Equivalent fractions and Ordering of fractions for JSS 1

Class: JSS 1
Term: First Term
Week: 10
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: NUMBER NUMERATION
Focal competence: Applying equivalent fractions while sharing items or money
Key competencies/values: Collaboration
Skills:

• Solve problems on quantitative aptitude involving fractions

Previous Lesson: and and Place value in binary numbers
Topic: Fractions
Subject Matter: Equivalent fractions, Ordering of fractions, Conversion of fractions to decimals and vise-versa, Conversion of fractions to percentages and vise-versa

Specific Objectives

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

Cognitive Domain

• Define equivalent fractions.
• Identify the numerator and denominator in a fraction.
• Convert fractions to decimals and decimals to fractions.
• Convert fractions to percentages and percentages to fractions.
• Arrange given fractions in ascending and descending order.

Affective Domain

• Appreciate the importance of fractions in everyday sharing.
• Collaborate with peers to solve problems involving fractions.

Psychomotor Domain

• Demonstrate the conversion of fractions using diagrams or models.
• Solve quantitative aptitude problems involving fractions.

Social Domain

• Participate actively in group discussions on fraction conversions.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Junior Secondary Schools 1
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Flash cards with worked examples on fractions
• Video player or projector to watch videos on how to Convert fractions to decimals and percentages or vice versa
• Fraction charts or diagrams
• Whiteboard and markers

Rationale for the Lesson

This lesson is essential for building a strong foundation in numerical reasoning, as fractions are fundamental to understanding quantities and proportions. It equips students with practical skills for everyday situations like sharing resources and interpreting data. Mastery of these concepts prepares students for more advanced mathematical topics.

Prerequisite/Previous Knowledge

Students should have a basic understanding of what a fraction represents, including simple fractions like halves, thirds, and quarters. They should also be familiar with basic multiplication and division operations.

Lesson Content/Board Summary

Fractions: Equivalent Fractions, Ordering, and Conversions

Fraction Notation

A fraction represents a part of a whole. It consists of two main parts:

1. Numerator: The top number, which shows how many parts are being considered.
2. Denominator: The bottom number, which shows the total number of equal parts the whole is divided into.

For example, in the fraction (frac{3}{4}), 3 is the numerator and 4 is the denominator.

Equivalent Fractions

Equivalent fractions are fractions that represent the same value, even though they have different numerators and denominators.

To find equivalent fractions, you multiply or divide both the numerator and the denominator by the same non-zero number.

Example:

To find an equivalent fraction for (frac{1}{2}):

1. Multiply numerator and denominator by 2: (frac{1 times 2}{2 times 2} = frac{2}{4})
2. Multiply numerator and denominator by 3: (frac{1 times 3}{2 times 3} = frac{3}{6})

So, (frac{1}{2}), (frac{2}{4}), and (frac{3}{6}) are all equivalent fractions.

Ordering of Fractions

To arrange fractions in ascending (smallest to largest) or descending (largest to smallest) order, you need to compare them. This is easiest when they have a common denominator.

Steps to order fractions:

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

Example: Arrange (frac{1}{2}), (frac{2}{3}), (frac{1}{4}) in ascending order.

1. LCM of 2, 3, 4 is 12.
2. Convert fractions:
   • (frac{1}{2} = frac{1 times 6}{2 times 6} = frac{6}{12})
   • (frac{2}{3} = frac{2 times 4}{3 times 4} = frac{8}{12})
   • (frac{1}{4} = frac{1 times 3}{4 times 3} = frac{3}{12})
3. Compare numerators: 3, 6, 8.

So, the ascending order is (frac{3}{12}, frac{6}{12}, frac{8}{12}), which means (frac{1}{4}, frac{1}{2}, frac{2}{3}).

Conversion of Fractions to Decimals and Vice-Versa

Fraction to Decimal

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

Example 1

Question: Convert (frac{3}{4}) to a decimal.

Solution:

Step 1: Divide the numerator by the denominator.

(3 div 4)

Step 2: Perform the division.

(3 div 4 = 0.75)

Answer: (0.75)

Decimal to Fraction

To convert a decimal to a fraction:

1. Write the decimal as a fraction with the decimal number as the numerator and a power of 10 (10, 100, 1000, etc.) as the denominator, corresponding to the number of decimal places.
2. Simplify the fraction to its lowest terms.

Example 2

Question: Convert (0.25) to a fraction.

Solution:

Step 1: Write the decimal as a fraction over a power of 10.

(0.25 = frac{25}{100}) (since there are two decimal places)

Step 2: Simplify the fraction.

(frac{25 div 25}{100 div 25} = frac{1}{4})

Answer: (frac{1}{4})

Conversion of Fractions to Percentages and Vice-Versa

Fraction to Percentage

To convert a fraction to a percentage, multiply the fraction by 100%.

Example 1

Question: Convert (frac{3}{5}) to a percentage.

Solution:

Step 1: Multiply the fraction by 100%.

(frac{3}{5} times 100%)

Step 2: Perform the multiplication.

(frac{300}{5}% = 60%)

Answer: (60%)

Percentage to Fraction

To convert a percentage to a fraction:

1. Write the percentage as a fraction with the number over 100.
2. Simplify the fraction to its lowest terms.

Example 2

Question: Convert (75%) to a fraction.

Solution:

Step 1: Write the percentage as a fraction over 100.

(75% = frac{75}{100})

Step 2: Simplify the fraction.

