Fractions, Ratio, Fraction-to, Ratio and Real, Life Sharing for Primary 5

Class: Primary 5
Term: 1st Term
Week: 3
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Meaning, Decimals and Percentages of Fractions.
Topic: FRACTIONS
Subject Matter: Meaning of ratio with examples, changing fractions to ratio, stating the relationship between fraction and ratio, application of ratio in real life sharing in a given ratio, quantitative aptitude on ratio

Specific Objectives

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

Cognitive Domain:

• State the meaning of ratio with examples.
• Identify the relationship between fractions and ratios.
• Change fractions to ratios.
• Solve problems involving sharing quantities in a given ratio.
• Solve quantitative aptitude problems on ratio.

Affective Domain:

• Appreciate the importance of ratio in daily life situations.
• Show interest in solving ratio problems.

Psychomotor Domain:

• Demonstrate the conversion of fractions to ratios.
• Apply the steps to share quantities in a given ratio accurately.

Social Domain:

• Participate actively in class discussions on ratio.
• Work collaboratively to solve ratio problems.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum
• State Unified Scheme of Work
• New General Mathematics for Primary Schools, Book 5

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart
• Flash cards
• Counters
• Abacus chart
• Quantitative aptitude book
• Fraction cards

Rationale for the Lesson

This lesson helps pupils understand how to compare quantities and share things fairly. It teaches them a practical skill used in everyday situations like dividing items among friends or understanding proportions in recipes.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic fractions and simple division.

Lesson Content/Board Summary

Ratio

Meaning of Ratio

Ratio is a way of comparing two or more quantities of the same kind. It shows how much of one quantity there is compared to another quantity. Ratios are written using a colon (:) symbol.

For example, if there are 3 boys and 5 girls in a group, the ratio of boys to girls is 3:5.

The following are other examples of ratio:

• The ratio of 2 apples to 7 oranges is 2:7.
• The ratio of 10 red balls to 4 blue balls is 10:4.

NOTE: Ratios should always be simplified to their lowest terms, just like fractions. For example, 10:4 can be simplified by dividing both numbers by 2, which gives 5:2.

Relationship Between Fraction and Ratio

Fractions and ratios are closely related. A ratio can be expressed as a fraction, and a fraction can be expressed as a ratio. Both represent a part of a whole or a comparison between two quantities.

For example, the ratio 3:5 can be written as the fraction 3/5. This means 3 parts out of 5 total parts (if the whole is considered as 5 parts). If we are comparing two separate quantities, like 3 boys to 5 girls, then the fraction 3/5 represents the number of boys compared to the number of girls.

Changing Fractions to Ratio

To change a fraction to a ratio, simply write the numerator as the first term and the denominator as the second term, separated by a colon.

Example 1: Change the fraction 2/3 to a ratio.

Solution:

The numerator is 2 and the denominator is 3.

So, 2/3 as a ratio is 2:3.

Example 2: Express the fraction 7/4 as a ratio.

Solution:

The numerator is 7 and the denominator is 4.

So, 7/4 as a ratio is 7:4.

Application of Ratio in Real Life Sharing

Ratios are used to share quantities fairly according to a given proportion. To share an amount in a given ratio, follow these steps:

Steps to share a quantity in a given ratio:

1. Add the parts of the ratio to find the total number of parts.
2. Divide the total quantity to be shared by the total number of parts. This gives the value of one part.
3. Multiply the value of one part by each number in the ratio to find each share.

Example 1: Share N750 between John and Mary in the ratio 2:3.

Solution:

Step 1: Find the sum of the ratio parts.

2 + 3 = 5 parts

Step 2: Find the value of one part.

Value of one part = Total amount / Total parts = N750 / 5 = N150

Step 3: Calculate each person’s share.

John’s share = 2 parts x N150/part = N300

Mary’s share = 3 parts x N150/part = N450

Check: N300 + N450 = N750 (This confirms the sharing is correct).

Example 2: A mother shares 40 sweets among her three children, Ada, Bola, and Chidi, in the ratio 1:2:5. How many sweets does each child get?

Solution:

Step 1: Find the sum of the ratio parts.

1 + 2 + 5 = 8 parts

Step 2: Find the value of one part.

Value of one part = Total sweets / Total parts = 40 sweets / 8 = 5 sweets

Step 3: Calculate each child’s share.

