Class: Primary Six (Pry 6)
Term: Second Term
Week: 2
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Number and Numeration
Previous Lesson: Order of Operation, BODMAS Meaning and Problems.
Topic: INDICES (Power)
Subject Matter: Writing numbers in index form, expressing numbers in index form using factors, multiplying numbers using index form, quantitative reasoning on indices.

Specific Objectives

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

Cognitive Domain:

Define index form and identify its components.
Write numbers in index form.
Express numbers in index form using prime factors.
Multiply numbers using index form.
Solve quantitative reasoning problems on indices.

Affective Domain:

Appreciate the importance of using index form to represent large numbers.
Show interest in solving mathematical problems involving indices.

Psychomotor Domain:

Accurately write given numbers in index form.
Correctly perform multiplication of numbers expressed in index form.

Work cooperatively with peers to solve problems related to indices.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum (Primary Mathematics)
State Unified Scheme of Work for Primary 6 Mathematics
New General Mathematics for Primary Schools, Book 6
https://www.mathsisfun.com/exponent.html
https://www.bbc.co.uk/bitesize/guides/zc6p3k7/revision/1

Instructional Materials

The teacher will teach this lesson with the aid of:

Textbook
Workbook
Multiplication chart
Whiteboard and markers/chalk

Rationale for the Lesson

This lesson helps pupils understand a simpler way to write repeated multiplication using index form. It enables them to work with large numbers more easily and forms a foundation for future mathematical concepts involving powers and roots.

Prerequisite/Previous Knowledge

Pupils should have a good understanding of multiplication, factors, and prime numbers.

Lesson Content/Board Summary

INDICES (POWER)

Meaning of Index Form (Power)

Index form, also known as power or exponential form, is a short way of writing repeated multiplication of the same number.

For example, 2 × 2 × 2 × 2 can be written as 2⁴.

In 2⁴:

2 is the base (the number being multiplied).
4 is the index or power or exponent (the number of times the base is multiplied by itself).

Writing Numbers in Index Form

To write a number in index form, identify the base and count how many times it is multiplied by itself.

Examples:

3 × 3 × 3 = 3³
5 × 5 = 5²
10 × 10 × 10 × 10 × 10 = 10⁵

Expressing Numbers in Index Form Using Factors

To express a number in index form using factors, find its prime factors and then write them in index form.

Steps:

Find the prime factors of the number.
Group identical prime factors.
Write each group in index form.

Example 1: Express 8 in index form.

8 = 2 × 4

= 2 × 2 × 2

= 2³

Example 2: Express 36 in index form.

36 = 2 × 18

= 2 × 2 × 9

= 2 × 2 × 3 × 3

= 2² × 3²

Multiplying Numbers Using Index Form

When multiplying numbers with the same base, add their powers (indices).

Rule: a^m × aⁿ = a^m+n

Examples:

2³ × 2² = 2³⁺² = 2⁵
3⁴ × 3¹ = 3⁴⁺¹ = 3⁵
5² × 5³ × 5¹ = 5²⁺³⁺¹ = 5⁶

Quantitative Reasoning on Indices

Quantitative reasoning problems involve applying the understanding of indices to solve puzzles or complete patterns.

Example: Complete the pattern:

2¹ = 2

2² = 4

2³ = 8

2⁴ = ?

Solution: 2⁴ = 2 × 2 × 2 × 2 = 16

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews their previous knowledge of multiplication and factors by asking questions like, “What is 3 multiplied by 3?” and “What are the factors of 12?”. The teacher then introduces the topic “Indices (Power)” by explaining that there is a shorter way to write repeated multiplication.
Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction.
Learning Point: Pupils recall prior knowledge and are introduced to the lesson topic.

Step 2: Meaning of Index Form

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains what index form is, defining the base and the index (power/exponent) with examples like 2 × 2 × 2 = 2³. The teacher writes the definitions and examples on the board.
Pupils’ Activity: Pupils listen, observe, and copy notes from the board.
Learning Point: Pupils understand the meaning of index form and its components.

Step 3: Writing Numbers in Index Form

Time: 7 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates how to write various repeated multiplications in index form, for example, 5 × 5 × 5 × 5 = 5⁴. The teacher provides more examples for pupils to practice on their own.
Pupils’ Activity: Pupils observe the examples and practice writing numbers in index form.
Learning Point: Pupils learn to correctly write numbers in index form.

Step 4: Expressing Numbers in Index Form Using Factors

Time: 7 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher guides pupils through the process of expressing numbers in index form by first finding their prime factors. Examples like 8 = 2³ and 36 = 2² × 3² are worked on the board.
Pupils’ Activity: Pupils follow the teacher’s guidance, participate in finding prime factors, and express numbers in index form.
Learning Point: Pupils can express given numbers in index form using their prime factors.

Step 5: Multiplying Numbers Using Index Form

Time: 7 minutes
Teaching Skill: Explanation/Rule Formulation
Teacher’s Activity: The teacher explains the rule for multiplying numbers with the same base (adding the powers). The teacher provides examples such as 2³ × 2² = 2⁵ and 3⁴ × 3¹ = 3⁵, showing the expansion and then the application of the rule.
Pupils’ Activity: Pupils listen to the explanation, understand the rule, and solve multiplication problems using index form.
Learning Point: Pupils learn and apply the rule for multiplying numbers in index form.

Step 6: Quantitative Reasoning on Indices

Time: 5 minutes
Teaching Skill: Problem Solving
Teacher’s Activity: The teacher presents simple quantitative reasoning problems related to indices, such as completing number patterns involving powers. The teacher guides pupils on how to approach these problems.
Pupils’ Activity: Pupils attempt to solve the quantitative reasoning problems presented by the teacher.
Learning Point: Pupils develop problem-solving skills related to indices.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

What is index form?
In 5⁴, what is the base and what is the index?
Write 7 × 7 × 7 in index form.
Express 16 in index form using prime factors.
Simplify 3² × 3³.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the definition of index form, how to write numbers in index form, and how to multiply numbers in index form. The teacher then assigns homework from the textbook.
Pupils’ Activity: Pupils listen to the summary and copy the homework.
Learning Point: Pupils consolidate their learning and receive further practice.

Home Task: Solve three new exercises on INDICES (Power). Show each step and check each answer.

Lesson Keywords

Index – A number that shows how many times a base number is multiplied by itself.
Power – Another name for index or exponent.
Base – The number that is multiplied by itself in an index form.
Exponent – Another name for index or power.
Factor – A number that divides another number exactly.
Prime Factor – A factor that is also a prime number.

Differentiation

For struggling learners, the teacher will provide additional simpler examples and use visual aids like flashcards with repeated multiplication and their index forms. For advanced learners, the teacher will provide more challenging problems involving larger numbers or multiple bases in multiplication, encouraging them to explore further properties of indices.

Note for teachers using this lesson plan

Ensure pupils grasp the concept of repeated multiplication before introducing index form. Encourage active participation and provide ample practice opportunities for each skill. Emphasize the rule for multiplying numbers with the same base, as it is a foundational concept. Use the multiplication chart as a visual aid to reinforce basic multiplication facts when finding factors.