Understanding the Law of Indices

Mathematics Primary 5 First Term Lesson Notes Week 5

Subject: Mathematics

Class: Primary 5

Term: First Term

Week: 5

Age: 10 years

Topic: The Law of Indices

Sub-topic:

1. Raised to Power Zero
2. Additive Law
3. Subtractive Law

Duration: 40 minutes

Behavioural Objectives: By the end of the lesson, pupils should be able to:

1. Understand the concept of any number raised to the power of zero.
2. Apply the additive law of indices.
3. Apply the subtractive law of indices.

Keywords:

• Indices
• Power
• Exponent
• Additive
• Subtractive

Set Induction: Start the lesson with a quick review of multiplication and division of numbers.

Entry Behaviour: Pupils should already be familiar with basic multiplication and division.

Learning Resources and Materials:

• Whiteboard and markers
• Number cards
• Charts showing examples of indices

Building Background/Connection to Prior Knowledge: Discuss with pupils how multiplication can be seen as repeated addition, which leads to the idea of exponents as repeated multiplication.

Embedded Core Skills:

• Critical thinking
• Problem-solving
• Analytical skills

Learning Materials:

• Whiteboard
• Markers
• Charts

Reference Books:

• Lagos State Scheme of Work

Instructional Materials:

• Number cards
• Example charts

Content:

1. Raised to Power Zero:

Any number raised to the power of zero is equal to 1.
Example: 5⁰ = 1

2. Additive Law (Multiplication Law):

When multiplying numbers with the same base, add their exponents.
Formula: a^m × aⁿ = a^m+n
Example: 2³ × 2² = 2³⁺² = 2⁵

3. Subtractive Law (Division Law):

When dividing numbers with the same base, subtract their exponents.
Formula: a^m ÷ aⁿ = a^m-n
Example: 4⁵ ÷ 4² = 4^5-2 = 4³

Evaluation

1. 7⁰ = ____
   a. 0 b. 7 c. 1 d. 49
2. 3² × 3³ = ____
   a. 3⁶ b. 3⁵ c. 3⁹ d. 3¹
3. 10⁴ ÷ 10² = ____
   a. 10² b. 10³ c. 10⁶ d. 10¹
4. 5¹ = ____
   a. 5 b. 1 c. 0 d. 25
5. 2³ × 2² = ____
   a. 2⁶ b. 2⁴ c. 2⁵ d. 2¹
6. 6⁰ = ____
   a. 0 b. 1 c. 6 d. 36
7. 9² × 9³ = ____
   a. 9⁵ b. 9⁶ c. 9⁹ d. 9⁸
8. 4⁰ = ____
   a. 4 b. 0 c. 1 d. 16
9. 2³ × 2² = ____
   a. 2⁵ b. 2⁶ c. 2⁴ d. 2⁷
10. 3⁴ ÷ 3² = ____
    a. 3⁶ b. 3² c. 3¹ d. 3⁴

Conclusion:

• The teacher goes around to mark and provides necessary feedback on the topic.

7⁰ = ____
a. 0
b. 7
c. 1
d. 49

3² × 3³ = ____
a. 3⁶
b. 3⁵
c. 3⁹
d. 3¹

10⁴ ÷ 10² = ____
a. 10²
b. 10³
c. 10⁶
d. 10¹

5¹ = ____
a. 5
b. 1
c. 0
d. 25

2³ × 2² = ____
a. 2⁶
b. 2⁴
c. 2⁵
d. 2¹

6⁰ = ____
a. 0
b. 1
c. 6
d. 36

9² × 9³ = ____
a. 9⁵
b. 9⁶
c. 9⁹
d. 9⁸

4⁰ = ____
a. 4
b. 0
c. 1
d. 16

2⁴ ÷ 2¹ = ____
a. 2⁵
b. 2³
c. 2⁴
d. 2²

8² ÷ 8⁰ = ____
a. 8²
b. 8⁰
c. 8¹
d. 8²

5³ ÷ 5² = ____
a. 5⁵
b. 5¹
c. 5⁶
d. 5²

(2⁴ × 2³) ÷ 2² = ____
a. 2⁵
b. 2⁶
c. 2⁷
d. 2⁴

7⁵ × 7⁰ = ____
a. 7⁵
b. 7⁰
c. 7¹
d. 7⁶

3³ × 3² = ____
a. 3⁵
b. 3⁴
c. 3⁶
d. 3³

10⁰ ÷ 10¹ = ____
a. 10⁰
b. 10^-1
c. 10¹
d. 10¹

What is the value of any number raised to the power of zero?
Any number raised to the power of zero equals 1.
Example: 7⁰ = 1

What does the additive law of indices state?
The additive law states that when multiplying numbers with the same base, you add the exponents.
Formula: a^m × aⁿ = a^m+n

What is the result of 2³ × 2²?
According to the additive law, 2³ × 2² = 2³⁺² = 2⁵

What does the subtractive law of indices describe?
The subtractive law states that when dividing numbers with the same base, you subtract the exponents.
Formula: a^m ÷ aⁿ = a^m-n

What is the result of 5⁴ ÷ 5²?
According to the subtractive law, 5⁴ ÷ 5² = 5^4-2 = 5²

What does 3⁰ equal?
Any number raised to the power of zero equals 1.
Example: 3⁰ = 1

How do you simplify 8⁵ × 8³?
According to the additive law, 8⁵ × 8³ = 8⁵⁺³ = 8⁸

What is the result of 6⁷ ÷ 6⁴?
According to the subtractive law, 6⁷ ÷ 6⁴ = 6^7-4 = 6³

What does 10⁰ × 10³ equal?
According to the additive law, 10⁰ × 10³ = 10⁰⁺³ = 10³

How do you simplify 2⁶ ÷ 2³?
According to the subtractive law, 2⁶ ÷ 2³ = 2^6-3 = 2³

What is the result of 9⁰?
Any number raised to the power of zero equals 1.
Example: 9⁰ = 1

What is the formula for multiplying numbers with different bases?
The law of indices does not apply to different bases; it only applies when the bases are the same.

What does the term ‘base’ refer to in indices?
The base is the number that is raised to a power.
Example: In 4³, 4 is the base.

How do you express 7⁵ ÷ 7² in simplified form?
According to the subtractive law, 7⁵ ÷ 7² = 7^5-2 = 7³

What is the result of 3² × 3⁰?
According to the additive law, 3² × 3⁰ = 3²⁺⁰ = 3²