Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Calculate and apply percentages in financial contexts.
• Solve problems using ratio and proportion.
• Calculate simple and compound interest for savings and loans.
• Convert between different units of measurement.
• Interpret numerical information from tables and charts.

Lesson summary

This week, we will delve deeper into numbers and calculations, building upon your existing knowledge from previous grades and applying it to more complex scenarios relevant to your daily lives as South African citizens. Understanding numbers and calculations is crucial for making informed decisions regarding personal finances, understanding data presented in the media, and participating effectively in the economy. From budgeting your pocket money to understanding interest rates on loans, this knowledge is empowering. We will focus on consolidating previously learned concepts and extending them to include ratio, proportion, rate, percentages, and financial calculations.

Lesson notes

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

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0. The word "percent" means "per hundred." To convert a fraction or decimal to a percentage, multiply by

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0. To convert a percentage to a decimal, divide by

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0. Finding a percentage of a quantity: Multiply the percentage (as a decimal) by the quantity.

Example: 25% of 200 = 0.25 200 = 50 Calculating percentage increase/decrease: `[(New Value - Original Value) / Original Value] 100`. If the result is positive, it's an increase; if negative, it's a decrease.

Example 1: A pair of shoes originally costs R

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0. They are on sale for 15% off. What is the sale price?

Step 1: Calculate the discount amount: 15% of R400 = 0.15 R400 = R60 Step 2: Subtract the discount from the original price: R400 - R60 = R340 Answer: The sale price is R

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0. Example 2: The price of bread increased from R14 to R

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6. What is the percentage increase?

Step 1: Find the difference: R16 - R14 = R2 Step 2: Divide the difference by the original price: R2 / R14 = 0.142857...

Step 3: Multiply by 100 to express as a percentage: 0.142857... 100 = 14.29% (rounded to two decimal places)

Answer: The price of bread increased by 14.29%. 2.2 Ratios and Proportions: A ratio compares two or more quantities.

It can be written as a:b, a/b, or "a to b." A proportion states that two ratios are equal (a/b = c/d).

Direct Proportion: As one quantity increases, the other quantity increases proportionally.

Indirect Proportion (Inverse Proportion): As one quantity increases, the other quantity decreases proportionally.

Example 3: A recipe for vetkoek requires 2 cups of flour for every 1 cup of water. What is the ratio of flour to water? If you want to make a larger batch using 6 cups of flour, how much water do you need?

Ratio of flour to water: 2:1 Setting up a proportion: 2/1 = 6/x (where x is the amount of water needed)

Solving for x: 2x = 6 => x = 3 Answer: You need 3 cups of water.

Example 4: It takes 4 workers 6 hours to paint a wall. How long will it take 8 workers, assuming they work at the same rate? This is an example of inverse proportion. More workers will take less time. Let x be the time taken by 8 workers. 4 workers 6 hours = 8 workers * x hours 24 = 8x x = 3 Answer: It will take 3 hours. 2.3 Simple and Compound Interest: Simple Interest: Interest is calculated only on the principal amount. `Interest = Principal Rate * Time` (I = PRT)

Compound Interest: Interest is calculated on the principal amount plus any accumulated interest.

The formula is: `A = P(1 + r/n)^(nt)`, where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Example 5: You invest R5000 in a savings account that pays 6% simple interest per year. How much interest will you earn after 3 years? I = PRT I = R5000 0.06 * 3 I = R900 Answer: You will earn R900 in interest.

Example 6: You invest R5000 in a savings account that pays 6% interest per year, compounded annually. How much will you have after 3 years? A = P(1 + r/n)^(nt) A = R5000(1 + 0.06/1)^(13) A = R5000(1.06)^3 A = R5000 1.191016 A = R5955.08 (rounded to two decimal places)

Answer: You will have R5955.08. 2.4 Units of Measurement and Conversions: It is essential to be able to work with different units of measurement (length, mass, volume, time) and convert between them.

Common conversions include: Length: 1 meter (m) = 100 centimeters (cm), 1 kilometer (km) = 1000 meters (m)

Mass: 1 kilogram (kg) = 1000 grams (g)

Volume: 1 liter (L) = 1000 milliliters (mL)

Time: 1 hour = 60 minutes, 1 minute = 60 seconds Example 7: Convert 3.5 kilometers to meters. 1 km = 1000 m 3.5 km = 3.5 1000 m = 3500 m Answer: 3.5 kilometers is equal to 3500 meters. 2.5 Interpreting Data: Understanding how to read and interpret data from tables, charts, and graphs is a critical life skill. Pay attention to the labels, scales, and legends to accurately understand the information being presented. Guided Practice (With Solutions)

Question 1: A cellphone costs R

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0. The store is offering a 20% discount. What is the sale price?

Solution: Calculate the discount: 20% of R2500 = 0.20 R2500 = R500 Subtract the discount from the original price: R2500 - R500 = R2000 Answer: The sale price is R

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0. Commentary: This question tests your understanding of percentages and discounts, a common scenario in retail settings.

Question 2: A recipe for samosas requires 3 cups of flour and 2 cups of water. If you want to make a larger batch using 9 cups of flour, how much water do you need?

Solution: Set up a proportion: 3/2 = 9/x Cross-multiply: 3x = 18 Solve for x: x = 6 Answer: You need 6 cups of water.

Commentary: This tests your understanding of direct proportion, applying it to a familiar recipe.

Question 3: You invest R8000 in a fixed deposit account that pays 8% simple interest per year for 5 years. How much interest will you earn?