Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Define ratio, rate, and percentage with real-world examples.
• Express ratios in their simplest form.
• Calculate simple percentages of whole numbers.
• Distinguish between ratios and rates.
• Solve basic word problems involving these concepts.

Lesson summary

This week, we begin our exploration of ratio, rate, and percentage. These are powerful mathematical tools that help us understand and compare quantities in our daily lives. Imagine sharing sweets with your friends, calculating the cost of airtime per minute, or understanding how much discount you're getting on a new pair of school shoes – ratio, rate, and percentage are all involved! In South Africa, understanding these concepts is crucial for informed decision-making when it comes to budgeting, understanding service delivery statistics, and participating in economic activities.

Lesson notes

2.1 Ratio: A ratio is a comparison of two or more quantities of the same kind. It tells us how much of one thing there is compared to another.

Ratios can be written in several ways: Using the word "to" (e.g., 3 to 5)

Using a colon (:) (e.g., 3:5) As a fraction (e.g., 3/5)

Important: The order matters!

A ratio of 3:5 is different from a ratio of 5:

3. Also, the units must be the same for both quantities. For example, you can't directly compare 3 apples to 5 oranges in a ratio unless you are thinking about them as a total number of fruit.

Example 1 (Simplifying Ratios): In a Grade 6 class, there are 12 girls and 18 boys. What is the ratio of girls to boys in its simplest form?

Step 1: Write the ratio: Girls to Boys = 12:18 Step 2: Find the greatest common factor (GCF) of 12 and

1

8. The GCF is

6. Step 3: Divide both sides of the ratio by the GCF: 12 ÷ 6 = 2 and 18 ÷ 6 = 3 Step 4: Write the simplified ratio: 2:3 So, the ratio of girls to boys in its simplest form is 2:

3. This means for every 2 girls, there are 3 boys.

Example 2 (Real-life ratio): Sipho has a spaza shop. For every 5 loaves of brown bread he sells, he sells 2 loaves of white bread. What is the ratio of brown bread sold to white bread sold?

The ratio is 5:

2. This means Sipho sells more brown bread than white bread. 2.2 Rate: A rate is a comparison of two quantities of different kinds. It tells us how much of one thing changes relative to another. Rates always involve units.

Common examples include: Speed (kilometers per hour - km/h) Price per item (rand per kilogram - R/kg)

Wages (rand per hour - R/hour)

Important: Always include the units when expressing a rate.

Example 1 (Calculating rate): A taxi travels 120 kilometers in 2 hours. What is its average speed?

Step 1: Identify the quantities: Distance = 120 km, Time = 2 hours Step 2: Divide the distance by the time to find the speed: 120 km ÷ 2 hours = 60 km/h The taxi's average speed is 60 kilometers per hour.

Example 2 (Real-life rate): Apples cost R15 for a 3 kg bag. What is the price per kilogram?

Step 1: Identify the quantities: Price = R15, Mass = 3 kg Step 2: Divide the price by the mass: R15 ÷ 3 kg = R5/kg The price per kilogram of apples is R5. 2.3 Percentage: A percentage is a special kind of ratio or fraction where the denominator is always

1

0

0. The word "percent" means "out of one hundred" or "per hundred". We use the symbol % to represent percentage.

Important: A percentage represents a part of a whole, where the whole is considered to be 100%.

Example 1 (Calculating Percentage): In a class of 40 learners, 20 learners walk to school. What percentage of learners walk to school?

Step 1: Write the fraction representing the proportion of learners who walk: 20/40 Step 2: Simplify the fraction: 20/40 = 1/2 Step 3: Convert the fraction to a percentage by multiplying by 100%: (1/2) 100% = 50% 50% of the learners walk to school. Example 2 (Calculating a percentage of a quantity): A shop is offering a 20% discount on a pair of shoes that originally costs R

3

0

0. How much is the discount?

Step 1: Convert the percentage to a decimal by dividing by 100: 20% ÷ 100 = 0.20 Step 2: Multiply the original price by the decimal: R300 0.20 = R60 The discount is R

6

0. Guided Practice (With Solutions)

Question 1: A recipe for vetkoek calls for 2 cups of flour and 1 cup of water. What is the ratio of flour to water? Express it in its simplest form.

Solution: Step 1: Write the ratio: Flour to Water = 2:1 Step 2: The ratio is already in its simplest form because 2 and 1 have no common factors other than

1. Answer: The ratio of flour to water is 2:

1. Question 2: A municipality fixed 45 potholes in 5 days. What is the rate of potholes fixed per day?

Solution: Step 1: Identify the quantities: Potholes = 45, Days = 5 Step 2: Divide the number of potholes by the number of days: 45 potholes ÷ 5 days = 9 potholes/day Answer: The rate is 9 potholes fixed per day.

Question 3: A school has 200 learners, and 60% of them play sports. How many learners play sports?

Solution: Step 1: Convert the percentage to a decimal: 60% ÷ 100 = 0.60 Step 2: Multiply the total number of learners by the decimal: 200 learners 0.60 = 120 learners Answer: 120 learners play sports.

Question 4: Simplify the ratio 24:

3

6. Solution: Step 1: Write the ratio: 24:36 Step 2: Find the greatest common factor (GCF) of 24 and

3

6. The GCF is

1

2. Step 3: Divide both sides of the ratio by the GCF: 24 ÷ 12 = 2 and 36 ÷ 12 = 3 Step 4: Write the simplified ratio: 2:3 Answer: The ratio of 24:36 simplifies to 2:

3. Independent Practice (Questions Only) In a fruit basket, there are 8 apples and 6 bananas. What is the ratio of apples to bananas in its simplest form? A car travels 360 km in 4 hours. What is its average speed in km/h? A soccer team won 75% of their games. If they played 20 games, how many games did they win?

Simplify the ratio 15:

4

5. If 3 kg of oranges cost R42, what is the cost per kilogram? A shop offers a 15% discount on a shirt that costs R200.