Percentages, Percentage of a Number, Increase, Decrease and Reasoning for Primary 6

Class: Primary 6
Term: 1st Term
Week: 7
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Numbers and Numeration
Previous Lesson: Ratio and Proportion, Direct, Inverse and Family Size Resource Ratio.
Topic: PERCENTAGES
Subject Matter: Expressing numbers as a percentage of another, calculating percentage of boys and girls in a class, calculating percentage increase, calculating percentage decrease, quantitative reasoning on percentages.

Specific Objectives

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

Cognitive Domain:

• Express a given number as a percentage of another.
• Calculate the percentage of a group (e.g., boys or girls) within a total.
• Calculate percentage increase from one value to another.
• Calculate percentage decrease from one value to another.
• Solve quantitative reasoning problems involving percentages.

Affective Domain:

• Appreciate the importance of percentages in real-life situations like discounts and profits.
• Participate actively in solving percentage problems.

Psychomotor Domain:

• Accurately apply formulas to solve problems on percentage increase and decrease.
• Present solutions to percentage problems clearly and logically.

Social Domain:

• Collaborate with peers to discuss and solve challenging percentage 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.
• New General Mathematics for Primary Schools Book 6.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Textbook
• Charts showing percentage formulas
• Posters with solved examples
• Workbook
• Real-life data (e.g., class population, price changes)

Rationale for the Lesson

This lesson helps pupils understand how percentages are used in everyday life, such as in shopping discounts, interest rates, and population statistics. Mastering percentages enables pupils to make informed decisions and interpret numerical information presented in percentage form.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of fractions, decimals, multiplication, and division.

Lesson Content/Board Summary

PERCENTAGES

1. Expressing a Number as a Percentage of Another

A percentage is a way of expressing a number as a fraction of 100. To express a number ‘A’ as a percentage of another number ‘B’, we use the formula:

Percentage = (A / B) × 100%

Example 1: Express 15 as a percentage of 60.

Solution:

Step 1: Write the fraction: 15/60

Step 2: Multiply by 100%:

(15 / 60) × 100%

= (1 / 4) × 100%

= 25%

Example 2: In a test, a pupil scored 35 marks out of 50. What percentage did the pupil score?

Solution:

Step 1: Write the fraction: 35/50

Step 2: Multiply by 100%:

(35 / 50) × 100%

= (7 / 10) × 100%

= 7 × 10%

= 70%

2. Calculating Percentage of Boys and Girls in a Class

To find the percentage of a specific group in a total, divide the number in that group by the total number and multiply by 100%.

Example: A class has 20 boys and 30 girls. Calculate the percentage of boys and girls in the class.

Solution:

Step 1: Find the total number of pupils:

Total = 20 boys + 30 girls = 50 pupils

Step 2: Calculate percentage of boys:

Percentage of boys = (Number of boys / Total pupils) × 100%

= (20 / 50) × 100%

= (2 / 5) × 100%

= 2 × 20%

= 40%

Step 3: Calculate percentage of girls:

Percentage of girls = (Number of girls / Total pupils) × 100%

= (30 / 50) × 100%

= (3 / 5) × 100%

= 3 × 20%

= 60%

NOTE: The sum of percentages of boys and girls should be 100% (40% + 60% = 100%).

3. Calculating Percentage Increase

Percentage increase occurs when a quantity goes up. It is calculated by finding the increase, dividing it by the original amount, and multiplying by 100%.

Formula: Percentage Increase = (Increase / Original Amount) × 100%

Where Increase = New Amount – Original Amount

Example 1: A shirt costing N500 increased to N600. Calculate the percentage increase.

Solution:

Step 1: Calculate the increase:

Increase = N600 – N500 = N100

Step 2: Apply the percentage increase formula:

Percentage Increase = (100 / 500) × 100%

= (1 / 5) × 100%

= 20%

Example 2: A worker’s salary of N20,000 was increased by 15%. What is the new salary?

Solution:

Step 1: Calculate the amount of increase:

Increase = 15% of N20,000

= (15 / 100) × 20,000

= 15 × 200

= N3,000

Step 2: Calculate the new salary:

New Salary = Original Salary + Increase

= N20,000 + N3,000

= N23,000

How to solve for Original Value after an increase:

If a value increased by X% to become Y, the Original Value = Y / (1 + X/100)

Example: After a 20% increase, a price is N1200. What was the original price?

Solution:

Step 1: Identify the new price (Y) and percentage increase (X):

Y = N1200, X = 20%

Step 2: Apply the formula:

Original Value = 1200 / (1 + 20/100)

= 1200 / (1 + 0.2)

= 1200 / 1.2

= N1000

4. Calculating Percentage Decrease

Percentage decrease occurs when a quantity goes down. It is calculated by finding the decrease, dividing it by the original amount, and multiplying by 100%.

Formula: Percentage Decrease = (Decrease / Original Amount) × 100%

Where Decrease = Original Amount – New Amount

Example 1: A car originally bought for N800,000 was sold for N640,000. Calculate the percentage decrease.

Solution:

Step 1: Calculate the decrease:

Decrease = N800,000 – N640,000 = N160,000

Step 2: Apply the percentage decrease formula:

Percentage Decrease = (160,000 / 800,000) × 100%

= (16 / 80) × 100%

= (1 / 5) × 100%

= 20%

Example 2: A shop offered a 10% discount on an item priced at N1500. What is the new price?

