Types, Comparing, Ordering and Decimal Conversion of Fractions for Primary 6

Class: Primary 6
Term: 1st Term
Week: 3
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Whole Numbers, Decimal Place Value, Expanded.
Topic: FRACTIONS
Subject Matter: Meaning and types of fractions, ordering fractions using less than greater than and equals, ordering fractions in ascending and descending order, expressing fractions as decimals and decimals as fractions, quantitative reasoning on fractions.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define a fraction and identify its parts.
• Identify and differentiate between proper, improper, and mixed fractions.
• Compare fractions using the symbols , and =.
• Order fractions in ascending and descending order.
• Convert fractions to decimals and decimals to fractions.
• Solve quantitative reasoning problems involving fractions.

Affective Domain:

• Appreciate the importance of fractions in everyday situations.
• Participate actively in class discussions and activities.

Psychomotor Domain:

• Use cardboard cuttings to represent different fractions.
• Correctly write and simplify fractions and decimals.
• Accurately apply comparison symbols and order fractions.

Social Domain:

• Collaborate effectively with peers during group activities.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4-6)
• State Unified Scheme of Work (Primary 6)
• New General Mathematics for Primary Schools Book 6

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Charts showing different types of fractions
• Posters with fraction examples
• Workbook
• Cardboard cuttings to demonstrate fractions
• Marker

Rationale for the Lesson

Understanding fractions is important for pupils because they are used in many daily activities, such as sharing items, measuring ingredients, and understanding discounts. This lesson helps pupils to perform operations with fractions and decimals accurately in real-life situations.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of whole numbers, division, and simple sharing concepts.

Lesson Content/Board Summary

FRACTIONS

Meaning of Fractions

A fraction represents a part of a whole or a collection. It consists of a numerator (the number of parts being considered) and a denominator (the total number of equal parts the whole is divided into).

Example: 1/2 means 1 part out of 2 equal parts.

Types of Fractions

The following are types of fractions:

• Proper Fraction: A fraction where the numerator is smaller than the denominator.

  Example: 2/5, 3/7

• Improper Fraction: A fraction where the numerator is equal to or greater than the denominator.

  Example: 7/4, 5/5

• Mixed Number: A number consisting of a whole number and a proper fraction.

  Example: 1 3/4, 2 1/2

• Equivalent Fractions: Fractions that represent the same value, even though they look different.

  Example: 1/2, 2/4, 3/6 are equivalent fractions.

Ordering Fractions

Comparing Fractions using , and =

To compare fractions, you can make their denominators the same or use cross-multiplication.

Method 1: Same Denominator

1. Find the Least Common Multiple (LCM) of the denominators. This will be the new common denominator.
2. Convert each fraction to an equivalent fraction with the common denominator.
3. Compare the numerators. The fraction with the larger numerator is the larger fraction.

Example 1: Compare 3/4 and 2/3.

Step 1: Find LCM of 4 and 3. LCM(4,3) = 12.

Step 2: Convert to equivalent fractions with denominator 12.

3/4 = (3 × 3) / (4 × 3) = 9/12

2/3 = (2 × 4) / (3 × 4) = 8/12

Step 3: Compare numerators: 9 > 8.

Therefore, 9/12 > 8/12, which means 3/4 > 2/3.

Method 2: Cross-Multiplication

1. Multiply the numerator of the first fraction by the denominator of the second fraction.
2. Multiply the numerator of the second fraction by the denominator of the first fraction.
3. Compare the products. The side with the larger product corresponds to the larger fraction.

Example 2: Compare 5/6 and 4/5.

Step 1: Cross-multiply.

5 × 5 = 25 (for 5/6)

4 × 6 = 24 (for 4/5)

Step 2: Compare products: 25 > 24.

Therefore, 5/6 > 4/5.

Ordering Fractions in Ascending and Descending Order

To order fractions, convert them to equivalent fractions with a common denominator (usually the LCD) and then arrange them based on their numerators.

Ascending Order: From smallest to largest.

Descending Order: From largest to smallest.

Example: Arrange the fractions 1/2, 2/3, 1/4 in ascending order.

Step 1: Find the LCM of the denominators (2, 3, 4). LCM(2,3,4) = 12.

Step 2: Convert each fraction to an equivalent fraction with denominator 12.

1/2 = (1 × 6) / (2 × 6) = 6/12

2/3 = (2 × 4) / (3 × 4) = 8/12

1/4 = (1 × 3) / (4 × 3) = 3/12

Step 3: Arrange the numerators in ascending order: 3, 6, 8.

Step 4: Write the fractions in ascending order:

3/12, 6/12, 8/12

Therefore, 1/4, 1/2, 2/3 (in their original forms).

Expressing Fractions as Decimals and Decimals as Fractions

Fractions as Decimals

To convert a fraction to a decimal, divide the numerator by the denominator.

Example 1: Convert 3/4 to a decimal.

Step 1: Divide the numerator (3) by the denominator (4).

3 ÷ 4 = 0.75

Example 2: Convert 1/5 to a decimal.

Step 1: Divide 1 by 5.

1 ÷ 5 = 0.2

Decimals as Fractions

To convert a decimal to a fraction, write the decimal as a fraction with a denominator that is a power of 10 (10, 100, 1000, etc.) based on the number of decimal places, then simplify the fraction.

NOTE: One decimal place means denominator 10, two decimal places means denominator 100, etc.

Example 1: Convert 0.6 to a fraction.

Step 1: Write the decimal as a fraction. Since there is one decimal place, the denominator is 10.

0.6 = 6/10

Step 2: Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). GCD(6,10) = 2.

