MATHEMATICS JSS 3 SECOND TERM LESSON NOTE

WEEK 5: INDICES AND LAWS OF INDICES

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Subject: Mathematics

Class: JSS 3

Term: Second Term

Week: 5

Age: 13 – 15 years

Duration: 40 Minutes

Topic: Indices and Laws of Indices

Sub-topic: Laws and Applications of Indices

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Behavioral Objectives

By the end of the lesson, students should be able to:

1. Define indices and explain their importance in mathematics.
2. State and explain the laws of indices.
3. Apply the laws of indices in simplifying expressions.
4. Solve simple index equations using index laws.

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Keywords

• Index – The power to which a number is raised.
• Base – The number being raised to a power.
• Exponent – Another word for index.
• Power – A way of expressing repeated multiplication of a number.
• Index Equation – An equation where the unknown is in the index.

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Set Induction (Entry Behavior)

The teacher will begin the lesson by asking students to write down the following expressions:

• 2 × 2 × 2 × 2
• 5 × 5 × 5
• 3 × 3

The teacher will then introduce the concept of indices as a shorter way of writing repeated multiplication.

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Learning Resources and Materials

1. Whiteboard and marker
2. Chart showing the laws of indices
3. Number charts
4. Mathematics textbooks

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Building Background / Connection to Prior Knowledge

Students have previously learned about multiplication and exponents in JSS 2. This lesson will extend their understanding by introducing the laws governing indices.

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Embedded Core Skills

• Critical Thinking – Applying the laws of indices to simplify expressions.
• Problem-Solving – Solving equations involving indices.
• Numeracy Skills – Understanding the concept of indices and exponentiation.

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Instructional Materials

• Mathematics textbook
• Whiteboard and marker
• Number charts showing powers of 2, 3, and 5

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Reference Books

• New General Mathematics for JSS 3
• Lagos State Scheme of Work
• Essential Mathematics for Junior Secondary School

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Lesson Content

Definition of Indices

Indices (or exponents) refer to the power to which a number is raised. For example:

• 2 raised to the power of 3 (written as 2³) means 2 × 2 × 2 = 8
• 5² means 5 × 5 = 25
• 10⁴ means 10 × 10 × 10 × 10 = 10,000

Laws of Indices

There are seven important laws of indices:

1. Multiplication Law:
   When multiplying numbers with the same base, add the indices.
   • Example: 2³ × 2⁴ = 2^(3+4) = 2⁷ = 128
2. Division Law:
   When dividing numbers with the same base, subtract the indices.
   • Example: 5⁶ ÷ 5² = 5^(6-2) = 5⁴ = 625
3. Negative Index Law:
   A negative index means taking the reciprocal of the base.
   • Example: 3⁻² = 1/3² = 1/9
4. Zero Index Law:
   Any number raised to the power of zero is 1.
   • Example: 10⁰ = 1, 5⁰ = 1
5. Power of a Power Law:
   When raising a power to another power, multiply the indices.
   • Example: (2³)⁴ = 2^(3×4) = 2¹²
6. Fractional Index Law:
   A fractional index represents a root.
   • Example: 64^(1/2) = square root of 64 = 8
7. Power of a Quotient Law:
   When a fraction is raised to a power, apply the power to both numerator and denominator.
   • Example: (3/4)² = 3²/4² = 9/16

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Application of the Laws of Indices

Using the laws above, we can simplify complex expressions:

1. Example 1:
   • 3⁴ × 3³ = 3^(4+3) = 3⁷ = 2187
2. Example 2:
   • 8⁵ ÷ 8² = 8^(5-2) = 8³ = 512
3. Example 3:
   • (5²)³ = 5^(2×3) = 5⁶ = 15625

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Evaluation Questions

Fill in the blanks (Choose the correct option a, b, c, or d):

1. 2⁴ × 2³ = 2^___
   a) 7
   b) 12
   c) 6
   d) 8
2. 9⁶ ÷ 9³ = 9^___
   a) 3
   b) 2
   c) 9
   d) 6
3. 5⁻² =
   a) 25
   b) 1/25
   c) -25
   d) 5
4. (10³)² =
   a) 10⁶
   b) 10⁵
   c) 10³
   d) 10⁹
5. x⁰ =
   a) 0
   b) 1
   c) x
   d) Undefined

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Class Activity Discussion (FAQs)

1. What is an index?
   An index is the power to which a number is raised.
2. What does it mean when an index is negative?
   A negative index means the reciprocal of the number raised to the positive power.
3. Why is any number raised to the power of zero equal to 1?
   Because the division rule states that x^m ÷ x^m = x^(m-m) = x⁰ = 1.
4. How do we simplify expressions with indices?
   By applying the laws of indices.

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Presentation Steps

1. Teacher Revises the Previous Topic.
2. Teacher Introduces the New Topic.
3. Teacher Explains the Laws of Indices.
4. Students Solve Practice Questions.

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Assessment (Short-answer Questions)

1. Simplify 4³ × 4².
2. Find the value of 9⁴ ÷ 9².
3. Express 1/16 using a negative index.
4. Solve 5^x = 125.
5. Evaluate (2³)².

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Conclusion

The teacher summarizes the laws of indices and their applications. Students are given further practice to reinforce understanding.

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