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 utilize temperature scales (Celsius and Fahrenheit).
• Calculate and interpret rates like speed and fuel consumption.
• Solve problems involving time zones.
• Interpret information from timetables, graphs, and maps.

Lesson summary

This week, we delve into the practical applications of measurement, focusing on time, temperature, and rates. These concepts are fundamental to everyday life in South Africa, from managing our time efficiently to understanding weather forecasts and calculating travel costs. Understanding these concepts will empower you to make informed decisions and solve practical problems encountered daily. Think about planning a trip to Durban; you need to estimate travel time, check the weather forecast (temperature) to pack appropriately, and calculate the cost of petrol based on the rate of fuel consumption. These are just some examples of why this topic is crucial.

Lesson notes

2.1 Time: Time is a fundamental concept we use to measure or designate a period. It is vital in daily life for scheduling activities, planning travel, and understanding historical events.

Units of Time: Second (s)

Minute (min): 1 min = 60 s Hour (h): 1 h = 60 min = 3600 s Day: 1 day = 24 h Month: Approximately 30 days (varying from 28-31)

Year: 1 year = 365 days (366 in a leap year)

Time Conversions: To convert between units of time, you either multiply or divide, depending on whether you are converting to a smaller or larger unit.

Smaller to larger: divide Larger to smaller: multiply Example 1: Converting hours to minutes. How many minutes are there in 3.5 hours? Since 1 hour = 60 minutes, then 3.5 hours = 3.5 * 60 = 210 minutes.

Example 2: Converting minutes to hours. Convert 150 minutes to hours. Since 60 minutes = 1 hour, then 150 minutes = 150 / 60 = 2.5 hours. 2.2 Temperature: Temperature is a measure of how hot or cold something is. The two commonly used scales are Celsius (°C) and Fahrenheit (°F). In South Africa, we predominantly use the Celsius scale. 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: To convert Celsius to Fahrenheit: °F = (°C × 9/5) + 32 To convert Fahrenheit to Celsius: °C = (°F - 32) × 5/9 Example 1: Convert 25°C to Fahrenheit. °F = (25 × 9/5) + 32 = 45 + 32 = 77°F Example 2: Convert 68°F to Celsius. °C = (68 - 32) × 5/9 = 36 × 5/9 = 20°C 2.3 Rates: A rate is a ratio that compares two quantities with different units. Common examples include speed, fuel consumption, and unit pricing.

Speed: Distance traveled per unit of time (e.g., kilometers per hour (km/h)). Speed = Distance / Time Distance = Speed Time Time = Distance / Speed Example 1: A car travels 300 km in 4 hours. What is its average speed? Speed = 300 km / 4 h = 75 km/h Example 2: A train travels at 120 km/h. How far will it travel in 2.5 hours? Distance = 120 km/h * 2.5 h = 300 km Fuel Consumption: Amount of fuel used per distance traveled (e.g., liters per 100 km (L/100km)). Fuel Consumption = (Fuel Used / Distance Traveled) 100 Example 1: A car uses 30 liters of petrol to travel 400 km. What is its fuel consumption? Fuel Consumption = (30 L / 400 km) * 100 = 7.5 L/100 km Unit Pricing: Price per unit of quantity (e.g., Rand per kilogram (R/kg)). This is helpful to compare costs effectively. Unit Price = Total Cost / Quantity Example 1: A 5 kg bag of potatoes costs R

4

0. What is the unit price? Unit Price = R40 / 5 kg = R8/kg 2.4 Time Zones: The Earth is divided into time zones, which are regions that observe a uniform standard time for legal, commercial, and social purposes. Understanding time zones is essential for international communication and travel. South Africa has a single time zone (South African Standard Time - SAST), which is UTC+

2. Example: If it is 10:00 AM in South Africa, what time is it in London (UTC+0)? London is UTC+0, and South Africa is UTC+

2. Therefore, London is 2 hours behind South Africa. So, in London, it would be 8:00 A

M. Guided Practice (With Solutions)

Question 1: A bus leaves Johannesburg at 8:30 AM and arrives in Durban at 4:00 P

M. How long was the journey?

Solution: First, find the total hours between 8:30 AM and 4:00 P

M. From 8:30 AM to 12:00 PM (noon) is 3 hours and 30 minutes.

From 12:00 PM to 4:00 PM is 4 hours. Total time = 3 hours 30 minutes + 4 hours = 7 hours 30 minutes.

Therefore, the journey was 7 hours and 30 minutes. We can also express this as 7.5 hours.

Question 2: The average temperature in Cape Town in January is 26°

C. What is this temperature in Fahrenheit?

Solution: Use the formula: °F = (°C × 9/5) + 32 °F = (26 × 9/5) + 32 = 46.8 + 32 = 78.8°F Therefore, 26°C is equal to 78.8°

F. Question 3: A car travels 600 km on a full tank of 50 liters. What is the car's fuel consumption in liters per 100 km?

Solution: Use the formula: Fuel Consumption = (Fuel Used / Distance Traveled) * 100 Fuel Consumption = (50 L / 600 km) * 100 = 8.33 L/100 km (approximately) Therefore, the car's fuel consumption is approximately 8.33 liters per 100 km.

Question 4: A flight from Johannesburg to London leaves at 11:00 PM SAST and takes 11 hours. What will the local time be in London when the flight lands?

Solution: SAST is UTC+2, and London is UTC+

0. Therefore, London is 2 hours behind Johannesburg. Add the flight duration to the departure time: 11:00 PM + 11 hours = 10:00 AM (next day) SAS

T. Subtract the time difference: 10:00 AM SAST - 2 hours = 8:00 AM London time.

Therefore, the flight will land in London at 8:00 AM the next day. Independent Practice (Questions Only)

Question 1: Convert 2 weeks and 3 days into hours.

Question 2: A recipe requires baking a cake at 180°

C. What is this temperature in Fahrenheit?

Question 3: A train travels at a speed of 85 km/h. How long will it take to travel 510 km?

Question 4: A shop sells oranges at R15 for a bag of 3 kg. What is the unit price per kilogram?