6 ÷ 2 / 10 ÷ 2 = 3/5

Example 2: Convert 0.25 to a fraction.

Step 1: Write as a fraction. Two decimal places means denominator 100.

0.25 = 25/100

Step 2: Simplify. GCD(25,100) = 25.

25 ÷ 25 / 100 ÷ 25 = 1/4

Quantitative Reasoning on Fractions

Quantitative reasoning problems on fractions involve applying fraction concepts to solve word problems or interpret patterns. These problems test understanding of fraction operations and their real-world applications.

Example: If 1/3 of a class are boys and there are 24 pupils in total, how many girls are in the class?

Step 1: Find the number of boys.

Number of boys = 1/3 of 24 = (1/3) × 24 = 8 boys.

Step 2: Find the number of girls.

Number of girls = Total pupils – Number of boys = 24 – 8 = 16 girls.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them to recall situations where they have divided something into parts, like sharing a cake or dividing a piece of land. The teacher then introduces the topic of fractions as a way to represent these parts.

Pupils’ Activity: Pupils respond to the teacher’s questions and share their experiences of dividing things into parts.

Learning Point: Pupils connect prior knowledge of division and sharing to the concept of fractions.

Step 2: Meaning and Types of Fractions

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher uses cardboard cuttings to demonstrate different fractions (e.g., cutting a circle into halves, quarters). The teacher explains the meaning of numerator and denominator and then defines and gives examples of proper, improper, mixed, and equivalent fractions, writing them on the board.

Pupils’ Activity: Pupils observe the demonstrations, identify the parts of a fraction, and copy definitions and examples into their notebooks.

Learning Point: Pupils understand the meaning of a fraction and can identify different types of fractions.

Step 3: Ordering Fractions (Comparing)

Time: 8 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher explains how to compare fractions using common denominators or cross-multiplication, working through examples on the board. The teacher guides pupils to use the symbols , or = correctly.

Pupils’ Activity: Pupils follow the teacher’s examples, ask questions for clarity, and practice comparing simple fractions using the given symbols.

Learning Point: Pupils learn methods for comparing fractions and can apply the correct comparison symbols.

Step 4: Ordering Fractions (Ascending/Descending)

Time: 8 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher explains how to order fractions in ascending and descending order by finding the Least Common Denominator (LCD). The teacher provides an example and works through the steps, ensuring pupils understand each stage.

Pupils’ Activity: Pupils pay attention to the steps for finding the LCD and ordering fractions. They attempt to solve similar problems in their workbooks or on their slates.

Learning Point: Pupils can arrange a set of fractions in ascending or descending order.

Step 5: Fractions as Decimals and Decimals as Fractions

Time: 8 minutes

Teaching Skill: Explanation/Conversion

Teacher’s Activity: The teacher explains how to convert fractions to decimals by dividing the numerator by the denominator. The teacher also demonstrates converting decimals to fractions by considering place value and simplifying the resulting fraction. Examples are provided for both conversions.

Pupils’ Activity: Pupils listen to the explanations, copy the examples, and practice converting fractions and decimals as guided by the teacher.

Learning Point: Pupils can express fractions as decimals and decimals as fractions.

Step 6: Quantitative Reasoning on Fractions

Time: 4 minutes

Teaching Skill: Application/Problem Solving

Teacher’s Activity: The teacher introduces quantitative reasoning problems involving fractions, explaining that these require applying fraction knowledge to solve practical scenarios. The teacher presents a simple word problem and guides pupils through its solution.

Pupils’ Activity: Pupils engage with the word problem, suggest possible solutions, and follow the teacher’s steps to arrive at the answer.

Learning Point: Pupils can apply fraction concepts to solve basic quantitative reasoning problems.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is a fraction?
2. Give two examples of a proper fraction and an improper fraction.
3. Compare 5/8 and 3/4 using , or =.
4. Arrange the fractions 1/3, 1/6, 1/2 in descending order.
5. Convert 0.75 to a fraction in its simplest form.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes

Teaching Skill: Summarization/Consolidation

Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the importance of understanding and applying fractions in daily life. The teacher assigns homework from the textbook.

Pupils’ Activity: Pupils listen to the summary and copy down the assigned homework.

Learning Point: Pupils consolidate their understanding and prepare for independent practice.

Home Task: Solve three new exercises on FRACTIONS. Show each step and check each answer.

Lesson Keywords

• Fraction – A part of a whole.
• Numerator – The top number in a fraction, showing how many parts are taken.
• Denominator – The bottom number in a fraction, showing the total number of equal parts.
• Proper fraction – A fraction where the numerator is smaller than the denominator.
• Improper fraction – A fraction where the numerator is equal to or greater than the denominator.
• Mixed number – A number made up of a whole number and a proper fraction.
• Equivalent fractions – Fractions that represent the same value.
• Ascending – Arranging from smallest to largest.
• Descending – Arranging from largest to smallest.
• Decimal – A number that uses a decimal point to show parts of a whole, based on powers of ten.
• LCD (Least Common Denominator) – The smallest common multiple of the denominators of two or more fractions.

Differentiation

For pupils who struggle, the teacher will provide additional visual aids, more hands-on activities with fraction manipulatives, and simplified examples. For advanced learners, the teacher will offer more complex quantitative reasoning problems or challenge them to explore operations with fractions.

Note for teachers using this lesson plan

Ensure to have a variety of visual aids, especially cardboard cuttings, to make the abstract concept of fractions concrete for Primary 6 pupils. Encourage active participation and group work. Provide ample practice opportunities for each concept before moving to the next. Pay close attention to pupils’ understanding of LCD, as it is foundational for ordering and adding/subtracting fractions.