Percentage, Ratio, and Proportion in Real-Life Situations

Grade 6 · Mathematics

Semester 2 | Period 6 | Week 33

Download the Lessonotes Mobile Liberia app for faster lesson access on Android and iPhone.

Get it on Google Play Get it on the Apple App Store

Subject: Mathematics

Semester: 2

Period: 6

Week: 33

School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 33
Lesson Duration: 45 minutes
Week & Period: Week 33, Period 6
Topic: Percentage, Ratio, and Proportion in Real-Life Situations
Sub-topic: Applications in Population, Health, and Commerce

Learning Objectives
By the end of the lesson, students should be able to:
Define percentage as per hundred
Relate percentages to ratios and fractions
Calculate percentages from given data
Solve real-life word problems on percentage, ratio, and proportion

Previous Knowledge
Students already know basic ratio, proportion, and fractions.

Instructional Materials
Mathematics textbook for Grade 6

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: If 40 out of 100 students passed an exam, what percent is that? Learners answer 40%.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definition

  • The word percentage comes from the Latin phrase per centum, which means “per hundred.”
  • It is written using the symbol %.
  • A percentage is therefore a way of expressing a number as a fraction of 100.

 

Relationship Between Fractions, Ratios, and Percentages

  • 12=0.5=50%=1:2.
  • Fractions, decimals, percentages, and ratios are just different ways of representing the same relationship.

 

Converting Between Forms

From Percentage to Fraction and Ratio:

  • 60% = 60/100 = 3:5.
  • 75% = 75/100 = 3:4.
  • 25% = 25/100 = 1:4.
  • 10% = 10/100 = 1:10.

From Fraction to Percentage:

  • 2/5=2/5×100=40%
  • 7/10=7/10×100=70%
  • 9/20=9/20×100=45%

From Ratio to Percentage:

  • 2:5 = 2/5 = 40%.
  • 3:8 = 3/8 = 37.5%.
  • 5:20 = 5/20 = 25%.

 

Applications of Percentages

  1. Exam Scores (Education)
  • Example: A student scores 72 out of 80.
  • Percentage = 72/80×100=90%.
  1. Health Data (Population/Science)
  • Example: If 15 out of 100 people have a disease, then 15% of the population is affected.
  • If in a town of 2000 people, 300 people are HIV positive:
    Percentage = 300/2000×100=15%
  1. Commerce (Discounts, Profits, Losses)
  • Example: A dress worth ₦5000 has 20% discount.
    • Discount = 20%×₦5000=₦1000
    • New price = ₦5000 – ₦1000 = ₦4000.
  • Example: A shopkeeper bought goods for ₦8000 and sold them for ₦9600.
    Profit = ₦1600.
    Profit percentage = 1600/8000×100=20%
  1. Daily Life (Banking/Interest)
  • Example: A bank gives 10% interest on ₦20,000 savings.
    Interest = 10%×20000=₦2000

Learners’ Activities (Expanded)

  • Learners convert given fractions (½, ⅔, ¾, ⅖, ⅝) into percentages.
  • Learners convert given percentages (20%, 33⅓%, 50%, 75%, 90%) into fractions and ratios.
  • Learners solve word problems involving exam scores, discounts, and profits.
  • Learners calculate percentages using classroom data (e.g., percentage of boys to total students).
  • Learners work in groups to prepare simple charts showing percentages of different categories.

 

Assessment Checks

  1. Express 45% as a fraction and as a ratio.
    • 45%=45/100=9:20 .
  2. A student scores 36 marks out of 50. Find the percentage.
    • 36/50×100=72%
  3. A trader buys an item for ₦6000 and sells it for ₦7200. Find the profit percentage.
    • Profit = ₦1200.
    • Profit% = 1200/6000×100=20%
  4. In a class of 40 pupils, 18 are girls. What percentage are girls?
    • 18/40×100=45%.
  5. If a bottle costs ₦200 and there is a 15% discount, what is the new price?
    • Discount = 15%×₦200=₦30 New price = ₦170.

 

Notes (Expanded & Detailed)

  • Percentages are another way of expressing ratios and fractions out of 100.
  • They are widely used in education (exam scores), commerce (discounts, profit/loss), science (population health data), and daily life (bank savings, interest).
  • Every percentage can be converted to a fraction and ratio, and vice versa.
  • Key reminders for learners:
    • Always divide by the total before multiplying by 100.
    • Always simplify fractions before writing as ratios.
    • Understand real-life applications to see the importance of percentages.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Percentages, ratios, and proportions are different forms of expressing parts of a whole.

Evaluation Method (Expanded):
Exit slip/quiz: Convert 3/5 to a percentage and ratio. Teacher will collect slips and provide oral feedback.

Assignment (Expanded):

  1. In a class of 40 students, 30 passed. Find the percentage who passed.
  2. A trader gives 25% discount on ₦8000. What is the new price?

Follow-up Activity:
Learners collect data at home (scores, money spent) and express in percentage form.

Differentiation / Inclusive Strategies
Use pictorial percentage bars for struggling learners. Advanced learners calculate real dataset percentages.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low