(frac{75 div 25}{100 div 25} = frac{3}{4})

Answer: (frac{3}{4})

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Video Presentation, Group Work, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Questioning/Recall

Teacher’s Activity: The teacher greets the students and reviews previous knowledge on basic fractions by asking questions like: “What is a fraction?” and “Can you give an example of a fraction and identify its numerator and denominator?” The teacher then introduces the topic of equivalent fractions, ordering, and conversions.

Pupils’ Activity: Students answer questions about basic fractions and listen attentively to the introduction of the new topic.

Learning Point: Basic fraction recall

Step 2: Equivalent Fractions

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains what equivalent fractions are and demonstrates how to find them using multiplication and division. The teacher uses flashcards to show different equivalent fractions (e.g., (frac{1}{2}), (frac{2}{4}), (frac{3}{6})).

Pupils’ Activity: Students observe the flashcards, listen to the explanation, and participate in identifying equivalent fractions.

Learning Point: Understanding equivalent fractions

Step 3: Ordering of Fractions

Time: 7 minutes

Teaching Skill: Explanation/Guided Practice

Teacher’s Activity: The teacher explains the steps for ordering fractions by finding a common denominator. The teacher works through an example on the board, guiding students to convert fractions and compare their numerators.

Pupils’ Activity: Students follow the steps, ask questions, and attempt to order a simple set of fractions with teacher guidance.

Learning Point: Ordering fractions method

Step 4: Fraction to Decimal Conversion

Time: 5 minutes

Teaching Skill: Video Presentation/Explanation

Teacher’s Activity: The teacher plays a short video demonstrating how to convert fractions to decimals by dividing the numerator by the denominator. After the video, the teacher explains the process clearly and works through an example.

Pupils’ Activity: Students watch the video, listen to the explanation, and observe the worked example.

Learning Point: Fraction to decimal conversion

Step 5: Decimal to Fraction Conversion

Time: 5 minutes

Teaching Skill: Video Presentation/Explanation

Teacher’s Activity: The teacher plays another video showing how to convert decimals to fractions, emphasizing writing the decimal over a power of ten and simplifying. The teacher then provides an additional example on the board.

Pupils’ Activity: Students watch the video, pay attention to the steps, and practice simplifying fractions.

Learning Point: Decimal to fraction conversion

Step 6: Fraction to Percentage Conversion and Vice-Versa

Time: 5 minutes

Teaching Skill: Video Presentation/Explanation

Teacher’s Activity: The teacher shows a video on converting fractions to percentages (multiplying by 100%) and percentages to fractions (dividing by 100 and simplifying). The teacher reinforces these concepts with quick examples.

Pupils’ Activity: Students watch the video and engage in quick mental conversions or simple examples.

Learning Point: Fraction-percentage conversions

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 are equivalent fractions?
2. Convert (frac{2}{5}) to a decimal.
3. Convert (0.7) to a fraction.
4. Convert (frac{1}{4}) to a percentage.
5. Arrange (frac{1}{3}, frac{1}{2}, frac{1}{6}) in ascending order.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Assessment of understanding

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on equivalent fractions, ordering, and conversions into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson content

Step 9: Conclusion

Time: 1 minute

Teaching Skill: Consolidation

Teacher’s Activity: The teacher briefly summarizes the key points of the lesson, emphasizing the interconnectedness of fractions, decimals, and percentages, and their practical application.

Pupils’ Activity: Students listen and reflect on the lesson’s main points.

Learning Point: Lesson summary and application

Continuous Assessment/Further Study

Type: Homework

Instruction: Complete the following exercises in your notebook:

1. Write two equivalent fractions for (frac{3}{7}).
2. Convert (0.6) to a fraction in its simplest form.
3. Convert (frac{7}{10}) to a percentage.
4. Convert (40%) to a fraction in its simplest form.
5. Arrange the following fractions in descending order: (frac{3}{4}, frac{1}{2}, frac{5}{8}).

Lesson Keywords

• Fraction – A part of a whole, represented by a numerator and a denominator.
• Numerator – The top number in a fraction, indicating the number of parts taken.
• Denominator – The bottom number in a fraction, indicating the total number of equal parts.
• Equivalent fractions – Fractions that represent the same value.
• Decimal – A number that uses a decimal point to show parts of a whole.
• Percentage – A fraction expressed as a number out of 100, denoted by the % symbol.
• Ascending order – Arranging numbers from smallest to largest.
• Descending order – Arranging numbers from largest to smallest.

Differentiation

For weaker learners: Provide additional visual aids such as fraction strips or circles to demonstrate equivalent fractions. Focus on one type of conversion at a time with more guided practice. Provide simplified worksheets with fewer steps.
For faster learners: Challenge them with more complex fractions, mixed numbers, or problems involving real-life scenarios like calculating discounts or proportions in recipes. Encourage them to explain their methods to peers.

Suggested Lesson Videos

For videos on equivalent fractions, ordering fractions, and conversions, search on YouTube for: JSS1 equivalent fractions ordering conversions

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have your flashcards ready for equivalent fractions and that the video player is set up for the conversion videos. Begin by quickly reviewing basic fraction concepts to ensure all students are on the same page. When teaching equivalent fractions, use concrete examples or diagrams to make the concept clear. For ordering fractions, guide students through finding the LCM carefully. During the conversion sections, after showing the videos, work through additional examples on the board, encouraging students to explain the steps. Allow ample time for students to copy the Board Summary notes after the main teaching and evaluation. Pay attention to common errors, such as incorrect division for fraction-to-decimal conversion or forgetting to simplify fractions. Encourage collaboration during practice activities and use the continuous assessment to gauge individual understanding.