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 compare temperatures in Celsius and Fahrenheit.
• Calculate and interpret rates like speed and cost per unit.
• Apply these concepts to schedules, bills, and budgets.
• Analyze and compare different deals based on rates.

Lesson summary

This week we delve into the essential concepts of time, temperature, and rates within the context of measurement. Understanding these measurements is crucial for navigating daily life in South Africa, from planning your commute to budgeting for electricity and understanding economic indicators. We will explore how time is measured and represented, how temperature affects our lives and how to interpret rates which are essential in understanding cost and speed. Why is this important? Imagine planning a trip from Johannesburg to Durban. You need to understand distances, travel times (incorporating potential delays), and fuel consumption rates.

Lesson notes

a) Time Time is a fundamental measurement that we use to sequence events and quantify durations. It is essential in almost every aspect of our lives.

Units of Time: The basic unit of time is the second (s).

Other common units include: Minute (min): 1 min = 60 s Hour (h): 1 h = 60 min = 3600 s Day: 1 day = 24 h Month: Approximately 30 days (varying by month)

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

Time Conversions: To convert between units of time, we use multiplication or division.

Example 1: How many minutes are in 3.5 hours?

Solution: 3.5 hours 60 minutes/hour = 210 minutes.

Example 2: How many hours are in 180 minutes?

Solution: 180 minutes / 60 minutes/hour = 3 hours.

Time Calculations: We often need to calculate durations or determine start/end times.

Example 3: A bus journey from Cape Town to Port Elizabeth takes 13 hours and 45 minutes.

If the bus leaves Cape Town at 18:30 (6:30 PM), at what time will it arrive in Port Elizabeth?

Solution: Add 13 hours to 18:30: 18:30 + 13:00 = 31:

3

0. Since there are only 24 hours in a day, subtract 24 hours: 31:30 - 24:00 = 07:

3

0. Add the 45 minutes: 07:30 + 0:45 = 08:

1

5. Therefore, the bus will arrive in Port Elizabeth at 08:15 the next day. b) Temperature Temperature measures the degree of hotness or coldness of an object or environment. In South Africa, we primarily use Celsius (°C).

Scales of Temperature: Celsius (°C): Water freezes at 0°C and boils at 100°

C. Fahrenheit (°F): Water freezes at 32°F and boils at 212°

F. Temperature Conversions: To convert from Celsius to Fahrenheit: °F = (°C 9/5) + 32 To convert from Fahrenheit to Celsius: °C = (°F - 32) 5/9 Example 4: Convert 25°C to Fahrenheit.

Solution: °F = (25 9/5) + 32 = 45 + 32 = 77°

F. Example 5: Convert 68°F to Celsius.

Solution: °C = (68 - 32) 5/9 = 36 * 5/9 = 20°

C. Temperature in Daily Life: Understanding temperature is important for clothing choices, cooking, health (e.g., body temperature), and agriculture (e.g., frost warnings). c) Rates A rate is a ratio that compares two quantities with different units. Rates are essential for understanding various real-world scenarios.

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

Cost per Unit: Price per item or quantity (e.g., Rands per kilogram, Rands per liter).

Consumption Rate: Quantity consumed per unit of time (e.g., liters of water per day, kWh of electricity per month).

Exchange Rate: The value of one currency in terms of another.

Calculating Rates: Rate = Quantity 1 / Quantity 2 Example 6: A car travels 300 km in 4 hours. Calculate the average speed.

Solution: Speed = Distance / Time = 300 km / 4 hours = 75 km/h.

Example 7: A 2-liter bottle of cool drink costs R

2

8. Calculate the cost per liter.

Solution: Cost per liter = Total cost / Volume = R28 / 2 liters = R14/liter.

Example 8: Your household uses 150 kWh of electricity in 30 days. What is the average daily consumption rate?

Solution: Consumption rate = Total consumption / Number of days = 150 kWh / 30 days = 5 kWh/day. Guided Practice (With Solutions)

Question 1: A taxi charges R15 per kilometer. How much will it cost to travel 25 km?

Solution: Cost = Rate Distance = R15/km * 25 km = R

3

7

5. Commentary:* This is a simple application of the cost per unit rate. We multiply the rate by the quantity (distance) to find the total cost.

Question 2: Convert 38°C to Fahrenheit.

Solution: °F = (38 9/5) + 32 = 68.4 + 32 = 100.4°F

Commentary:* We use the formula for converting Celsius to Fahrenheit. Be careful to follow the order of operations.

Question 3: A borehole pump delivers 500 liters of water in 2 hours. What is the flow rate in liters per minute?

Solution: First, convert hours to minutes: 2 hours 60 minutes/hour = 120 minutes Flow rate = Volume / Time = 500 liters / 120 minutes = 4.17 liters/minute (approximately).

Commentary:* This problem requires two steps: converting time units and then calculating the rate. Paying attention to the units is crucial.

Question 4: If a worker earns R480 for working 8 hours, what is their hourly wage?

Solution: Hourly Wage = Total Earnings / Number of Hours = R480 / 8 hours = R60/hour.

Commentary:* A straightforward calculation of a rate (earnings per hour). Independent Practice (Questions Only)

Question 1: A train journey from Pretoria to Durban is scheduled to take 12 hours and 15 minutes.

If the train departs Pretoria at 22:45 (10:45 PM), what time is it scheduled to arrive in Durban?

Question 2: Convert 95°F to Celsius.

Question 3: A tap is leaking water at a rate of 25 milliliters per minute. How many liters of water will be wasted in one day? (Remember: 1 liter = 1000 milliliters)

Question 4: A shop sells potatoes for R45 per 5 kg bag. What is the cost per kilogram of potatoes?

Question 5: You are comparing two cell phone data packages. Package A offers 5 GB of data for R150, while Package B offers 8 GB of data for R

2

2

0. Which package offers a lower cost per GB?

Question 6: A car's fuel consumption is 8 liters per 100 km.