Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Define and write ratios in different ways.
• Simplify ratios to their simplest form.
• Tell the difference between ratios and rates.
• Calculate percentages of whole numbers.
• Solve simple word problems.

Lesson summary

This week, we embark on an exciting journey into the world of ratios, rates, and percentages. These mathematical tools are essential for understanding and interpreting the world around us. From comparing the price of groceries at different stores to understanding the impact of sales tax, ratios, rates, and percentages are indispensable in everyday life. Think about cooking – recipes use ratios! Think about sports – calculating winning percentages! Think about saving money – understanding interest rates! In South Africa, this knowledge empowers you to make informed decisions as consumers, entrepreneurs, and citizens.

Lesson notes

2.1 Ratios: Comparing Quantities A ratio is a way to compare two or more quantities of the same kind. It shows how much of one thing there is compared to another.

Ratios can be written in several ways: Using a colon (:): For example, if there are 3 apples and 5 oranges, the ratio of apples to oranges is 3:

5. As a fraction: The same ratio can be written as 3/

5. Using words: We can say "the ratio of apples to oranges is 3 to 5." Important: The order in which you write the ratio matters! 3:5 is different from 5:

3. The first number always refers to the first quantity mentioned.

Example 1: In a Grade 6 class, there are 15 boys and 10 girls.

The ratio of boys to girls is 15:

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0. The ratio of girls to boys is 10:

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5. The ratio of boys to the total number of students is 15:25 (15 + 10 = 25). 2.2 Simplifying Ratios Just like fractions, ratios can be simplified. To simplify a ratio, divide each part of the ratio by the highest common factor (HCF) of the numbers.

Example 2: Simplify the ratio 12:

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8. The HCF of 12 and 18 is

6. Divide both parts of the ratio by 6: 12 ÷ 6 = 2 and 18 ÷ 6 =

3. The simplified ratio is 2:3. 2.3 Rates: Comparing Different Kinds of Quantities A rate is a ratio that compares two quantities of different kinds.

Think of it like this: ratios compare similar things (apples to oranges), while rates compare dissimilar things (distance to time). Rates often involve units.

Example 3: A car travels 200 kilometers in 4 hours. The rate is 200 kilometers / 4 hours, which simplifies to 50 kilometers per hour (km/h). This is a speed, which is a type of rate.

Example 4: The shop sells 3 oranges for R

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2. The rate is R12 / 3 oranges, which simplifies to R4 per orange. 2.4 Percentages: Parts out of 100 A percentage is a special type of ratio that compares a number to

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

Example 5: 25% means 25 out of 100, which can be written as the fraction 25/100. 2.5 Calculating Percentages of Whole Numbers To find a percentage of a whole number, we can use the following steps: Convert the percentage to a fraction by dividing it by

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0. Multiply the fraction by the whole number.

Example 6: What is 20% of 80? Convert 20% to a fraction: 20/100 = 1/5 Multiply the fraction by 80: (1/5) * 80 = 16 Therefore, 20% of 80 is

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6. Example 7: Nomusa has 300 marbles. She gives 40% of them to her friend Sipho. How many marbles did Nomusa give to Sipho? Convert 40% to a fraction: 40/100 = 2/5 Multiply the fraction by 300: (2/5) * 300 = 120 Nomusa gave Sipho 120 marbles. Guided Practice (With Solutions)

Question 1: In a fruit basket, there are 8 bananas and 6 apples. What is the ratio of apples to bananas in its simplest form?

Solution: Write the ratio of apples to bananas: 6:8 Find the HCF of 6 and 8: The HCF is

2. Divide both parts of the ratio by 2: 6 ÷ 2 = 3 and 8 ÷ 2 =

4. The simplified ratio is 3:

4. Commentary: This question focuses on writing and simplifying ratios. We identify the quantities and then simplify by finding the highest common factor.

Question 2: A baker uses 2 cups of flour for every 1 cup of sugar in a cake recipe. What is the ratio of flour to sugar? If the baker wants to make a larger cake and uses 6 cups of flour, how much sugar will they need to use, maintaining the same ratio?

Solution: The ratio of flour to sugar is 2:

1. To maintain the ratio, we need to find what to multiply 2 by to get 6. 6 / 2 =

3. Multiply the amount of sugar (1 cup) by the same number (3): 1 * 3 = 3 cups. The baker will need 3 cups of sugar.

Commentary: This question focuses on understanding equivalent ratios. We find a multiplier to maintain the correct proportions.

Question 3: A runner completes a 10 km race in 1 hour. What is the runner's average speed in kilometers per hour (km/h)?

Solution: Speed = Distance / Time Speed = 10 km / 1 hour Speed = 10 km/h

Commentary: This question introduces the concept of rate and its calculation using distance and time. It emphasizes understanding the units (km/h).

Question 4: Calculate 35% of

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0. Solution: Convert 35% to a fraction: 35/100 Multiply the fraction by 200: (35/100) * 200 Simplify: 35 * 2 = 70 Therefore, 35% of 200 is

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0. Commentary: This question focuses on calculating percentages of whole numbers. We cover the conversion of percentages to fractions and the multiplication process.

Question 5: A store offers a 15% discount on a shirt that originally costs R

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0. How much is the discount in Rand?

Solution: Convert 15% to a fraction: 15/100 Multiply the fraction by R80: (15/100) * R80 Simplify: (15 * 80) / 100 = 1200/100 = R12 The discount is R

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2. Commentary: This question applies percentages to a real-world scenario (discounts). It reinforces the understanding of calculating a percentage of a quantity. Independent Practice (Questions Only) In a class of 40 students, 16 are wearing blue shirts. What is the ratio of students wearing blue shirts to the total number of students? Simplify the ratio.