Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Identify and represent simple fractions.
• Solve word problems using fractions.
• Compare fractions with the same denominator.
• Recognize equivalent fractions like 1/2 and 2/4.
• Understand a fraction as part of a whole.

Lesson summary

Fractions are a fundamental part of mathematics and are essential for understanding the world around us. In South Africa, we encounter fractions daily, from sharing food with family and friends to measuring ingredients for a delicious malva pudding. Understanding fractions helps us to be fair, accurate, and confident in our everyday lives. This week, we will focus on simple fractions and how they apply to real-life situations we experience in our communities. We'll explore concepts like halves, quarters, thirds, fifths, and tenths, and learn how to identify, represent, and compare them.

Lesson notes

What is a Fraction? A fraction represents a part of a whole. The whole can be a single object, like a pizza, or a group of objects, like a bag of oranges.

A fraction has two parts: Numerator: The number on top of the line. It tells us how many parts we have.

Denominator: The number below the line. It tells us how many equal parts the whole is divided into. For example, in the fraction 1/4 (one quarter): 1 is the numerator (we have one part) 4 is the denominator (the whole is divided into four equal parts) Common Fractions Let's look at some common fractions and how they are used: Half (1/2): The whole is divided into two equal parts. Imagine sharing a vetkoek equally between two friends. Each friend gets 1/2 (one half) of the vetkoek.

Quarter (1/4): The whole is divided into four equal parts. Think of cutting a birthday cake into four equal slices for four guests. Each guest gets 1/4 (one quarter) of the cake.

Third (1/3): The whole is divided into three equal parts. Picture sharing a loaf of bread equally amongst three family members. Each person gets 1/3 (one third) of the loaf.

Fifth (1/5): The whole is divided into five equal parts. Imagine a packet of sweets shared equally among five children. Each child receives 1/5 (one fifth) of the sweets.

Tenth (1/10): The whole is divided into ten equal parts. Consider a chocolate bar with ten squares. If you eat one square, you have eaten 1/10 (one tenth) of the bar. Representing Fractions Fractions can be represented in various ways: Concrete Objects: Using real objects like fruits, vegetables, or building blocks to show fractions.

Example: To show 1/2, you can cut an apple into two equal pieces.

Diagrams: Using drawings or pictures to represent fractions.

Example: Drawing a circle and dividing it into four equal parts, then shading one part to represent 1/

4. Symbols: Using numbers and a line to represent fractions (e.g., 1/2, 3/4). Comparing Fractions (Same Denominator) When fractions have the same denominator, the fraction with the larger numerator is bigger.

Example: Which is bigger: 2/5 or 3/5? Since both fractions have the denominator 5, we compare the numerators: 2 and

3. Since 3 is bigger than 2, 3/5 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 having half a pizza (1/2). If you cut that half into two equal pieces, you now have two quarters (2/4) of the pizza. You still have the same amount of pizza, just cut into smaller pieces.

Worked example

Sharing Mangoes: Zola has 6 mangoes and wants to share them equally with her friend Thando. How many mangoes will each person get? What fraction of the mangoes does each person receive?

Solution:

There are two people (Zola and Thando).

They share 6 mangoes equally, so each person gets 6 / 2 = 3 mangoes.

Each person receives 3 out of the 6 mangoes, which can be represented as the fraction 3/6.

3/6 is equivalent to 1/

2. Each person receives half (1/2) of the mangoes.

Baking a Cake: Maria is baking a cake and the recipe calls for 1/4 cup of sugar. If she wants to make two cakes, how much sugar will she need?

Solution:

One cake needs 1/4 cup of sugar.

Two cakes will need 1/4 + 1/4 = 2/4 cups of sugar.

2/4 is equivalent to 1/

2. Maria needs 1/2 cup of sugar.

Sharing a Chocolate Bar: Sipho has a chocolate bar with 10 squares. He eats 2 squares. What fraction of the chocolate bar did he eat? What fraction is remaining?

Solution:

The chocolate bar has 10 squares, so the denominator is

1

0.

Sipho ate 2 squares, so the fraction he ate is 2/

1

0.

The remaining squares are 10 - 2 =

8.

The fraction of the chocolate bar remaining is 8/

1

0.

Guided Practice (With Solutions)

Question: Nomusa has a pizza cut into 8 slices. She eats 3 slices. What fraction of the pizza did Nomusa eat?

Solution:

The pizza is cut into 8 slices (denominator = 8).

Nomusa ate 3 slices (numerator = 3).

Fraction of pizza eaten: 3/

8. Commentary:* This question directly tests the ability to identify the numerator and denominator in a simple scenario.

Question: A bag contains 5 apples. Two of the apples are red. What fraction of the apples are red?

Solution:

There are 5 apples in total (denominator = 5).

2 apples are red (numerator = 2).

Fraction of red apples: 2/

5. Commentary:* This problem links fractions to identifying parts of a group, reinforcing the concept of a fraction representing a part of a whole.

Question: Lerato has a ribbon. She cuts it into four equal pieces. She uses one piece to tie her hair. What fraction of the ribbon did she use?

Solution:

The ribbon is divided into 4 equal pieces (denominator = 4).

Lerato used 1 piece (numerator = 1).

Fraction of ribbon used: 1/

4. Commentary:* This question uses a real-life scenario (hair ribbon) to illustrate fractions, making it more relatable.

Question: Thabo has a packet of 10 biscuits. He gives half of the biscuits to his sister. How many biscuits does his sister get? What fraction of the biscuits does his sister get?

Solution:

Half of 10 is 10 / 2 =

5. His sister gets 5 biscuits.

Therefore, his sister gets 5/10 of the biscuits

Commentary:* This combines fraction knowledge with division and highlights the concept of a half.

Independent Practice (Questions Only)

A chocolate bar is divided into 5 equal pieces. John eats 2 pieces. What fraction of the chocolate bar did John eat?

There are 10 marbles in a bag. 3 marbles are blue. What fraction of the marbles are blue?

A pizza is cut into 4 equal slices. Sarah eats one slice. What fraction of the pizza did Sarah eat?

Nomsa has a cake. She cuts it into 3 equal parts. She gives one part to her friend. What fraction of the cake did she give to her friend?

A garden has 10 flowers. Half of the flowers are roses. How many roses are there? What fraction of the flowers are roses?

A team plays 5 soccer matches. They win 4 matches. What fraction of the matches did they win?

A loaf of bread is cut into 10 slices. You eat 3 slices. What fraction of the bread did you eat? What fraction of the bread is remaining?

Peter has a collection of 8 toy cars. 2 of them are red. What fraction of his toy cars are red?

You share a pie equally among 4 friends. What fraction of the pie does each friend get?

Lerato has 5 apples. She eats one apple each day for two days. What fraction of the apples did she eat?