**Lesson Plan: Rational and Non-Rational Numbers and Compound Interest**
**Grade Level**: Junior Secondary 3
**Duration**: 90 minutes
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### Objective:
By the end of the lesson, students will be able to:
1. Define and differentiate between rational and non-rational (irrational) numbers.
2. Identify examples of rational and non-rational numbers.
3. Understand the concept of compound interest and solve basic problems involving compound interest.
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### Materials Needed:
- Whiteboard and markers
- Projector and computer for presentations
- Handouts with examples and practice problems
- Scientific calculators
- Graph paper
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### Lesson Breakdown:
#### **Introduction (10 minutes)**:
1. **Greeting and Warm-up Activity** (5 minutes):
- Briefly review previous lesson topics.
- Quick mental math exercise to activate students' thinking.
2. **Objective Overview** (5 minutes):
- Share the objectives of today's lesson with students.
- Briefly explain how the lesson will be organized.
#### **Part 1: Rational and Non-Rational Numbers (30 minutes)**:
3. **Definition and Explanation** (10 minutes):
- Define rational numbers: Numbers that can be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers, and \(b \neq 0\).
- Define non-rational (irrational) numbers: Numbers that cannot be expressed as simple fractions. They have non-repeating, non-terminating decimal expansions.
- Give examples of each using the whiteboard and projector.
4. **Guided Practice** (10 minutes):
- Distribute handouts with a list of numbers.
- Ask students to categorize each number as rational or non-rational.
- Review answers as a class and explain any misconceptions.
5. **Independent Practice** (10 minutes):
- Provide another set of example problems for individual work.
- Walk around the classroom to offer assistance and check for understanding.
#### **Part 2: Compound Interest (50 minutes)**:
6. **Definition and Formula** (10 minutes):
- Explain the concept of compound interest vs. simple interest.
- Introduce the compound interest formula:
\[
A = P \left( 1 + \frac{r}{n} \right)^{nt}
\]
where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial sum of money).
- \(r\) = annual interest rate (decimal).
- \(n\) = number of times the interest is compounded per year.
- \(t\) = time the money is invested for in years.
7. **Worked Example** (10 minutes):
- Go through a detailed example on the board:
- Principal amount (\(P\)) = $1,000
- Annual interest rate (\(r\)) = 5% (0.05)
- Compounded annually (\(n = 1\))
- Time (\(t\)) = 3 years
- Calculate \(A\).
8. **Guided Practice** (15 minutes):
- Distribute practice problems on the handout.
- Students work in pairs to solve problems.
- Review answers together, explain steps and correct any errors.
9. **Extension Activity** (10 minutes):
- Introduce problems with different compounding frequencies (annually, semi-annually, quarterly, monthly).
- Provide graph paper for students to graph the growth of investment over time for different compounding periods.
10. **Independent Practice** (5 minutes):
- Additional problems for students to solve individually.
#### **Conclusion and Assessment (10 minutes)**:
11. **Summary** (5 minutes):
- Recap the key points about rational and non-rational numbers.
- Review compound interest formula and its application.
12. **Exit Ticket** (5 minutes):
- Hand out a quick quiz on both topics to assess understanding.
- Collect for grading and feedback.
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### Homework:
1. **Worksheet**: Complete a worksheet with problems on identifying rational and non-rational numbers and more compound interest problems.
2. **Real-World Application**: Ask students to find a real-life example where compound interest is used and write a short paragraph about it.
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### Reflection:
- After the lesson, reflect on what went well and what could be improved.
- Note any students who may need further support or enrichment.
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This lesson plan is designed to be comprehensive and engaging, ensuring that students grasp the differences between rational and non-rational numbers as well as understand how to compute and apply compound interest in various contexts.