Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate time durations and work with time zones.
• Convert between Celsius and Fahrenheit.
• Calculate and interpret rates like speed and unit costs.
• Solve problems using the Distance, Speed, and Time formula.

Lesson summary

This week, we delve into the practical world of measurement, focusing on time, temperature, and rates. These are fundamental concepts that impact our daily lives in countless ways, from planning our schedules and understanding the weather to managing budgets and interpreting news reports. In South Africa, where issues like load shedding, seasonal agriculture, and fluctuating petrol prices are prevalent, a strong grasp of these concepts is crucial for making informed decisions and navigating everyday challenges.

Lesson notes

2.1 Time Units of Time: We measure time using various units: seconds (s), minutes (min), hours (hr), days, weeks, months, years. Understanding the relationships between these units is vital: 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 month ≈ 30 days (approximately – months vary in length) 1 year = 365 days (366 in a leap year)

Time Conversions: Converting between time units is a common task. To convert to a smaller unit, multiply; to convert to a larger unit, divide.

Example: Convert 3.5 hours to minutes. Since 1 hour = 60 minutes, 3.5 hours = 3.5 60 = 210 minutes.

Example: Convert 7200 seconds to hours. Since 1 minute = 60 seconds and 1 hour = 60 minutes, 7200 seconds / 60 = 120 minutes. Then, 120 minutes / 60 = 2 hours.

Time Zones: The world is divided into time zones to account for the Earth's rotation. South Africa is in the South African Standard Time (SAST) zone, which is GMT+

2. This means it is two hours ahead of Greenwich Mean Time. When traveling or communicating with people in different time zones, it's crucial to adjust for the time difference.

Example: If it's 10:00 AM in London (GMT), it's 12:00 PM in Johannesburg (SAST).

Elapsed Time: Calculating elapsed time involves finding the difference between two points in time.

Example: If a movie starts at 7:30 PM and ends at 9:45 PM, the elapsed time is 2 hours and 15 minutes. 2.2 Temperature Temperature Scales: The two common temperature scales are Celsius (°C) and Fahrenheit (°F). Celsius is the standard in South Africa.

Conversion Formulas: To convert from Celsius to Fahrenheit: °F = (°C 9/5) + 32 To convert from Fahrenheit to Celsius: °C = (°F - 32) 5/9 Interpreting Temperature: Understanding temperature is vital for various reasons, from deciding what to wear to monitoring food safety. A typical summer day in Gauteng might be 25°C to 30°C, while a cold winter night could be around 5°C or even below freezing (0°C).

Example: Convert 25°C to Fahrenheit. °F = (25 9/5) + 32 = 45 + 32 = 77°F

Example: Convert 68°F to Celsius. °C = (68 - 32) 5/9 = 36 * 5/9 = 20°C 2.3 Rates Definition: A rate is a ratio that compares two different quantities. Common examples include speed (distance/time), unit cost (price/quantity), and exchange rates (currency conversion).

Speed: Speed is the rate at which an object moves. It's calculated as Distance/Time.

Formula: Speed = Distance / Time Rearrangements: Distance = Speed Time Time = Distance / Speed

Example: A car travels 240 km in 3 hours. What is its average speed? Speed = 240 km / 3 hours = 80 km/h Unit Cost: Unit cost is the cost of one item or unit. It's calculated as Total Cost / Number of Units.

Example: A pack of 6 apples costs R

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0. What is the unit cost of each apple? Unit Cost = R30 / 6 apples = R5 per apple Exchange Rates: Exchange rates tell you how much one currency is worth in another currency.

Example: If the exchange rate is R18 per US Dollar, then $1 is equal to R

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8. To convert Rands to Dollars, divide by the exchange rate. To convert Dollars to Rands, multiply by the exchange rate. If you have R360, how many US Dollars can you buy? Dollars = R360 / R18 = $20 Guided Practice (With Solutions)

Question 1: A train leaves Cape Town at 08:45 and arrives in Johannesburg at 20:15 the same day. How long did the journey take?

Solution: Calculate the time from 08:45 to 12:00 (noon): 3 hours and 15 minutes.

Calculate the time from 12:00 to 20:15: 8 hours and 15 minutes.

Add the two times together: 3 hours 15 minutes + 8 hours 15 minutes = 11 hours 30 minutes.

Therefore, the journey took 11 hours and 30 minutes.

Question 2: The temperature in Durban is 35°

C. What is this temperature in Fahrenheit?

Solution: Use the conversion formula: °F = (°C * 9/5) + 32 Substitute the value of °C: °F = (35 * 9/5) + 32 Calculate: °F = (63) + 32 = 95°F Therefore, 35°C is equal to 95°

F. Question 3: A taxi travels 150 km in 2.5 hours. Calculate its average speed.

Solution: Use the formula: Speed = Distance / Time Substitute the values: Speed = 150 km / 2.5 hours Calculate: Speed = 60 km/h Therefore, the taxi's average speed is 60 km/h.

Question 4: A packet of chips costs R12.

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0. What is the cost of 5 packets of chips?

Solution: This is a unit cost problem.

Calculate the total cost: R12.50/packet * 5 packets = R62.50 Therefore, 5 packets of chips cost R62.

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0. Independent Practice (Questions Only) Convert 2 hours and 45 minutes to minutes. What is the temperature of 10°C in Fahrenheit? A bus travels 360 km at an average speed of 80 km/h. How long does the journey take? A store sells oranges at R4.50 each. How much will 12 oranges cost? If the exchange rate is R15 per British Pound, how many Rands will you get for £50?

A soccer match starts at 3:00 PM and ends at 4:45 PM. How long does the match last? The temperature in Johannesburg is 20°C, and the temperature in New York is 70°F. Which city is warmer? (Show your working). A construction worker earns R85 per hour.