Celsius (°C): Used in South Africa and most of the world. Water freezes at 0°C and boils at 100°

C. Fahrenheit (°F): Used primarily in the United States. Water freezes at 32°F and boils at 212°

F. Conversion Formulas: °F = (°C × 9/5) + 32 °C = (°F - 32) × 5/9 Example 3: Convert 25°C to Fahrenheit.

Solution: Apply the formula: °F = (25 × 9/5) + 32 °F = (45) + 32 °F = 77 Therefore, 25°C is equal to 77°

F. Example 4: Convert 68°F to Celsius.

Solution: Apply the formula: °C = (68 - 32) × 5/9 °C = (36) × 5/9 °C = 20 Therefore, 68°F is equal to 20°C. 2.3 Rates Definition: A rate is a ratio that compares two quantities with different units. Common examples include speed (distance per time), unit cost (price per item), and salary (money per time).

Formula: Rate = Quantity 1 / Quantity 2 Speed: Speed = Distance / Time. Units for speed can be km/h (kilometers per hour), m/s (meters per second), etc.

Unit Cost: Unit Cost = Total Cost / Number of Items. Units for unit cost can be R/item (Rands per item), R/kg (Rands per kilogram), etc.

Example 5: A car travels 360 km in 4 hours. What is its average speed?

Solution: Apply the formula: Speed = Distance / Time Speed = 360 km / 4 hours Speed = 90 km/h The average speed of the car is 90 km/h.

Example 6: A shop sells 5 kg of oranges for R

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5. What is the unit cost per kilogram?

Solution: Apply the formula: Unit Cost = Total Cost / Number of Items Unit Cost = R45 / 5 kg Unit Cost = R9/kg The unit cost of the oranges is R9 per kilogram.

Example 7: Maria earns R480 for working 8 hours. What is her hourly rate?

Solution: Apply the formula: Rate = Total Earnings / Number of Hours Rate = R480 / 8 hours Rate = R60/hour Maria earns R60 per hour. Guided Practice (With Solutions)

Question 1: A movie starts at 19:15 and ends at 21:

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0. How long is the movie?

Solution: Subtract the start time from the end time: 21:30 - 19:15 = 2 hours and 15 minutes. The movie is 2 hours and 15 minutes long.

Commentary: This question tests the ability to calculate elapsed time using 24-hour notation. It's a straightforward subtraction, but careful attention to minutes is necessary.

Question 2: Convert 30°C to Fahrenheit.

Solution: Apply the formula: °F = (°C × 9/5) + 32 °F = (30 × 9/5) + 32 °F = (54) + 32 °F = 86 30°C is equal to 86°

F. Commentary: This problem reinforces the temperature conversion formula. Students should remember the order of operations (multiplication before addition).

Question 3: A train travels 600 km in 5 hours. What is its average speed?

Solution: Apply the formula: Speed = Distance / Time Speed = 600 km / 5 hours Speed = 120 km/h The average speed of the train is 120 km/h.

Commentary: This is a basic rate problem. Students need to identify the distance and time, and apply the speed formula correctly.

Question 4: A packet of sweets costs R12.

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0. If you buy 8 packets, what is the total cost? And what is the cost of each packet?

Solution: To calculate the total cost, we can write: Total Cost = Number of packets * Cost per packet Total Cost = 8 packets * R12.50 per packet = R100.