Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Convert between different units of time.
• Interpret and convert temperature between Celsius and Fahrenheit.
• Calculate and interpret rates like speed, cost, and fuel consumption.
• Solve practical problems using these measurements.
• Understand time zones and their impact.

Lesson summary

This week, we delve into the crucial area of measurement, focusing on time, temperature, and rates. These concepts are not just abstract ideas; they are fundamental to navigating our daily lives, from scheduling transport and cooking meals to understanding electricity bills and comparing prices. In South Africa, where issues like load shedding and fluctuating fuel prices impact our communities directly, a solid understanding of these measurements empowers us to make informed decisions and manage our resources effectively. Understanding these concepts also lays a foundation for interpreting data and statistics reported in the media, impacting our ability to engage in civic discourse.

Lesson notes

2.1 Time Time is a continuous measurement used to sequence events and quantify the duration between them. We commonly use seconds (s), minutes (min), hours (h), days, weeks, months, and years. Understanding how to convert between these units is vital.

Conversions: 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: The duration between two points in time. This is often calculated by subtracting the start time from the end time.

Example 1: A taxi ride starts at 07:45 and ends at 08:

2

0. How long was the taxi ride?

Solution: From 07:45 to 08:00 is 15 minutes.

From 08:00 to 08:20 is 20 minutes.

Total time: 15 minutes + 20 minutes = 35 minutes.

Example 2: A soccer match starts at 15:00 and lasts for 90 minutes plus 10 minutes of extra time. What time does the match end?

Solution: 90 minutes = 1 hour and 30 minutes. 1 hour and 30 minutes + 10 minutes = 1 hour and 40 minutes. 15:00 + 1 hour = 16:00. 16:00 + 40 minutes = 16:

4

0. The match ends at 16:

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0. Example 3: Time Zones Johannesburg is in the South African Standard Time (SAST) zone, which is UTC+

2. New York City is in the Eastern Standard Time (EST) zone, which is UTC-5 during standard time.

If it is 10:00 in Johannesburg, what time is it in New York City?

Solution: The time difference between Johannesburg and New York is 2 - (-5) = 7 hours. Since New York is west of Johannesburg, we subtract the time difference from Johannesburg's time. 10:00 - 7 hours = 03:

0

0. Therefore, it is 03:00 in New York City. 2.2 Temperature Temperature measures the degree of hotness or coldness of an object or environment. The most common scales are Celsius (°C) and Fahrenheit (°F). Celsius (°C): Water freezes at 0°C and boils at 100°

C. Fahrenheit (°F): Water freezes at 32°F and boils at 212°

F. Conversion Formulas: °F = (°C × 9/5) + 32 °C = (°F - 32) × 5/9 Example 1: Convert 25°C to Fahrenheit.

Solution: °F = (25 × 9/5) + 32 °F = (45) + 32 °F = 77°F Example 2: Convert 68°F to Celsius.

Solution: °C = (68 - 32) × 5/9 °C = (36) × 5/9 °C = 20°C 2.3 Rates A rate is a ratio that compares two quantities with different units. Common examples include speed (distance/time), cost per unit (price/quantity), and fuel consumption (liters/kilometer).

Speed: Calculated as distance divided by time. Units are often km/h (kilometers per hour) or m/s (meters per second).

Cost per Unit: Calculated as total cost divided by the number of units. Units could be R/kg (Rand per kilogram), R/item (Rand per item), etc.

Fuel Consumption: Calculated as liters of fuel used divided by kilometers traveled. Units are often L/100km (liters per 100 kilometers).

Example 1: A car travels 300 km in 4 hours. Calculate its average speed.

Solution: Speed = Distance / Time Speed = 300 km / 4 hours Speed = 75 km/h Example 2: A 2.5 kg bag of potatoes costs R

3

5. Calculate the cost per kilogram.

Solution: Cost per kg = Total cost / Quantity Cost per kg = R35 / 2.5 kg Cost per kg = R14/kg Example 3: A car uses 45 liters of petrol to travel 600 km. Calculate the fuel consumption in L/100km.

Solution: Fuel Consumption = (Liters / Kilometers) * 100 km Fuel Consumption = (45 liters / 600 km) * 100 km Fuel Consumption = 7.5 L/100km Guided Practice (With Solutions)

Question 1: A bus leaves Cape Town at 09:15 and arrives in Johannesburg at 18:30 the next day. How long did the bus trip take?

Solution: From 09:15 to 09:15 the next day is 24 hours.

From 09:15 to 18:15 is 9 hours.

From 18:15 to 18:30 is 15 minutes. Total time = 24 hours + 9 hours + 15 minutes = 33 hours and 15 minutes.

Question 2: The temperature in Durban is 30°

C. What is this temperature in Fahrenheit?

Solution: °F = (°C × 9/5) + 32 °F = (30 × 9/5) + 32 °F = (54) + 32 °F = 86°F Question 3: A worker earns R480 for working 8 hours. What is their hourly rate of pay?

Solution: Hourly Rate = Total Earnings / Number of Hours Hourly Rate = R480 / 8 hours Hourly Rate = R60/hour Question 4: A marathon runner completes a 42.2 km marathon in 3 hours and 30 minutes. What was their average speed in km/h?

Solution: Convert 3 hours 30 minutes to hours: 3.5 hours. Speed = Distance / Time Speed = 42.2 km / 3.5 hours Speed = 12.06 km/h (approximately) Independent Practice (Questions Only) A train journey is scheduled to take 7 hours and 45 minutes.

If the train departs at 11:20, what time is it expected to arrive? Convert 104°F to Celsius. A shop sells oranges for R15 per dozen. How much does one orange cost? A taxi travels 120 km in 1 hour and 30 minutes. Calculate its average speed in km/h. A family uses 150 liters of water per day. Calculate their water consumption in liters per week. A recipe requires an oven temperature of 180°C. What is this temperature in Fahrenheit? A cyclist travels 60 km at an average speed of 20 km/h. How long does the journey take? If the price of petrol is R20.50 per liter, how much will it cost to fill a 50-liter tank?