Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate with different time units.
• Interpret and convert between Celsius and Fahrenheit.
• Calculate and interpret rates like speed and cost per unit.
• Solve practical problems in South African contexts.
• Analyse data from tables and graphs related to these topics.

Lesson summary

This week, we delve into the practical applications of measurement, focusing specifically on time, temperature, and rates. Understanding these concepts is crucial for everyday life in South Africa. From managing your daily schedule and understanding weather forecasts to calculating travel times and comparing prices, these skills are essential for informed decision-making and effective participation in our society. Whether you're catching a taxi, cooking a meal, or budgeting for your household expenses, these measurements are constantly at play.

Lesson notes

2. 1. Time Time is a fundamental concept in our lives. We measure time in various units, and it's important to be able to convert between them.

Units of Time: Seconds (s), Minutes (min), Hours (h), Days, Weeks, Months, Years.

Conversions: 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 month ≈ 30 days (Average) –

Note: It varies depending on the specific month. For precise calculations, use the number of days in that particular month. 1 year = 365 days (366 days in a leap year) 1 year = 12 months Example 1: A bus journey from Johannesburg to Durban takes 8 hours and 30 minutes.

If the bus leaves Johannesburg at 7:45 AM, what time will it arrive in Durban?

Solution: Add the hours: 7:45 AM + 8 hours = 3:45 P

M. Add the minutes: 3:45 PM + 30 minutes = 4:15 P

M. Therefore, the bus will arrive in Durban at 4:15 P

M. Example 2: A construction project is scheduled to last for 18 months. How many weeks is this approximately?

Solution: Convert months to days: 18 months * 30 days/month = 540 days.

Convert days to weeks: 540 days / 7 days/week ≈ 77.14 weeks.

Therefore, the project is scheduled to last approximately 77 weeks. 2.

2. Temperature Temperature measures how hot or cold something is. We commonly use Celsius (°C) in South Africa, but Fahrenheit (°F) is used in some other countries.

Units of Temperature: Celsius (°C), Fahrenheit (°F)

Conversion Formulas: °F = (°C 9/5) + 32 °C = (°F - 32) 5/9 Example 3: The weather forecast predicts a high of 30°C in Cape Town. What is this temperature in Fahrenheit?

Solution: Apply the conversion formula: °F = (30 * 9/5) + 32 Calculate: °F = (54) + 32 °F = 86 Therefore, 30°C is equal to 86°

F. Example 4: A recipe from an American cookbook requires an oven temperature of 350°

F. What is this temperature in Celsius?

Solution: Apply the conversion formula: °C = (350 - 32) * 5/9 Calculate: °C = (318) * 5/9 °C ≈ 176.67 Therefore, 350°F is approximately equal to 177°C (round to the nearest whole number). 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 population density (people/area).

Speed: Distance traveled per unit of time (e.g., km/h, m/s).

Cost per unit: Price per item or amount (e.g., Rands per kilogram, Rands per liter).

Population density: Number of people living per unit of area (e.g., people/km²).

Example 5: A taxi travels 120 km in 2 hours. What is its average speed?

Solution: Apply the formula: Speed = Distance / Time Calculate: Speed = 120 km / 2 hours Speed = 60 km/h Therefore, the taxi's average speed is 60 km/h.

Example 6: A 5 kg bag of potatoes costs R

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5. What is the cost per kilogram?

Solution: Apply the formula: Cost per unit = Total cost / Quantity Calculate: Cost per kilogram = R45 / 5 kg Cost per kilogram = R9/kg Therefore, the cost per kilogram of potatoes is R

9. Example 7: A township with an area of 5 km² has a population of 25,000 people. What is the population density?

Solution: Apply the formula: Population Density = Number of people / Area Calculate: Population Density = 25,000 people / 5 km² Population Density = 5,000 people/km² Therefore, the population density is 5,000 people per square kilometre. Guided Practice (With Solutions)

Question 1: A soccer match starts at 3:00 PM and lasts for 90 minutes, plus 5 minutes of extra time. What time does the match end?

Solution: Convert minutes to hours and minutes: 90 minutes = 1 hour and 30 minutes.

Add the regular playing time: 3:00 PM + 1 hour 30 minutes = 4:30 P

M. Add the extra time: 4:30 PM + 5 minutes = 4:35 P

M. Answer: The match ends at 4:35 P

M. This requires understanding time calculations in a practical context.

Question 2: The temperature in Johannesburg is 25°

C. What is this temperature in Fahrenheit?

Solution: Use the conversion formula: °F = (°C * 9/5) + 32 Substitute the value: °F = (25 * 9/5) + 32 Calculate: °F = (45) + 32 °F = 77 Answer: 25°C is equal to 77°

F. This reinforces the temperature conversion formula.

Question 3: A car travels 360 km in 4 hours. What is its average speed in km/h?

Solution: Use the formula: Speed = Distance / Time Substitute the values: Speed = 360 km / 4 hours Calculate: Speed = 90 km/h Answer: The car's average speed is 90 km/h. This reinforces rate calculations (specifically, speed).

Question 4: If 2 liters of milk cost R30, what is the cost per liter?

Solution: Use the formula: Cost per liter = Total cost / Number of liters Substitute the values: Cost per liter = R30 / 2 liters Calculate: Cost per liter = R15/liter Answer: The cost per liter of milk is R

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5. This reinforces rate calculations (specifically, cost per unit). Independent Practice (Questions Only)

A movie starts at 8:15 PM and lasts for 2 hours and 40 minutes. What time will the movie end? Convert 40°C to Fahrenheit. A train travels 450 km at a speed of 75 km/h. How long will the journey take? If a 2.5 kg bag of oranges costs R50, what is the cost per kilogram?