Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Perform calculations involving percentages in financial contexts.
• Apply ratio and proportion to solve problems.
• Convert between different units of measurement.
• Estimate values and perform mental calculations.
• Use a calculator effectively and appropriately.

Lesson summary

Mathematical Literacy at the Grade 11 level builds upon prior knowledge of numbers and calculations, extending these concepts to solve more complex real-world problems. A strong foundation in number sense and calculation skills is critical for navigating everyday life in South Africa. This includes managing personal finances, understanding statistics presented in the media, interpreting maps and plans, and making informed decisions about purchasing goods and services. The ability to accurately perform calculations, estimate values, and interpret numerical data empowers individuals to be active and responsible citizens.

Lesson notes

2. 1.

Percentages: A percentage is a way of expressing a number as a fraction of

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0. The symbol "%" means "per cent" or "out of 100." Percentages are used extensively in finance, statistics, and everyday life.

Finding a Percentage of a Number: To find x% of a number, multiply the number by x/

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0. Example: What is 15% of R250? (15/100) R250 = R37.50 Percentage Increase/Decrease: Percentage Increase: [(New Value - Original Value) / Original Value] 100% Percentage Decrease: [(Original Value - New Value) / Original Value] 100%

Example: A loaf of bread increased in price from R12 to R

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5. What is the percentage increase? [(R15-R12)/R12] 100% = 25% Profit and Loss: Profit Percentage: [(Selling Price - Cost Price) / Cost Price] 100% Loss Percentage: [(Cost Price - Selling Price) / Cost Price] 100%

Example: A street vendor buys vetkoek for R3 each and sells them for R5 each. What is the profit percentage? [(R5-R3)/R3] 100% = 66.67% (approximately)

Simple Interest: Simple interest is calculated only on the principal amount. Simple Interest (SI) = (Principal Rate * Time) / 100, where Principal is the initial amount, Rate is the interest rate per year, and Time is the number of years. Total Amount = Principal + SI

Example: You invest R5000 at a simple interest rate of 8% per year for 3 years. What is the total amount after 3 years? SI = (R5000 8 * 3) / 100 = R

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0. Total Amount = R5000 + R1200 = R6200 2.

2. Ratio and Proportion: A ratio compares two or more quantities. A proportion is a statement that two ratios are equal.

Ratios can be written as a:b, a/b, or "a to b." Sharing in a Ratio: To divide a quantity in the ratio a:b, divide the total quantity into (a+b) parts and then allocate 'a' parts to one person and 'b' parts to another.

Example: Two siblings, Thando and Zandi, inherit R15000 in the ratio 2:

3. How much does each sibling receive?

Total parts: 2+3 =

5. Each part: R15000/5 = R

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0. Thando receives 2 R3000 = R

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0. Zandi receives 3 * R3000 = R

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0. Scaling: Scaling involves increasing or decreasing quantities proportionally.

Example: A recipe for pap requires 2 cups of maize meal and 4 cups of water. If you want to make a larger batch using 6 cups of maize meal, how much water do you need?

The ratio of maize meal to water is 2:4 (or 1:2). If you have 6 cups of maize meal, you need 6 2 = 12 cups of water.

Map Reading: Map scales represent the relationship between distances on a map and corresponding distances on the ground.

A scale of 1:50000 means that 1 cm on the map represents 50000 cm (or 500 meters) on the ground.

Example: On a map with a scale of 1:50000, the distance between two towns is 8 cm. What is the actual distance between the towns in kilometers? Actual distance = 8 cm 50000 = 400000 cm = 4000 meters = 4 kilometers. 2.

3. Units of Measurement and Conversions: Understanding and converting between different units of measurement is essential for solving practical problems. Familiarity with both metric and, to a lesser extent, imperial units is necessary.

Metric to Metric Conversions: Length: 1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm Mass: 1 kg = 1000 g; 1 tonne = 1000 kg Volume: 1 L = 1000 mL Metric to Imperial Conversions (Approximate): 1 inch ≈ 2.54 cm 1 foot ≈ 30.48 cm 1 mile ≈ 1.609 km 1 kg ≈ 2.2 lbs 1 litre ≈ 0.264 US gallons

Example: A piece of wood is measured as 2.5 meters long. What is its length in centimeters? 2.5 m 100 cm/m = 250 cm. 2.

4. Estimation and Mental Calculations: Developing estimation skills allows for quick approximations and helps in verifying the reasonableness of calculated answers. Mental calculation techniques include rounding numbers, using compatible numbers, and breaking down complex calculations into simpler steps.

Example: Estimate the cost of 7 items priced at R19.99 each. Round R19.99 to R

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0. Estimated cost: 7 R20 = R140. 2.

5. Calculator Usage: Calculators are valuable tools for performing complex calculations, but it's important to understand their limitations and use them appropriately. Learners should be familiar with basic calculator functions, including addition, subtraction, multiplication, division, percentages, and memory functions. It's crucial to double-check the input and ensure the calculator is in the correct mode (e.g., degree or radian mode for trigonometric functions – though not applicable to this week's focus). Always interpret the calculator's output in the context of the problem. Guided Practice (With Solutions)

Question 1: A shop is having a 20% off sale on all clothing. A shirt originally priced at R180 is on sale. What is the sale price of the shirt?

Solution: Calculate the discount amount: 20% of R180 = (20/100) * R180 = R36 Subtract the discount from the original price: R180 - R36 = R144 The sale price of the shirt is R

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4. Commentary: This question applies the concept of percentage decrease in a real-world shopping scenario.

Question 2: Sandile and Aisha are saving money to buy a second-hand car.