Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Convert units of time for real-world scenarios.
• Interpret and convert between Celsius and Fahrenheit.
• Calculate and interpret rates like speed and cost.
• Solve problems involving time zones.
• Apply formulas to solve measurement problems.

Lesson summary

This week, we delve into the crucial area of measurement, focusing on time, temperature, and rates. Understanding these concepts is fundamental to navigating daily life in South Africa. From managing your time effectively to understanding weather reports and calculating taxi fares, these skills are essential for financial literacy, informed decision-making, and overall well-being. For example, understanding rates helps you compare cellphone data deals or loan interest rates. Accurately interpreting temperature is critical for understanding weather forecasts, which impacts farmers, commuters, and households alike.

Lesson notes

2.1 Time: Units of Time: The standard units of time are seconds (s), minutes (min), hours (h), days, weeks, months, and years. It's crucial to understand the relationships between these units: 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 month ≈ 30 days (on average; varies by month) 1 year = 365 days (366 days in a leap year)

Time Calculations: We often need to calculate durations, start times, or end times. The key is to be systematic.

Example 1: A bus journey from Johannesburg to Durban takes 7 hours and 45 minutes.

If the bus leaves Johannesburg at 8:30 AM, at what time will it arrive in Durban?

Solution: Add the hours: 8:30 AM + 7 hours = 3:30 PM Add the minutes: 3:30 PM + 45 minutes = 4:15 PM Therefore, the bus will arrive in Durban at 4:15 P

M. Time Zones: The Earth is divided into time zones. Understanding time zone differences is important, especially for international communication and travel. South Africa operates on South African Standard Time (SAST), which is UTC+

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

Solution: Johannesburg is UTC+2, meaning it's 2 hours ahead of London.

Therefore, in London, it would be 10:00 AM - 2 hours = 8:00 AM. 2.2 Temperature: Temperature Scales: The two most common temperature scales are Celsius (°C) and Fahrenheit (°F). In South Africa, we primarily use Celsius.

Conversion Formulas: Celsius to Fahrenheit: °F = (°C × 9/5) + 32 Fahrenheit to Celsius: °C = (°F - 32) × 5/9 Interpreting Temperature: Understand what different temperatures mean in the context of weather, cooking, etc. For example, a comfortable room temperature is around 22°

C. Example 3: Convert 30°C to Fahrenheit.

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

F. Example 4: The weather forecast in Cape Town predicts a high of 77°

F. What is this temperature in Celsius?

Solution: °C = (77 - 32) × 5/9 °C = 45 × 5/9 °C = 25 Therefore, 77°F is equal to 25°C. 2.3 Rates: Definition: A rate is a ratio that compares two quantities with different units. Common examples include speed (distance/time), fuel consumption (litres/kilometre), and wage rates (Rands/hour).

Formula: Rate = Quantity 1 / Quantity 2 Calculating Rates: You need to identify the two quantities being compared and then perform the division.

Example 5: A car travels 360 km in 4 hours. What is its average speed?

Solution: Speed = Distance / Time Speed = 360 km / 4 hours Speed = 90 km/h Therefore, the car's average speed is 90 km/h.

Unit Cost: Unit cost is a rate that expresses the cost per single unit of a product or service. This allows for easy price comparison.

Example 6: A 5kg bag of potatoes costs R

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5. What is the unit cost per kilogram?

Solution: Unit Cost = Total Cost / Number of Units Unit Cost = R45 / 5 kg Unit Cost = R9/kg Therefore, the unit cost of potatoes is R9 per kilogram.

Wage Rates: This calculates earnings based on hourly work.

Example 7: You work 20 hours in a week and earn R

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0. What is your hourly wage rate?

Solution: Hourly Wage Rate = Total Earnings / Number of Hours Worked Hourly Wage Rate = R1800 / 20 hours Hourly Wage Rate = R90/hour Therefore, your hourly wage rate is R90 per hour. Guided Practice (With Solutions)

Question 1: A train leaves Cape Town at 11:45 AM and arrives in Johannesburg at 6:15 PM the next day. How long was the journey?

Solution: Time from 11:45 AM to 11:45 AM the next day: 24 hours.

Time from 11:45 AM to 6:15 PM: 6 hours and 30 minutes (18:15 - 11:45 = 6 hours 30 minutes)

Total journey time: 24 hours + 6 hours 30 minutes = 30 hours and 30 minutes.

Therefore, the journey was 30 hours and 30 minutes long. The key here is to break the time into manageable segments.

Question 2: Convert 20°C to Fahrenheit and 95°F to Celsius.

Solution: Celsius to Fahrenheit: °F = (20 × 9/5) + 32 = 36 + 32 = 68°F Fahrenheit to Celsius: °C = (95 - 32) × 5/9 = 63 × 5/9 = 35°C Therefore, 20°C is 68°F, and 95°F is 35°

C. Remember to use the correct formula for each conversion.

Question 3: A taxi charges R15 for the first kilometer and R8 for each additional kilometer. How much will it cost to travel 12 km?

Solution: Cost for the first kilometer: R15 Number of additional kilometers: 12 km - 1 km = 11 km Cost for the additional kilometers: 11 km × R8/km = R88 Total cost: R15 + R88 = R103 Therefore, it will cost R103 to travel 12 km. Identify fixed costs and variable costs.

Question 4: A worker earns R65 per hour. If they work 35 hours in a week, what is their gross weekly wage?

Solution: Gross weekly wage = Hourly rate × Number of hours worked Gross weekly wage = R65/hour × 35 hours Gross weekly wage = R2275 Therefore, their gross weekly wage is R

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5. Question 5: If a runner completes a 10km race in 45 minutes, what is their average speed in kilometers per hour?