Ada’s share = 1 part x 5 sweets/part = 5 sweets

Bola’s share = 2 parts x 5 sweets/part = 10 sweets

Chidi’s share = 5 parts x 5 sweets/part = 25 sweets

Check: 5 + 10 + 25 = 40 sweets.

Quantitative Aptitude on Ratio

Quantitative aptitude questions on ratio often involve comparing quantities, finding unknown values, or solving word problems that require understanding ratios and fractions.

Example 1: The ratio of boys to girls in a class is 4:5. If there are 20 boys, how many girls are there?

Solution:

Let the number of boys be 4x and the number of girls be 5x.

We are given that the number of boys is 20.

So, 4x = 20

Step 1: Solve for x.

Divide both sides by 4: x = 20 / 4 = 5

Step 2: Find the number of girls.

Number of girls = 5x = 5 * 5 = 25 girls.

Therefore, there are 25 girls in the class.

Example 2: If 3 out of every 7 pupils in a school play football, and there are 210 pupils in the school, how many pupils play football?

Solution:

The fraction of pupils who play football is 3/7.

Total number of pupils = 210.

Step 1: Find the number of pupils who play football.

Number of pupils who play football = (3/7) * 210

Step 2: Calculate the value.

= (3 * 210) / 7

= 630 / 7

= 90 pupils.

Therefore, 90 pupils play football.

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 about sharing items among friends. The teacher then introduces the topic “Ratio” as a way to compare and share quantities.
Pupils’ Activity: Pupils respond to greetings and share their experiences of sharing items. They listen attentively to the teacher’s introduction.
Learning Point: Pupils are prepared for the lesson and understand the relevance of the topic.

Step 2: Meaning of Ratio

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the meaning of ratio using simple language and gives examples, writing them on the board. The teacher also shows how ratios can be simplified.
Pupils’ Activity: Pupils listen, ask questions for clarity, and copy notes from the board, practicing simplifying ratios.
Learning Point: Pupils understand what ratio means and how to express it.

Step 3: Relationship Between Fraction and Ratio

Time: 6 minutes
Teaching Skill: Explanation/Discussion
Teacher’s Activity: The teacher explains the close relationship between fractions and ratios, showing how one can be written as the other using examples.
Pupils’ Activity: Pupils observe the examples and participate in a short discussion about the connection.
Learning Point: Pupils identify the connection between fractions and ratios.

Step 4: Changing Fractions to Ratio

Time: 5 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher demonstrates how to convert fractions to ratios with clear examples on the board.
Pupils’ Activity: Pupils observe the steps and practice converting given fractions into ratios.
Learning Point: Pupils learn how to change fractions into ratios.

Step 5: Application of Ratio in Real Life Sharing

Time: 10 minutes
Teaching Skill: Problem Solving/Demonstration
Teacher’s Activity: The teacher explains the steps for sharing quantities in a given ratio and solves several real-life examples on the board, guiding pupils through each step.
Pupils’ Activity: Pupils pay attention to the steps, ask questions, and attempt to solve similar problems in their notebooks.
Learning Point: Pupils learn to apply ratios to share quantities in real-life situations.

Step 6: Quantitative Aptitude on Ratio

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher introduces quantitative aptitude problems related to ratio and guides pupils through solving examples on the board.
Pupils’ Activity: Pupils follow the teacher’s guidance and solve the aptitude problems.
Learning Point: Pupils develop problem-solving skills for ratio-based aptitude questions.

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. Define ratio and give two examples.
2. State the relationship between a fraction and a ratio.
3. Change the fraction 5/8 to a ratio.
4. Share N900 between two friends in the ratio 4:5.
5. If the ratio of red pens to blue pens is 3:2 and there are 15 red pens, how many blue pens are there?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Homework Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson on ratio, fractions, and their applications. The teacher then assigns homework to reinforce learning.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their understanding and practice at home.

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

Lesson Keywords

• Ratio – A comparison of two or more quantities of the same kind.
• Fraction – A part of a whole, often written as a numerator over a denominator.
• Quantity – An amount or number of something.
• Simplify – To reduce a ratio or fraction to its lowest terms.
• Share – To divide something among a group of people.

Differentiation

For pupils who are struggling, the teacher will provide additional simpler examples and one-on-one support. More advanced pupils will be given challenging word problems involving multiple ratios or larger numbers to solve independently or in small groups.

Note for teachers using this lesson plan

Ensure pupils grasp the concept of simplification of ratios as it is fundamental. Use visual aids like counters or flashcards to make the comparison of quantities more concrete. Encourage pupils to come up with their own real-life examples of ratios.