Index and Indices – Primary 5 Mathematics First Term Lesson Note

This Primary 5 Mathematics First Term lesson note on Index and Indices explains index notation in a simple, classroom-friendly way. Pupils learn how a number can be written as repeated multiplication, identify the base and index, and solve simple problems using powers.

Lesson Information

Subject: Mathematics
Class: Primary 5 (Basic 5)
Term: First Term
Week: 3
Topic: Index and Indices
Sub-topic: Meaning of index and indices and simple applications
Duration: 40 minutes

Learning Objectives

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

define index and indices;
identify the base and index in a number written in index form;
write repeated multiplication in index form;
expand simple index notation into repeated multiplication; and
calculate simple powers.

Keywords

Index, indices, power, exponent, base, repeated multiplication.

Set Induction

Write 2 × 2 × 2 × 2 on the board. Ask: “Can we write this in a shorter way?” Explain that mathematics has a convenient way of showing repeated multiplication. This leads to the idea of index notation.

Entry Behaviour and Instructional Materials

Pupils should already understand multiplication and repeated multiplication. Use a whiteboard, marker or chalk, multiplication charts, flashcards and simple objects such as bottle tops or beads for demonstration.

Meaning of Index and Indices

An index is the small number written above and to the right of a base. It tells us how many times the base is multiplied by itself. The plural of index is indices.

For example, in 2⁴:

2 is the base.
4 is the index or power.
2⁴ = 2 × 2 × 2 × 2 = 16.

Index notation therefore gives us a shorter way of writing repeated multiplication.

Worked Examples

3² = 3 × 3 = 9
4³ = 4 × 4 × 4 = 64
5⁴ = 5 × 5 × 5 × 5 = 625
10² = 10 × 10 = 100
6³ = 6 × 6 × 6 = 216

Reading Index Notation

When we see 7², we read it as “seven raised to the power two” or “seven to the power of two.” It means 7 × 7, not 7 × 2.

Teacher and Learner Activities

Teacher’s activities:

Revise multiplication and the previous lesson on Notation of Numbers.
Introduce repeated multiplication using familiar numbers.
Explain the base, index and power.
Demonstrate how to convert repeated multiplication to index form and back again.
Give guided examples and correct errors.

Learners’ activities:

Observe the examples on the board.
Identify bases and indices.
Convert repeated multiplication to index form.
Expand index notation into repeated multiplication.
Work independently and compare answers with classmates.

Class Activity

Complete the following:

Write 2 × 2 × 2 in index form.
Write 5 × 5 × 5 × 5 in index form.
Expand 3⁴.
Calculate 4².
Identify the base and index in 9³.

Evaluation Questions

The small number written above a base is called the ______. (a) digit (b) index (c) factor (d) product
The plural of index is ______. (a) indexes (b) indices (c) powers (d) bases
What does 2⁵ mean?
Calculate 6².
Write 7 × 7 × 7 in index form.
In 8⁴, identify the base and the index.

Assessment

Define index.
Define indices.
Write 3 × 3 × 3 × 3 in index form.
Write 5³ as repeated multiplication.
Calculate 4³.

Common Mistakes to Avoid

Do not multiply the base by the index. For example, 3² means 3 × 3, not 3 × 2.
Do not confuse the base with the index.
Count the number of repeated factors carefully when writing the power.

Frequently Asked Questions

What is an index?

An index is the small number that tells how many times a base is multiplied by itself.

What is the plural of index?

The plural is indices.

What is the base in 5³?

The base is 5, while 3 is the index.

Why do we use indices?

Indices make repeated multiplication shorter and easier to write and read.

Conclusion

Guide pupils to summarise the lesson: the base is the number being multiplied, while the index tells how many times the base occurs as a factor. Give extra practice to pupils who need support.

Homework

Write 8 × 8 × 8 in index form.
Expand 9².
Calculate 5³.
Identify the base and index in 10².
Explain in one sentence why index notation is useful.