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 apply temperature readings in Celsius and Fahrenheit.
• Calculate and interpret rates like speed, flow, and consumption.
• Solve problems involving elapsed time.
• Interpret graphs and tables with this data.

Lesson summary

This week, we delve into the vital topic of measurement, specifically focusing on time, temperature, and rates. These are fundamental skills that are used daily, from planning your travel to school, understanding weather forecasts, calculating your electricity consumption, to making informed purchasing decisions. In a country like South Africa, where efficient resource management and financial literacy are crucial, understanding these measurements is essential for everyday life and responsible citizenship. For example, understanding water usage rates during droughts or electricity consumption during loadshedding is critically important.

Lesson notes

A. Time Measurement and Conversions: Time is a fundamental measurement that we use every day. We need to understand how to convert between different units of time.

Units of Time: Second (s)

Minute (min): 1 minute = 60 seconds Hour (hr): 1 hour = 60 minutes Day: 1 day = 24 hours Month: Approximately 30 days (it varies!)

Year: 365 days (366 in a leap year)

Conversions: To convert between units, we multiply or divide by the appropriate conversion factor.

Example 1: Convert 2.5 hours to minutes. Since 1 hour = 60 minutes, we multiply: 2.5 hours 60 minutes/hour = 150 minutes.

Example 2: Convert 180 seconds to minutes. Since 1 minute = 60 seconds, we divide: 180 seconds / 60 seconds/minute = 3 minutes.

Elapsed Time: Calculating the time elapsed between two events requires careful consideration of hours, minutes, and sometimes seconds.

Example 3: A soccer match starts at 15:30 and ends at 17:

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5. How long was the match?

From 15:30 to 16:00 is 30 minutes.

From 16:00 to 17:00 is 1 hour.

From 17:00 to 17:15 is 15 minutes.

Total time: 30 minutes + 1 hour + 15 minutes = 1 hour 45 minutes.

B. Temperature Measurement: Temperature is a measure of how hot or cold something is. We primarily use Celsius (°C) in South Africa, but Fahrenheit (°F) is also used, particularly in some international contexts. 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 4: Convert 25°C to Fahrenheit. °F = (25 9/5) + 32 = 45 + 32 = 77°F Example 5: Convert 68°F to Celsius. °C = (68 - 32) 5/9 = 36 * 5/9 = 20°C

C. Rates: A rate is a ratio that compares two quantities with different units. Common examples include speed (distance/time), flow rate (volume/time), and consumption rates (quantity/time).

Speed: How fast something is moving. Commonly measured in kilometers per hour (km/h) or meters per second (m/s).

Formula: Speed = Distance / Time Flow Rate: How much of something flows per unit of time. Examples include liters per minute (L/min) for water flow or cubic meters per hour (m³/hr) for gas flow.

Formula: Flow Rate = Volume / Time Consumption Rate: How much of something is used per unit of time. Examples include liters per kilometer (L/km) for car fuel consumption or kilowatt-hours per month (kWh/month) for electricity usage.

Formula: Consumption Rate = Quantity / Time Example 6: A car travels 300 km in 4 hours. Calculate the average speed. Speed = 300 km / 4 hours = 75 km/h Example 7: A tap fills a 20-liter bucket in 5 minutes. Calculate the flow rate. Flow Rate = 20 liters / 5 minutes = 4 liters/minute Example 8: A household uses 450 kWh of electricity in a month. Calculate the average daily consumption. Assume a month has 30 days. Daily Consumption = 450 kWh / 30 days = 15 kWh/day Guided Practice (With Solutions)

Question 1: A bus trip from Cape Town to Johannesburg is scheduled to take 18 hours.

If the bus leaves Cape Town at 06:00, at what time is it expected to arrive in Johannesburg?

Solution: Starting time: 06:00 Duration: 18 hours Arrival time: 06:00 + 18 hours = 24:00 (midnight) which is the same as 00:00 the next day.

Adding another 18 hours results in 00:00 + 18 hours = 18:

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0. Therefore, the bus is expected to arrive in Johannesburg at 00:00 (midnight) the next day.

Or 18:

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0. Question 2: The temperature in Durban is 30°

C. What is the equivalent temperature in Fahrenheit?

Solution: °F = (°C 9/5) + 32 °F = (30 9/5) + 32 °F = 54 + 32 °F = 86°F Therefore, 30°C is equal to 86°

F. Question 3: A water tank with a volume of 1200 liters is filled at a rate of 8 liters per minute. How long will it take to fill the tank completely?

Solution: Time = Volume / Flow Rate Time = 1200 liters / 8 liters/minute Time = 150 minutes To convert to hours: 150 minutes / 60 minutes/hour = 2.5 hours Therefore, it will take 150 minutes or 2.5 hours to fill the tank.

Question 4: Sipho drives his taxi from Pretoria to Polokwane, a distance of 300km.

He wants to arrive by 11:

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0. If he leaves Pretoria at 07:30 and travels at an average speed of 90km/h, will he arrive on time?

Solution: Calculate travel time: Time = Distance / Speed = 300 km / 90 km/h = 3.33 hours Convert 0.33 hours to minutes: 0.33 hours 60 minutes/hour = 20 minutes (approximately)

Total travel time: 3 hours and 20 minutes Arrival time: 07:30 + 3 hours 20 minutes = 10:50 Sipho will arrive at 10:50, which is before 11:

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0. Therefore, he will arrive on time. Independent Practice (Questions Only) Convert 540 minutes to hours.

A movie starts at 20:15 and ends at 22:

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0. How long is the movie? The temperature in Johannesburg drops from 28°C to 15°C overnight. What is the temperature difference in Celsius? What are the two temperatures in Fahrenheit? A petrol pump dispenses 45 liters of petrol in 3 minutes. Calculate the flow rate of the petrol pump in liters per second. A household’s geyser uses 3 kW of electricity per hour.