Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define ratio, rate, and percentage with real-world examples.
• Express ratios in their simplest form.
• Calculate common rates like speed and cost per item.
• Convert between common fractions, decimals, and percentages.
• Solve simple problems using these concepts.

Lesson summary

Ratio, rate, and percentage are fundamental mathematical concepts that help us understand the relationships between quantities. This week, we will begin our journey into these concepts, building a strong foundation for future mathematical studies. These concepts are incredibly relevant in our everyday lives in South Africa. For instance, understanding ratios helps us share sweets fairly with our friends or mix concrete for a building project. Rates help us understand the speed of a taxi or the cost per loaf of bread. Percentages are everywhere, from discounts at clothing stores to understanding how much tax is added to a bill.

Lesson notes

Ratio: A ratio is a way of comparing two or more quantities. It shows how much of one thing there is compared to another.

A ratio can be written in several ways: Using a colon (e.g., 3:2) As a fraction (e.g., 3/2) Using the word "to" (e.g., 3 to 2)

Important: The order matters! 3:2 is different from 2:

3. Example 1: In a class, there are 15 boys and 20 girls. What is the ratio of boys to girls?

Boys: Girls = 15:20 To simplify the ratio, we find the highest common factor (HCF) of 15 and 20, which is

5. Divide both sides of the ratio by 5: 15 ÷ 5 : 20 ÷ 5 Simplified ratio: 3:4 Therefore, the ratio of boys to girls in the class is 3:

4. This means for every 3 boys, there are 4 girls.

Example 2: Nomusa is making a traditional Zulu bead bracelet. She uses 7 red beads, 5 blue beads, and 3 yellow beads. What is the ratio of red beads to blue beads to yellow beads?

Red: Blue: Yellow = 7:5:3 Since 7, 5, and 3 have no common factors other than 1, the ratio is already in its simplest form.

Rate: A rate is a ratio that compares two quantities with different units. It tells us how much of one quantity there is for each unit of another quantity. Common examples include speed (distance/time), price per item (cost/quantity), and earnings per hour (money/time).

Example 1: A taxi travels 120 kilometers in 2 hours. What is the average speed of the taxi in kilometers per hour (km/h)? Rate = Distance / Time Rate = 120 km / 2 hours Rate = 60 km/h Therefore, the average speed of the taxi is 60 kilometers per hour.

Example 2: A spaza shop sells 5 apples for R

2

0. What is the cost per apple? Rate = Cost / Quantity Rate = R20 / 5 apples Rate = R4 per apple Therefore, each apple costs R

4. Percentage: A percentage is a way of expressing a number as a fraction of

1

0

0. The word "percent" means "out of 100". The symbol for percentage is %.

Converting Fractions to Percentages: To convert a fraction to a percentage, multiply the fraction by 100/100 (which is equal to 1, so it doesn't change the value) and then simplify.

Example 1: Convert 1/4 to a percentage. (1/4) (100/100) = 100/4 % 100/4 = 25 Therefore, 1/4 = 25% Example 2: Convert 3/5 to a percentage. (3/5) (100/100) = 300/5 % 300/5 = 60 Therefore, 3/5 = 60% Converting Decimals to Percentages: To convert a decimal to a percentage, multiply the decimal by 100 and add the % sign.

Example 1: Convert 0.25 to a percentage. 25 100 = 25 Therefore, 0.25 = 25% Example 2: Convert 0.8 to a percentage. 8 100 = 80 Therefore, 0.8 = 80% Converting Percentages to Fractions: To convert a percentage to a fraction, write the percentage as a fraction with a denominator of 100, and then simplify the fraction.

Example 1: Convert 40% to a fraction. 40% = 40/100 Simplify by dividing both numerator and denominator by their HCF (20): 40/20 / 100/20 40/100 = 2/5 Therefore, 40% = 2/5 Example 2: Convert 75% to a fraction. 75% = 75/100 Simplify by dividing both numerator and denominator by their HCF (25): 75/25 / 100/25 75/100 = 3/4 Therefore, 75% = 3/4 Converting Percentages to Decimals: To convert a percentage to a decimal, divide the percentage by

1

0

0. Example 1: Convert 30% to a decimal. 30% = 30 / 100 30 / 100 = 0.3 Therefore, 30% = 0.3 Example 2: Convert 85% to a decimal. 85% = 85 / 100 85 / 100 = 0.85 Therefore, 85% = 0.85 Guided Practice (With Solutions)

Question 1: In a fruit basket, there are 6 oranges and 9 bananas. What is the ratio of oranges to bananas in its simplest form?

Solution: Ratio of oranges to bananas = 6:9 The HCF of 6 and 9 is

3. Divide both sides by 3: 6 ÷ 3 : 9 ÷ 3 = 2:3 The simplified ratio is 2:

3. Commentary: We found the ratio and then simplified it by dividing both sides by their highest common factor.

Question 2: A car travels 300 km in 5 hours. What is the average speed of the car in km/h?

Solution: Rate = Distance / Time Rate = 300 km / 5 hours Rate = 60 km/h

Commentary: We used the formula for rate (distance/time) and substituted the given values to find the speed.

Question 3: Convert 2/5 to a percentage.

Solution: (2/5) (100/100) = 200/5 % 200/5 = 40 Therefore, 2/5 = 40%

Commentary: We multiplied the fraction by 100% to convert it into a percentage.

Question 4: Convert 65% to a decimal.

Solution: 65% = 65 / 100 65 / 100 = 0.65 Therefore, 65% = 0.65

Commentary: To convert percentage to decimal divide the percentage value by

1

0

0. Independent Practice (Questions Only) In a class of 40 learners, 16 are wearing blue shirts. What is the ratio of learners wearing blue shirts to the total number of learners? Simplify the ratio. A tap leaks 15 liters of water in 3 hours. What is the rate of water leakage in liters per hour? Convert 7/10 to a percentage. Convert 0.35 to a percentage. Convert 12% to a fraction in its simplest form. Convert 90% to a decimal. A recipe for vetkoek requires 3 cups of flour and 2 cups of water. What is the ratio of flour to water? A bus travels 240 km in 4 hours. Calculate the average speed of the bus. Express 1/8 as a percentage.