Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Convert common fractions to decimals.
• Convert decimals to common fractions.
• Compare and order fractions and decimals.
• Recognize and use equivalent forms.

Lesson summary

This week, we delve deeper into the relationship between whole numbers, common fractions, and decimals. Understanding these concepts is crucial because they are fundamental to everyday life in South Africa. From calculating the cost of groceries at your local spaza shop to understanding percentages in sports statistics or even calculating distances on maps, fractions and decimals are constantly used. We’ll build upon your existing knowledge and explore how these different types of numbers relate to each other. This week, we'll focus particularly on converting between these forms and comparing their values.

Lesson notes

This week, we delve deeper into the relationship between whole numbers, common fractions, and decimals. Understanding these concepts is crucial because they are fundamental to everyday life in South Africa. From calculating the cost of groceries at your local spaza shop to understanding percentages in sports statistics or even calculating distances on maps, fractions and decimals are constantly used. We’ll build upon your existing knowledge and explore how these different types of numbers relate to each other. This week, we'll focus particularly on converting between these forms and comparing their values. By the end of this week, you will be able to: Objective 1: Convert common fractions to decimals (with denominators that are factors of 10, 100, and 1000). (CAPS: Number, Operations and Relationships - Fractions)

Objective 2: Convert decimals to common fractions (with denominators of 10, 100, and 1000). (CAPS: Number, Operations and Relationships - Fractions)

Objective 3: Compare and order common fractions and decimals using the symbols >, 1/

2. Example 2: Order the following from smallest to largest: 0.25, 1/5, 0.

3. Step 1:* Convert all to decimals: 1/5 = 2/10 = 0.2 Step 2:* Now we have 0.25, 0.2, and 0.

3. Step 3:* Ordering from smallest to largest: 0.2, 0.25, 0.

3. Step 4:* Therefore, the original order is 1/5, 0.25, 0.3 2.5 Equivalent Fractions and Decimals Equivalent fractions and decimals represent the same value but are written differently. For example, 1/2, 2/4, 5/10, and 0.5 are all equivalent. We use equivalent fractions and decimals all the time when simplifying calculations. Guided Practice (With Solutions)

Question 1: Convert 3/5 to a decimal.

Solution: To convert 3/5 to a decimal, we need to make the denominator

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0. We can do this by multiplying both the numerator and denominator by 2. (3 x 2) / (5 x 2) = 6/10 = 0.

6. Commentary: We chose 2 because 5 multiplied by 2 gives us 10, making it easy to write as a decimal.

Question 2: Convert 0.8 to a fraction in its simplest form.

Solution: 0.8 is eight-tenths, so it is 8/

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0. To simplify, we find the greatest common factor of 8 and 10, which is

2. Divide both numerator and denominator by 2: (8 ÷ 2) / (10 ÷ 2) = 4/

5. Commentary: Always simplify your fractions to their lowest terms.

Question 3: Which is greater: 0.4 or 2/5?

Solution: Convert 2/5 to a decimal. 2/5 = (2 x 2) / (5 x 2) = 4/10 = 0.

4. Therefore, 0.4 = 2/

5. Commentary: Converting to a common form (decimal in this case) makes comparison straightforward.

Question 4: Arrange the following from smallest to largest: 1/4, 0.3, 1/

5. Solution: Convert all to decimals: 1/4 = 0.25, 0.3 is already a decimal, and 1/5 = 0.

2. Ordering from smallest to largest: 0.2, 0.25, 0.

3. Therefore, the original order is 1/5, 1/4, 0.

3. Commentary: Ensure you answer using the original form asked in the question.

Question 5: Express 0.6 as a fraction and simplify to its lowest terms.

Solution: 0.6 represents six-tenths, which can be written as 6/

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0. Both 6 and 10 are divisible by

2. Therefore, (6÷2)/(10÷2) = 3/

5. Commentary: Simplification involves dividing both the numerator and denominator by their greatest common factor. Independent Practice (Questions Only) Convert 2/5 to a decimal. Convert 0.75 to a fraction in its simplest form.

Which is smaller: 0.9 or 4/5? Arrange the following from largest to smallest: 3/4, 0.6, 2/

5. Express 0.4 as a fraction and simplify to its lowest terms. Convert 1/8 to a decimal. Express 0.05 as a fraction in its simplest form.

Which is greater: 1/2 or 0.45? Sipho spent 0.3 of his money on a sweet and 1/4 of his money on a juice. Which did he spend more on? Write 3/25 as a decimal. Real-life Applications / Integration Shopping at the Supermarket: Imagine your mother gives you R20 to buy bread and milk. Bread costs R12.50 and milk costs R6.

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5. Use decimals to calculate the total cost (R12.50 + R6.75 = R19.25) and how much change you should receive (R20 - R19.25 = R0.75). You could also express the price of each item as a fraction of the total money.

Sharing Food Equally: You and three friends are sharing a pizza that is cut into 8 slices. You want to determine what fraction of the pizza each person receives. Each person gets 2 slices, which is 2/8 of the pizza.

You can also express this as a decimal: 2/8 = 1/4 = 0.

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5. This shows each person receives 0.25 or 25% of the pizza.

Following a Recipe: Many recipes use fractions and decimals to indicate the amount of each ingredient. For example, a recipe might call for 1/2 cup of flour or 0.75 teaspoons of salt. Understanding fractions and decimals is essential for accurately measuring ingredients and baking successfully. Differentiation, Remediation and Extension Remediation (For Struggling Learners): Use concrete materials like fraction bars or pie charts to visually represent fractions and decimals. Focus on converting simple fractions (1/2, 1/4, 1/5) to decimals and vice versa.