PERCENTAGES

Subject :

Mathematics

Topic :

PERCENTAGES

Class :

Basic 6 / Primary 6

 

Term :

 

Second Term

Week :

 

Week 3

Instructional Materials :

• Pictures
• Wall Posters
• Related Online Videos
• Role Playing

 

Reference Materials

• Scheme of Work
• Online Information
• Textbooks
• Workbooks
• 9 Year Basic Education Curriculum

Previous Knowledge :

The pupils have previous knowledge of money in their previous classes

 

 

Behavioural Objectives :  At the end of the lesson, the pupils should be able to

1. Understand the concept of percentage
2. Be able to express percentages as fractions and decimals
3. Solve simple maths sums on percentages
4. Be able to convert percentages to decimals and fractions-continued-addition-and and vice versa
5. Understand how to use percentages to solve real-world problems, including scaling and unit conversion.

 

Content :

In mathematics, a percentage is a way of expressing a number as a fraction of 100. It is often used to compare two or more quantities or to express a part of a whole. For example, if a student scores 80% on a test, it means they got 80 out of 100 questions correct.

To calculate a percentage, you first need to convert the percentage to a fraction. For example, 50% can be written as the fraction 50/100. Then, you can use this fraction to find the percentage of a number by multiplying the number by the fraction. For example, to find 50% of 20, you would multiply 20 by the fraction 50/100 to get 10.

Percentages are often expressed as a decimal or fraction, but they can also be written as a whole number with a % sign, such as 50% or 75%. In mathematical terms, a percentage is a ratio that compares a number to 100. For example, 50% can be written as the fraction 50/100 or the decimal 0.50, which both represent the same ratio of 50 out of 100.

 

To convert a percentage to a fraction:

1. Write the percentage as a fraction with a denominator of 100. For example, 50% can be written as 50/100.
2. Simplify the fraction, if necessary. For example, 50/100 can be simplified to 1/2.

What is 50% expressed as a fraction?

a. 50/100

b. 100/50

c. 1/2

d. 2/1

 

What is 25% expressed as a fraction?

a. 25/100

b. 100/25

c. 1/4

d. 4/1

 

What is 75% expressed as a fraction?

a. 75/100

b. 100/75

c. 3/4

d. 4/3

 

What is 10% expressed as a fraction?

a. 10/100

b. 100/10

c. 1/10

d. 10/1

 

What is 100% expressed as a fraction?

a. 100/100

b. 1/1

c. 0/100

d. 100/0

To convert a fraction to a percentage:

1. Multiply the fraction by 100. For example, 1/2 x 100 = 50.
2. Add a % sign to express the result as a percentage. For example, 50 becomes 50%.

To convert a percentage to a decimal:

1. Write the percentage as a fraction with a denominator of 100. For example, 50% can be written as 50/100.
2. Divide the numerator by the denominator to convert the fraction to a decimal. For example, 50/100 = 0.50.

What is 1/2 expressed as a percentage?

a. 50%

b. 25%

c. 75%

d. 100%

 

What is 1/4 expressed as a percentage?

a. 50%

b. 25%

c. 75%

d. 100%

 

What is 3/4 expressed as a percentage?

a. 50%

b. 25%

c. 75%

d. 100%

 

What is 1/10 expressed as a percentage?

a. 50%

b. 25%

c. 10%

d. 100%

 

What is 1/1 expressed as a percentage?

a. 50%

b. 100%

c. 75%

d. 0%

To convert a decimal to a percentage:

1. Multiply the decimal by 100. For example, 0.50 x 100 = 50.
2. Add a % sign to express the result as a percentage. For example, 50 becomes 50%.

It’s important to remember that a percentage is just a way of expressing a number as a fraction of 100, so converting between percentages, fractions, and decimals is just a matter of changing the way the number is written

 

 

 

To express one number as a percentage of another, you can follow these steps:

1. Divide the number you want to express as a percentage by the total number.

For example, if you want to express the number of students who passed a test as a percentage of the total number of students who took the test, you would divide the number of students who passed by the total number of students:

passing students / total students

2. Multiply the result by 100 to express the answer as a percentage.

For example, if 25 students passed out of 50 total students, the percentage of students who passed would be 50%:

(25 students / 50 students) x 100 = 50%

You can also express the result as a fraction or decimal, if desired. For example, the result above could also be expressed as the fraction 1/2 or the decimal 0.50.

 

Percentage increase is the amount by which a quantity has increased as a percentage of its original value. For example, if the price of a product increases from $100 to $120, the percentage increase would be 20%. This can be calculated by dividing the increase ($20) by the original value ($100) and multiplying by 100: (20/100) x 100 = 20%.

Percentage decrease is the amount by which a quantity has decreased as a percentage of its original value. For example, if the price of a product decreases from $100 to $80, the percentage decrease would be 20%. This can be calculated by dividing the decrease ($20) by the original value ($100) and multiplying by 100: (20/100) x 100 = 20%.

 

The formula for calculating percentage decrease is:

Percentage decrease = (Decrease / Original value) x 100

For example, if the price of a product decreases from $100 to $80, the percentage decrease would be calculated as follows:

Percentage decrease = (80 – 100) / 100 x 100 = 20%

The formula for calculating percentage increase is:

Percentage increase = (Increase / Original value) x 100

For example, if the price of a product increases from $100 to $120, the percentage increase would be calculated as follows:

Percentage increase = (120 – 100) / 100 x 100 = 20%

 

Presentation

The topic is presented step by step

 

Step 1:

The class teacher revises the previous topics

 

Step 2.

He introduces the new topic

 

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

 

Evaluation :

1. A dress is on sale for 20% off its regular price of $50. What is the sale price of the dress? a. $10 b. $40 c. $60 d. $70
2. The population of a town increases from 10,000 to 12,000 over the course of a year. What is the percentage increase in the population? a. 10% b. 20% c. 25% d. 30%
3. The price of a gallon of gasoline decreases from $4.00 to $3.50. What is the percentage decrease in the price? a. 12.5% b. 15% c. 25% d. 30%
4. A company’s profits increase from $100,000 to $150,000 over the course of a year. What is the percentage increase in the company’s profits? a. 50% b. 60% c. 70% d. 80%
5. The value of a stock decreases from $50 to $45. What is the percentage decrease in the value of the stock? a. 10% b. 15% c. 20% d. 25%
6. A student’s grade point average increases from 3.0 to 3.5 over the course of a semester. What is the percentage increase in the student’s GPA? a. 16.7% b. 25% c. 33.3% d. 50%
7. The cost of a new car decreases from $30,000 to $25,000. What is the percentage decrease in the cost of the car? a. 16.7% b. 20% c. 25% d. 30%
8. The price of a movie ticket increases from $10 to $12. What is the percentage increase in the price of the ticket? a. 20% b. 25% c. 33.3% d. 50%
9. The value of a house increases from $200,000 to $250,000 over the course of a year. What is the percentage increase in the value of the house? a. 25% b. 30% c. 35% d. 40%
10. The population of a city decreases from 50,000 to 45,000 over the course of a year. What is the percentage decrease in the population? a. 10% b. 15% c. 20% d. 25%

Answers: 1) b; 2) b; 3) b; 4) a; 5) c; 6) c; 7) c; 8) a; 9) a; 10) c.

 

Conclusion :

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where  the needs arise.