Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and represent simple fractions.
• Compare and order simple fractions with the same denominator.
• Solve word problems involving fractions.
• Recognise and name equivalent fractions.
• Understand how fractions relate to a whole.

Lesson summary

Fractions are everywhere around us! Whether you're sharing a slab of chocolate with your friends, measuring ingredients for a koeksister recipe, or figuring out how much of your airtime you've used, you're using fractions. Understanding fractions helps us to fairly share, accurately measure, and solve everyday problems. This week, we'll be focusing on understanding and applying simple fractions (halves, quarters, thirds, fifths, sixths, eighths, and tenths) in real-life South African contexts. Being able to work with fractions is a crucial skill that will help you throughout your schooling and in many practical situations.

Lesson notes

What is a Fraction? A fraction represents a part of a whole. Imagine a perfectly round vetkoek. If you cut it into equal pieces, each piece represents a fraction of the whole vetkoek.

A fraction has two main parts: Numerator: The top number, which tells us how many parts we have.

Denominator: The bottom number, which tells us the total number of equal parts the whole is divided into.

We write a fraction like this: Numerator / Denominator. For example, 1/2 (one half).

Understanding the Denominator: The denominator is very important! It tells us the size of the parts. The bigger the denominator, the smaller each part. For example, imagine sharing a loaf of bread. If you share it with 2 people (denominator of 2), each person gets a bigger piece than if you share it with 8 people (denominator of 8).

Examples of Simple Fractions: 1/2 (One half): The whole is divided into 2 equal parts, and we have 1 of those parts. Imagine cutting a boerewors roll in half. 1/4 (One quarter): The whole is divided into 4 equal parts, and we have 1 of those parts. Think about dividing a pizza into 4 slices. 1/3 (One third): The whole is divided into 3 equal parts, and we have 1 of those parts. Imagine sharing a loaf of bread amongst 3 people. 1/5 (One fifth): The whole is divided into 5 equal parts, and we have 1 of those parts. 1/6 (One sixth): The whole is divided into 6 equal parts, and we have 1 of those parts. 1/8 (One eighth): The whole is divided into 8 equal parts, and we have 1 of those parts. Think of a cake cut into 8 slices. 1/10 (One tenth): The whole is divided into 10 equal parts, and we have 1 of those parts.

Representing Fractions: We can represent fractions using: Diagrams: Draw a shape (like a circle, square, or rectangle) and divide it into the number of parts shown by the denominator. Then, shade the number of parts shown by the numerator.

Concrete Materials: Use objects like counters, blocks, or even slices of biltong to represent the whole and its parts.

Example: To represent 3/4, draw a rectangle. Divide it into 4 equal parts. Shade 3 of those parts. Comparing Fractions with the Same Denominator: When fractions have the same denominator, comparing them is easy! The fraction with the larger numerator is the bigger fraction.

Example: Which is bigger: 2/5 or 4/5? Since the denominators are the same (5), we compare the numerators. 4 is bigger than 2, so 4/5 is bigger than 2/

5. Equivalent Fractions: Equivalent fractions are different fractions that represent the same amount.

Example: 1/2 and 2/4 are equivalent fractions. Imagine a chocolate bar. Cutting it in half (1/2) gives you the same amount as cutting it into four pieces and taking two of them (2/4). To find equivalent fractions, you can multiply or divide both the numerator and the denominator by the same number.

Example: To find an equivalent fraction for 1/3, we can multiply both the numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/

6. So, 1/3 and 2/6 are equivalent fractions.

Fractions and the Whole: A fraction shows part of a whole. If the numerator and denominator are the same, the fraction represents the whole.

Example: 4/4 represents the whole. Imagine a pizza cut into 4 slices. If you have all 4 slices, you have the whole pizza.

Word Problems with Fractions: Let's look at some examples of how fractions are used in everyday situations: Example 1: Sipho has a koeksister. He eats 1/2 of it. How much of the koeksister did he eat? Sipho ate one out of two equal parts of the koeksister.

Example 2: Aisha has a packet of 10 chips. She gives 2/5 of them to her friend Thando. How many chips did Thando receive? First, find 1/5 of 10: 10 / 5 = 2 chips Then, find 2/5 of 10: 2 x 2 = 4 chips Thando received 4 chips. Guided Practice (With Solutions)

Question 1: Draw a diagram to represent the fraction 2/

3. Solution: Draw a rectangle. Divide the rectangle into 3 equal parts (because the denominator is 3). Shade 2 of the parts (because the numerator is 2).

Commentary: This question tests your ability to visually represent a fraction. Make sure the parts are as equal as possible when drawing.

Question 2: Which is smaller: 1/4 or 3/4? Explain your answer.

Solution: 1/4 is smaller than 3/

4. Both fractions have the same denominator (4), so we compare the numerators. 1 is smaller than 3, therefore 1/4 is smaller.

Commentary: This question focuses on comparing fractions with the same denominator. Remember to focus on the numerator when the denominators are the same.

Question 3: Lerato has a chocolate bar divided into 6 equal pieces. She eats 1/3 of the chocolate bar. How many pieces did she eat?

Solution: We need to find 1/3 of

6. Divide the total number of pieces (6) by the denominator (3): 6 / 3 =

2. Lerato ate 2 pieces of chocolate.

Commentary: This question combines understanding fractions with a real-life scenario. Remember to identify what the "whole" is in the problem (the whole chocolate bar) and what fraction of it is being considered.