Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate percentages and percentage changes (discounts, markups).
• Apply ratio and proportion to solve practical problems.
• Use different methods of calculation (mental, calculator).
• Work with and convert different units of measurement.
• Interpret and use scales and maps to calculate distances and areas.

Lesson summary

This week, we delve deeper into the world of numbers and calculations, focusing specifically on applying these skills to solve real-world problems. Understanding how to work with numbers effectively is crucial for making informed decisions about your finances, understanding statistics in the news, and even planning everyday activities. Whether you are budgeting your pocket money, comparing cell phone deals, or calculating the best route to school, a solid understanding of numbers is essential. In South Africa, where financial literacy and access to resources are often challenges, mastering these skills can empower you to make smarter choices and improve your quality of life.

Lesson notes

2.1 Percentages and Percentage Change A percentage is a way of expressing a number as a fraction of

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0. The word "percent" means "out of 100." So, 25% means 25 out of 100, or 25/100, which can be simplified to 1/4 or 0.

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5. Calculating a Percentage: To find a percentage of a number, multiply the number by the percentage (expressed as a decimal).

Example: What is 15% of R200? 15% = 15/100 = 0.15 15% of R200 = 0.15 R200 = R30 Percentage Increase/Decrease (Percentage Change): Percentage change tells us how much a quantity has increased or decreased relative to its original value.

The formula is: Percentage Change = [(New Value - Original Value) / Original Value] 100% If the result is positive, it's a percentage increase. If the result is negative, it's a percentage decrease.

Example: A shop sells a t-shirt for R

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0. They increase the price to R

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0. What is the percentage increase? Original Value = R80 New Value = R100 Percentage Increase = [(R100 - R80) / R80] 100% = (R20 / R80) 100% = 0.25 100% = 25%

Example: A loaf of bread cost R15 last year, and now it costs R

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2. What is the percentage decrease? Original Value = R15 New Value = R12 Percentage Decrease = [(R12 - R15) / R15] 100% = (-R3 / R15) 100% = -0.2 100% = -20% 2.2 Ratio and Proportion A ratio compares two or more quantities.

It can be written in several ways: a:b (e.g., 2:3) a to b (e.g., 2 to 3) a/b (e.g., 2/3) A proportion states that two ratios are equal. If a/b = c/d, then the ratios a:b and c:d are in proportion.

Solving Proportions: The "cross-multiplication" method is often used. If a/b = c/d, then ad = bc.

Example: If 3 apples cost R12, how much will 7 apples cost? Let x be the cost of 7 apples.

We can set up a proportion: 3/12 = 7/x Cross-multiply: 3x = 12 7 3x = 84 x = 84 / 3 = 28 Therefore, 7 apples will cost R28. 2.3 Units of Measurement and Conversion We use units to measure length (meters, centimeters, kilometers), mass (kilograms, grams), volume (liters, milliliters), time (seconds, minutes, hours, days), and temperature (degrees Celsius).

Conversion: Converting between units involves multiplying or dividing by a conversion factor.

Example: Convert 5 kilometers to meters. 1 kilometer = 1000 meters 5 kilometers = 5 1000 meters = 5000 meters

Example: Convert 2 hours to minutes. 1 hour = 60 minutes 2 hours = 2 60 minutes = 120 minutes 2.4 Maps and Scales A map is a representation of an area. A scale on a map shows the relationship between a distance on the map and the corresponding distance on the ground.

Scales can be expressed as: Ratio scale: 1:100,000 (This means 1 cm on the map represents 100,000 cm (or 1 km) on the ground).

Statement scale: 1 cm represents 1 km.

Linear scale: A line divided into segments representing distances on the ground.

Example: A map has a scale of 1:50,

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0. Two towns are 4 cm apart on the map. What is the actual distance between the towns? 1 cm on the map represents 50,000 cm on the ground. 4 cm on the map represents 4 50,000 cm = 200,000 cm on the ground.

Convert cm to km: 200,000 cm = 2000 m = 2 km Therefore, the actual distance between the towns is 2 km. Guided Practice (With Solutions)

Question 1: A shop offers a 20% discount on a pair of shoes that originally cost R

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0. What is the discounted price?

Solution: Calculate the discount amount: 20% of R450 = 0.20 R450 = R90 Subtract the discount from the original price: R450 - R90 = R360 Answer: The discounted price is R

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0. Question 2: A recipe for vetkoek requires 500g of flour to make 20 vetkoek. You want to make 30 vetkoek. How much flour do you need?

Solution: Set up a proportion: 500g / 20 vetkoek = x g / 30 vetkoek Cross-multiply: 20x = 500 30 20x = 15000 x = 15000 / 20 = 750 Answer: You need 750g of flour.

Question 3: Convert 3.5 meters to centimeters.

Solution: 1 meter = 100 centimeters 5 meters = 3.5 100 centimeters = 350 centimeters Answer: 3.5 meters is equal to 350 centimeters.

Question 4: On a map with a scale of 1:25,000, a park is represented by a square with sides of 2 cm. What is the actual area of the park in square meters?

Solution: 1 cm on the map represents 25,000 cm on the ground. 2 cm on the map represents 2 25,000 cm = 50,000 cm on the ground.

Convert cm to meters: 50,000 cm = 500 meters. The park is a square with sides of 500 meters. Area of the park = side side = 500 m * 500 m = 250,000 square meters.

Answer: The actual area of the park is 250,000 square meters. Independent Practice (Questions Only)

Question 1: A store buys a soccer ball for R150 and marks it up by 40%. What is the selling price of the soccer ball?

Question 2: A salary increases from R5000 to R

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0. What is the percentage increase?

Question 3: If 4 litres of paint cover 20 square meters, how many litres of paint are needed to cover 35 square meters?

Question 4: Convert 2500 grams to kilograms.

Question 5: You need to be at school at 7:30 AM.