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Subject: Mathematics
Semester: 2
Period: 6
Week: 31
School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 5
Date: Week 31
Lesson Duration: 45 minutes
Week & Period: Week 31, Period 6
Topic: Ratio, Proportion, and Rates
Sub-topic: Introduction to ratio, proportion, and rates
Learning Objectives
By the end of the lesson, students should be able to:
- Define and write ratios.
- Express ratios in simplest form.
- Compare two or more ratios.
- Explain the concept of proportion and identify equal ratios.
- Define rates and give examples such as speed and cost per item.
Previous Knowledge
Students already know basic multiplication, division, and fractions.
Instructional Materials
Mathematics textbook for Grade 5, counters, colored water for mixing activity, flash cards.
Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher shows two bowls of beads (8 red, 4 blue) and asks learners: “How can we compare the number of red beads to the number of blue beads?”
B – Building Knowledge (Main Lesson Body)
Time: 25–30 minutes
Definition of Ratio:
A ratio is a way of comparing two or more quantities of the same kind by division. It shows how many times one number contains another or how one quantity relates to another.
- A ratio can be written in three forms:
- Using a colon (:) → 3:5
- As a fraction → 3/5
- In words → 3 to 5
Examples of Ratios:
- If there are 8 boys and 4 girls, the ratio of boys to girls is 8:4, which simplifies to 2:1.
- A box has 12 red balls and 18 blue balls. The ratio of red to blue is 12:18 = 2:3.
- If there are 25 students and 15 are girls, then the ratio of girls to total students is 15:25 = 3:5.
Simplest Form of a Ratio:
- To simplify a ratio, divide both terms by their Greatest Common Divisor (GCD).
- This makes the ratio easier to understand.
- Examples:
- 12:16 ÷ 4 = 3:4
- 18:24 ÷ 6 = 3:4
- 50:100 ÷ 50 = 1:2
Comparing Ratios:
- To compare two ratios, write them in fraction form and reduce to see if they are equal.
- Examples:
- Compare 2:3 and 4:6 → 2/3 = 4/6 → both equal, so the ratios are the same.
- Compare 5:10 and 3:6 → 5/10 = 1/2; 3/6 = 1/2 → equal ratios.
- Compare 6:8 and 3:5 → 6/8 = 3/4; 3/5 = 3/5 → not equal.
Definition of Proportion:
A proportion is a statement that shows two ratios are equal.
- Example: 2:3 = 4:6 (both equal 2/3) → this is a proportion.
- Another example: 5:10 = 1:2 → proportion holds true.
Definition of Rate:
A rate is a type of ratio that compares two quantities of different kinds or units.
- Rates are very common in daily life.
- Examples:
- Speed: Distance ÷ Time → If a car covers 60 km in 2 hours, the speed is 60 ÷ 2 = 30 km/hr.
- Price per item: If L$500 buys 10 oranges, the cost per orange is L$500 ÷ 10 = L$50 each.
- Work rate: If a person makes 20 baskets in 5 days, the rate is 4 baskets/day.
Learners’ Activities (Expanded):
- Classroom Ratio Exercise:
- Learners count and write ratios such as boys:girls, chairs:tables, books:pencils.
- Example: 12 chairs and 8 tables → ratio = 12:8 = 3:2.
- Simplification on the Board:
- Teacher gives examples like 18:27, 20:60, 25:100.
- Learners simplify them step by step.
- Mixing Activity:
- Learners mix juice concentrate and water in given ratios (e.g., 1:2, 2:5).
- They observe how the taste changes depending on the ratio.
- Proportion Matching Game:
- Teacher writes pairs of ratios on cards.
- Learners match ratios that form proportions (e.g., 3:6 and 1:2).
- Word Problems on Rates:
- “If 5 pens cost L$250, what is the price per pen?”
- “If a cyclist covers 120 km in 4 hours, what is his speed per hour?”
- “If a tap fills 30 liters in 10 minutes, what is the rate per minute?”
Assessment Checks (Expanded):
- Simplify 18:24.
- Write the ratio of 15 boys to 25 students in simplest form.
- Is 3:4 equal to 6:8? Explain why.
- Write a proportion from these numbers: 2, 3, 4, 6.
- If 12 apples cost L$600, what is the cost per apple?
- If a bus travels 200 km in 5 hours, what is its speed per hour?
- A bag has 10 red balls and 15 green balls. Write the ratio of red to total balls.
Notes (Expanded & Detailed):
- A ratio compares similar quantities.
- A proportion shows that two ratios are equal.
- A rate compares different types of quantities.
- Ratios, proportions, and rates are very useful in daily life:
- Recipes (2 cups flour : 1 cup sugar).
- Prices (L$500 per bag of rice).
- Speed (60 km/hour).
- Maps (scale 1 cm : 5 km).
- By mastering these concepts, learners will be able to solve real-life problems involving comparison, fairness, sharing, shopping, traveling, and measuring efficiency.
C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Teacher reviews ratio, simplest form, proportion, and rate with real-life examples.
Evaluation Method (Expanded):
Exit slip/quiz: Write the ratio of 10 pencils to 5 erasers. Simplify it. Teacher collects and provides feedback.
Assignment (Expanded):
Simplify: (a) 24:36 (b) 15:45. State whether 2:5 and 8:20 are in proportion.
Follow-up Activity:
Learners find examples of rates at home (e.g., fuel price per liter, food items per cost).
Differentiation / Inclusive Strategies
Use concrete objects for slower learners. Allow peer teaching for proportion.
Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☐ Medium ☐ Low