Class: Primary 6
Term: Second Term
Week: 3
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Indices, Index.
Topic: RATIO AND PERCENTAGES
Subject Matter: Expressing a number as a percentage of another number, solving ratio word problems, profit and loss percent, quantitative reasoning on ratio percentage profit and loss.

Specific Objectives

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

Cognitive Domain:

Calculate the ratio of given numbers.
Express a number as a percentage of another number.
Calculate profit and loss percentages in given problems.
Solve quantitative reasoning problems on ratio, percentage, profit, and loss.

Affective Domain:

Participate actively in solving problems involving ratio and percentages.
Appreciate the importance of ratio, percentage, profit, and loss in everyday situations.

Psychomotor Domain:

Accurately solve word problems involving ratio and percentages.
Demonstrate the steps for calculating profit and loss percentages.

Work collaboratively with peers to solve mathematical problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Primary 4-6 Mathematics.
State Unified Scheme of Work for Primary 6 Mathematics.
Universal Basic Education (UBE) Primary 6 Mathematics Textbook.
https://www.mathsisfun.com/percentages.html

Instructional Materials

The teacher will teach this lesson with the aid of:

Textbook
Workbook
Multiplication chart
Flashcards with simple ratio and percentage problems

Rationale for the Lesson

This lesson helps pupils understand how to compare quantities using ratios and express parts of a whole as percentages. These concepts are important for managing money, understanding discounts, and interpreting statistics encountered in daily life.

Prerequisite/Previous Knowledge

Pupils should have a basic understanding of fractions, decimals, multiplication, and division.

Lesson Content/Board Summary

RATIO AND PERCENTAGES

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 can be written as a:b or a/b.

When solving ratio word problems, it is important to:

Identify the quantities being compared.
Write the ratio in its simplest form.
Use the ratio to find unknown quantities.

Expressing a Number as a Percentage of Another Number

To express one number as a percentage of another, divide the first number by the second number and then multiply the result by 100%.

Formula: (Part / Whole) x 100%

Example: To express 20 as a percentage of 80:

(20 / 80) x 100% = (1/4) x 100% = 25%

Profit and Loss Percent

Profit: This occurs when the selling price of an item is greater than its cost price. Profit = Selling Price – Cost Price.

Loss: This occurs when the selling price of an item is less than its cost price. Loss = Cost Price – Selling Price.

To calculate profit or loss percentage, we use the cost price as the base:

Profit Percentage = (Profit / Cost Price) x 100%
Loss Percentage = (Loss / Cost Price) x 100%

Quantitative Reasoning on Ratio, Percentage, Profit and Loss

Quantitative reasoning involves solving problems using numbers and mathematical concepts. Problems in this area combine ratio, percentage, profit, and loss in various scenarios, requiring pupils to apply their understanding of these concepts to find solutions.

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 what they know about fractions and decimals. The teacher then introduces the topic by asking how they compare quantities, like comparing the number of boys to girls in the class or understanding discounts in shops.
Pupils’ Activity: Pupils respond to the teacher’s questions and share their prior knowledge of fractions and decimals.
Learning Point: Pupils connect prior knowledge to the new topic and understand the relevance of ratio and percentages.

Step 2: Introduction to Ratio and Solving Ratio Word Problems

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what ratio is and how to express it. The teacher then guides pupils through solving simple ratio word problems using real-life examples, such as sharing items in a given ratio.
Pupils’ Activity: Pupils listen attentively, ask questions, and attempt to solve simple ratio problems guided by the teacher.
Learning Point: Pupils understand the definition of ratio and how to solve basic ratio word problems.

Step 3: Expressing a Number as a Percentage of Another Number

Time: 8 minutes
Teaching Skill: Explanation/Guided Practice
Teacher’s Activity: The teacher explains the concept of percentage and demonstrates how to express one number as a percentage of another using the formula (Part/Whole) x 100%. The teacher provides examples and allows pupils to practice.
Pupils’ Activity: Pupils follow the explanation, take notes, and work through example problems on expressing numbers as percentages.
Learning Point: Pupils learn how to express a number as a percentage of another.

Step 4: Calculating Profit and Loss Percent

Time: 8 minutes
Teaching Skill: Explanation/Problem Solving
Teacher’s Activity: The teacher defines profit and loss, explaining how to calculate profit/loss amount and then profit/loss percentage, always relating it to the cost price. The teacher presents word problems involving buying and selling to illustrate these concepts.
Pupils’ Activity: Pupils listen to the definitions, understand the formulas for profit and loss percentage, and attempt to solve problems presented by the teacher.
Learning Point: Pupils understand profit and loss and can calculate their respective percentages.

Step 5: Quantitative Reasoning on Ratio, Percentage, Profit and Loss

Time: 6 minutes
Teaching Skill: Critical Thinking/Application
Teacher’s Activity: The teacher introduces quantitative reasoning problems that combine elements of ratio, percentage, profit, and loss. The teacher guides pupils on how to break down such problems and identify the appropriate steps to solve them.
Pupils’ Activity: Pupils observe how to approach complex problems and attempt to apply the learned concepts to solve them.
Learning Point: Pupils develop skills in solving multi-concept quantitative reasoning problems.

Step 6: Class Activity/Practice

Time: 5 minutes
Teaching Skill: Group Work/Monitoring
Teacher’s Activity: The teacher gives pupils a few practice questions covering all aspects of the lesson (ratio, percentage expression, profit/loss percentage, and a simple quantitative reasoning problem). Pupils work in small groups or individually.
Pupils’ Activity: Pupils solve the practice questions, clarifying doubts with the teacher or their peers.
Learning Point: Pupils reinforce their understanding through practice and peer learning.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

What is a ratio?
How do you express 15 as a percentage of 60?
If an item bought for N400 is sold for N500, what is the profit percentage?
If an item bought for N700 is sold for N600, what is the loss percentage?

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
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the real-life applications of ratio and percentages. The teacher then gives a take-home assignment.
Pupils’ Activity: Pupils listen to the summary and copy down the assignment.
Learning Point: Pupils recap the lesson and consolidate their understanding.

Home Task: Solve three new exercises on RATIO AND PERCENTAGES. Show each step and check each answer.

Lesson Keywords

Ratio – A comparison of two or more quantities of the same kind.
Percentage – A way of expressing a number as a fraction of 100 (per hundred).
Profit – The gain made when the selling price is more than the cost price.
Loss – The amount lost when the selling price is less than the cost price.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex word problems or introduce concepts like compound ratios. For pupils needing extra support, the teacher can provide simpler problems, work through examples step-by-step, and offer one-on-one guidance.

Note for teachers using this lesson plan

Encourage pupils to use visual aids like bar models or fraction strips to understand ratio and percentage concepts better. Emphasize real-life examples to make the lesson more relatable and engaging. Ensure that all pupils understand the difference between profit and loss and how to correctly identify the cost price for percentage calculations.