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 Celsius and Fahrenheit temperatures.
• Calculate and interpret rates like speed and unit pricing.
• Use formulas to solve measurement problems.

Lesson summary

This week, we delve into the world of measurement, focusing specifically on time, temperature, and rates. These concepts are fundamental to navigating everyday life in South Africa and beyond. From managing your time to understanding weather forecasts and calculating costs, these skills are essential for informed decision-making. Imagine planning a trip from Johannesburg to Cape Town – you need to understand distances, speeds (rates), and time zones. Or, consider reading a weather report to decide what to wear – understanding temperatures in Celsius is crucial. Understanding rates is key to budgeting, comparing prices, and calculating loan repayments.

Lesson notes

2.1 Time Time is a fundamental aspect of our lives. We use it to schedule activities, measure durations, and understand historical events.

Units of Time: 1 second (s) 1 minute (min) = 60 seconds 1 hour (h) = 60 minutes 1 day = 24 hours 1 week = 7 days 1 month = Approximately 30 days (but can vary: February has 28 or 29, others have 31) 1 year = 365 days (366 in a leap year) 1 decade = 10 years 1 century = 100 years 1 millennium = 1000 years Time Conversions: To convert between units, we multiply or divide.

Remember: Smaller to Larger: Divide (e.g., seconds to minutes)

Larger to Smaller: Multiply (e.g., hours to minutes)

Example 1: How many minutes are there in 3.5 hours? 1 hour = 60 minutes 3.5 hours = 3.5 60 minutes = 210 minutes Example 2: How many hours are there in 540 minutes? 1 hour = 60 minutes 540 minutes = 540 / 60 hours = 9 hours Example 3: Sipho started working at 08:30 and finished at 17:

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5. How long did he work?

From 08:30 to 17:00 is 8 hours and 30 minutes.

From 17:00 to 17:15 is 15 minutes. Total time = 8 hours 30 minutes + 15 minutes = 8 hours 45 minutes. 2.2 Temperature Temperature measures how hot or cold something is. We commonly use Celsius (°C) in South Africa, but Fahrenheit (°F) is also used in some contexts.

Temperature Scales: 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 1: Convert 25°C to Fahrenheit. °F = (25 9/5) + 32 °F = (45) + 32 °F = 77°F Example 2: Convert 68°F to Celsius. °C = (68 - 32) 5/9 °C = (36) 5/9 °C = 20°C Understanding Temperature: Pay attention to temperature when planning outdoor activities. A temperature of 35°C is very hot and requires precautions like staying hydrated and avoiding strenuous activity during the hottest part of the day. A temperature of 5°C is cold and requires warm clothing. 2.3 Rates A rate compares two quantities with different units. Common examples include speed, fuel consumption, and unit pricing.

Speed: Speed = Distance / Time Distance = Speed Time Time = Distance / Speed Units of Speed: kilometers per hour (km/h), meters per second (m/s)

Fuel Consumption: Litres per 100 kilometers (L/100km) - How many litres of fuel a vehicle uses to travel 100km Kilometers per litre (km/L) - How many kilometers a vehicle can travel per litre of fuel.

Unit Pricing: Cost per unit (e.g., price per kilogram, price per liter)

Example 1: Speed A car travels 360 km in 4 hours. What is its average speed? Speed = Distance / Time Speed = 360 km / 4 hours Speed = 90 km/h Example 2: Fuel Consumption A car uses 30 liters of petrol to travel 450 km. What is its fuel consumption in L/100km?

We use ratios: `30 litres / 450 km = x litres / 100 km` To solve for x: `x = (30 litres 100 km) / 450 km = 6.67 litres` The fuel consumption is 6.67 L/100km.

Example 3: Unit Pricing A 2 kg bag of potatoes costs R

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0. A 5 kg bag costs R

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0. Which is the better value? 2 kg bag: R30 / 2 kg = R15/kg 5 kg bag: R70 / 5 kg = R14/kg The 5 kg bag is the better value (lower price per kilogram). Guided Practice (With Solutions)

Question 1: Convert 2 hours and 30 minutes into minutes.

Solution: 1 hour = 60 minutes 2 hours = 2 60 minutes = 120 minutes Total minutes = 120 minutes + 30 minutes = 150 minutes Question 2: The weather forecast predicts a high of 30°

C. What is this temperature in Fahrenheit?

Solution: °F = (°C 9/5) + 32 °F = (30 9/5) + 32 °F = (54) + 32 °F = 86°F Question 3: A train travels from Pretoria to Durban, a distance of 600 km, in 8 hours. What is its average speed in km/h?

Solution: Speed = Distance / Time Speed = 600 km / 8 hours Speed = 75 km/h Question 4: A taxi charges R15 per kilometre for the first 5 kilometres and R12 per kilometre for every kilometre after that. How much will a 12 km trip cost?

Solution: Cost of the first 5 km: 5 km R15/km = R75 Distance after the first 5 km: 12 km - 5 km = 7 km Cost of the remaining 7 km: 7 km R12/km = R84 Total cost: R75 + R84 = R159 Independent Practice (Questions Only) Convert 3 days and 6 hours into hours. Convert 45°F to Celsius. A cyclist travels 45 km in 2 hours and 15 minutes. What is their average speed in km/h? A car's fuel tank has a capacity of 50 litres. If the car's fuel consumption is 8 L/100km, how far can the car travel on a full tank? A shop sells apples at R8 each or a bag of 6 apples for R

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2. Which is the better buy?

A bus leaves Cape Town at 09:45 and arrives in George at 16:

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0. How long was the journey? If the speed limit on a highway is 120 km/h, how long will it take to travel 420km, assuming you drive at the speed limit? A certain recipe requires an oven temperature of 180°C. What is this temperature in Fahrenheit? A company charges R250 for a plumber for the first hour, then R180 for each hour after that. How much would it cost if the plumber worked for 3.5 hours? A rectangular plot of land measures 20 metres long and 15 metres wide.