Solution:

Step 1: Calculate the amount of discount (decrease):

Discount = 10% of N1500

= (10 / 100) × 1500

= 10 × 15

= N150

Step 2: Calculate the new price:

New Price = Original Price – Discount

= N1500 – N150

= N1350

How to solve for Original Value after a decrease:

If a value decreased by X% to become Y, the Original Value = Y / (1 – X/100)

Example: After a 25% discount, a dress costs N900. What was the original price?

Solution:

Step 1: Identify the new price (Y) and percentage decrease (X):

Y = N900, X = 25%

Step 2: Apply the formula:

Original Value = 900 / (1 – 25/100)

= 900 / (1 – 0.25)

= 900 / 0.75

= N1200

5. Quantitative Reasoning on Percentages

Quantitative reasoning problems involve applying percentage concepts to solve word problems that require logical thinking.

Example 1: If 40% of a number is 20, what is the number?

Solution:

Step 1: Let the number be ‘x’.

40% of x = 20

Step 2: Convert percentage to fraction:

(40 / 100) × x = 20

Step 3: Solve for x:

(2 / 5) × x = 20

x = 20 × (5 / 2)

x = 10 × 5

x = 50

Example 2: In a village, 75% of the population are farmers. If there are 300 farmers, what is the total population?

Solution:

Step 1: Let the total population be ‘P’.

75% of P = 300

Step 2: Convert percentage to fraction:

(75 / 100) × P = 300

Step 3: Solve for P:

(3 / 4) × P = 300

P = 300 × (4 / 3)

P = 100 × 4

P = 400

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 questions related to fractions and decimals, linking them to everyday scenarios like getting marks in a test. The teacher then introduces the topic “Percentages” and explains that it is a special type of fraction.

Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction of the new topic.

Learning Point: Pupils recall prior knowledge and are prepared for the new lesson.

Step 2: Expressing a Number as a Percentage of Another

Time: 8 minutes

Teaching Skill: Explanation/Demonstration

Teacher’s Activity: The teacher explains what a percentage is and demonstrates how to express a number as a percentage of another using the formula (A/B) * 100%. The teacher works through Example 1 and 2 from the board summary, guiding pupils through each step.

Pupils’ Activity: Pupils observe, listen, and copy notes. They attempt to solve similar problems as guided by the teacher.

Learning Point: Pupils learn to express one number as a percentage of another.

Step 3: Calculating Percentage of Boys and Girls in a Class

Time: 7 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides pupils to apply the concept of expressing a number as a percentage to calculate the percentage of boys and girls in a class. The teacher uses the example from the board summary, ensuring pupils understand the total number is the denominator.

Pupils’ Activity: Pupils actively participate in solving the example problem, contributing to finding the total and calculating the individual percentages.

Learning Point: Pupils can calculate the percentage of a specific group within a total.

Step 4: Calculating Percentage Increase

Time: 7 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher explains the concept of percentage increase, providing the formula: (Increase / Original Amount) * 100%. The teacher demonstrates how to calculate the increase and then the percentage increase using the examples from the board summary. The teacher also briefly explains how to find the original value if the new value and percentage increase are known.

Pupils’ Activity: Pupils listen, ask questions for clarification, and copy the formulas and examples into their notebooks.

Learning Point: Pupils learn to calculate percentage increase and understand how to find original values.

Step 5: Calculating Percentage Decrease

Time: 7 minutes

Teaching Skill: Explanation/Problem Solving

Teacher’s Activity: The teacher explains the concept of percentage decrease, providing the formula: (Decrease / Original Amount) * 100%. The teacher demonstrates how to calculate the decrease and then the percentage decrease using the examples from the board summary. The teacher also briefly explains how to find the original value if the new value and percentage decrease are known.

Pupils’ Activity: Pupils pay attention, clarify doubts, and record the formulas and examples.

Learning Point: Pupils learn to calculate percentage decrease and understand how to find original values.

Step 6: Quantitative Reasoning on Percentages

Time: 6 minutes

Teaching Skill: Application/Critical Thinking

Teacher’s Activity: The teacher introduces quantitative reasoning problems related to percentages. The teacher guides pupils through solving the examples from the board summary, emphasizing careful reading and understanding of the problem before applying the appropriate percentage concept.

Pupils’ Activity: Pupils attempt to solve the problems, discussing possible approaches with the teacher and their peers.

Learning Point: Pupils can apply percentage concepts to solve word 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. Define percentage.
2. Express 20 as a percentage of 80.
3. A class has 25 boys and 15 girls. What percentage of the class are girls?
4. A book price increased from N400 to N500. Calculate the percentage increase.
5. A shirt costing N1200 was sold at a 10% discount. What was the new price?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 0 minutes

Teacher’s Activity: The teacher summarizes the key points of the lesson on percentages and assigns homework involving various percentage calculations and word problems.

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

Learning Point: Pupils consolidate their understanding and apply learned concepts independently.

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

Lesson Keywords

• Percentage – A fraction out of 100.
• Increase – To become larger in amount or value.
• Decrease – To become smaller in amount or value.
• Original Amount – The initial value before any change.
• Quantitative Reasoning – Solving problems that involve numerical and logical thinking.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more complex word problems and multi-step percentage questions. For pupils needing additional support, the teacher will provide simplified examples, offer one-on-one guidance, and use visual aids to reinforce understanding of basic percentage calculations.

Note for teachers using this lesson plan

Ensure that pupils have a solid understanding of fractions and decimals before introducing percentages. Use real-life examples relevant to the pupils’ experiences to make the lesson engaging. Encourage pupils to show all their working steps clearly, especially for percentage increase and decrease problems. Provide ample practice opportunities both in class and as homework.