Download the Lessonotes Mobile Liberia app for faster lesson access on Android and iPhone.
Subject: Mathematics
Semester: 2
Period: 6
Week: 32
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 32
Lesson Duration: 45 minutes
Week & Period: Week 32, Period 6
Topic: Proportion – Concept, Expression, and Word Problems
Sub-topic: Identifying and Solving Proportions
Learning Objectives
By the end of the lesson, students should be able to:
Define proportion as equality of two ratios
Write and solve proportions correctly
Identify proportional relationships in real-life situations
Solve word problems involving proportion
Previous Knowledge
Students already know ratios and how to simplify them.
Instructional Materials
Mathematics textbook for Grade 6
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: If 2 pencils cost ₦100, how much will 4 pencils cost? Learners guess, teacher leads into proportion.
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition
- A proportion is an equation that states that two ratios are equal.
- In other words, if two fractions are equal, we say they are in proportion.
Notation and Form
- A proportion is written as:
- a/b=c/d
- or as a:b=c:d.
- Here, a,b,c,d are numbers, and b,d≠0
Examples
- 2/3=4/6 → 2:3 = 4:6.
- 5/10=1/2.
- A recipe uses 2 cups of sugar for 5 cups of flour. To make the same recipe with 10 cups of flour, sugar must be in the same proportion: 2:5=x:10.
Solving Proportions
- Method: Cross Multiplication
- If a/b=c/d, then a/d=b/c.
Example 1:
Solve 2/3=x/9.
→ Cross multiply: 2×9=3×x.
→ 18=3x.
→ x=6.
Example 2:
If 4 pencils cost ₦200, how much do 10 pencils cost?
Ratio: 4:200 = 10:x.
Cross multiply: 4x=2000.
→ x=₦500.
Word Problem Applications
- Price Proportion (Direct proportion)
If 3 books cost ₦900, how much will 5 books cost?
→ 3:900 = 5:x.
→ 3x=4500.
→ x=₦1500. - Map Scale
A map has a scale 1:100,000 (meaning 1 cm = 1 km).
If two towns are 8 cm apart on the map, actual distance = 8 km. - Classroom Proportion
If the ratio of boys to girls is 3:2 and there are 18 boys, how many girls are there?
→ 3:2 = 18:x.
Cross multiply: 3x=36.
→ x=12. - Speed/Time
A car travels 60 km in 2 hours. At the same speed, how far will it travel in 5 hours?
→ 60:2 = x:5.
Cross multiply: 2x=300.
→ x=150km.
Learners’ Activities (Expanded)
- Learners solve proportion examples in pairs or groups.
- Learners use classroom data (e.g., boys to girls) to form proportions.
- Learners apply proportions to prices of items in the local market.
- Learners measure distances on a simple map to find real distances.
- Learners create their own word problems involving proportions.
Assessment Checks
- If 6 pencils cost ₦300, how much do 10 pencils cost?
- Solution: 6:300 = 10:x → 6x = 3000 → x = ₦500.
- Solve: 5/8=x/32.
- Solution: 5×32=8x5 8x → 160=x=20.
- A map scale is 1:50,000. If two towns are 12 cm apart on the map, find actual distance.
- Solution: 12 cm × 50,000 = 600,000 cm = 6 km.
- If 4 men can dig a well in 12 days, how long will 6 men take?
- Solution involves inverse proportion: 4:12=6:x x=9 days.
Notes (Expanded & Detailed)
- Proportion shows that two ratios are equal.
- Direct proportion: As one quantity increases, the other also increases. Example: more items → higher cost.
- Inverse proportion: As one quantity increases, the other decreases. Example: more workers → less time needed.
- Cross multiplication is the standard method for solving proportion problems.
- Proportion is useful in:
- Pricing and shopping
- Maps and scales
- Recipes and mixing ingredients
- Speed, distance, and time calculations
- Classroom data comparisons
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Ratios can be extended into proportions which help in solving real-life scaling problems.
Evaluation Method (Expanded):
Exit slip/quiz: Solve x:16 = 3:12. Teacher will collect slips and provide oral feedback.
Assignment (Expanded):
- If 5 kg of rice costs ₦4000, how much will 8 kg cost?
- A scale map shows 1 cm = 5 km. If two towns are 12 cm apart, find actual distance.
Follow-up Activity:
Learners use household price comparisons to form and solve proportions.
Differentiation / Inclusive Strategies
Provide visual maps and simple price charts for struggling learners. Challenge advanced learners with multi-step word problems.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☑ Medium ☑ Low