Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: First Term
Week: 1
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Modular Arithmetic: Integers and Applications.
Topic: NUMBER BASES (I)
Subject Matter: Decimal base (Base 10) and other bases e.g. base 2 (binary) base 7 (days of the week) etc., Conversion from Base 10 to other bases, conversion from other bases to base 10.

Specific Objectives

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

Cognitive Domain:

Identify number bases other than binary (base 2) and denary (base 10).
Convert numbers from base 10 to other bases.
Convert numbers from other bases to base 10.
Convert numbers with decimal fractions from other bases to base 10.

Affective Domain:

Appreciate the importance of different number systems in various applications.
Show interest in solving problems involving number base conversions.

Psychomotor Domain:

Accurately perform calculations for converting numbers between different bases.

Collaborate with peers to solve conversion problems.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Senior Secondary School Mathematics.
State Unified Scheme of Work for Senior Secondary School Mathematics.
New General Mathematics for Senior Secondary Schools 1.

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing the conversion from one base (except base 2) to another base.

Rationale for the Lesson

This lesson helps pupils understand different ways numbers are represented, which is important in everyday situations like reading digital clocks, understanding computer systems, and even recognizing unique number patterns. Understanding number bases helps pupils appreciate the flexibility of the number system beyond the familiar base 10.

Prerequisite/Previous Knowledge

Pupils are assumed to have basic knowledge of number systems, place values, and fundamental arithmetic operations (addition, subtraction, multiplication, and division).

Lesson Content/Board Summary

NUMBER BASES (I)

Decimal Base (Base 10)

The decimal base, also known as base 10 or denary, is the number system commonly used in daily life. It uses ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

In base 10, the position of each digit determines its value, which is a power of 10. For example, 345₁₀ means (3 × 10²) + (4 × 10¹) + (5 × 10⁰).

Other Number Bases

Other number bases are systems that use a different count of unique digits. The number of digits used defines the base.

The following are examples of other number bases:

Binary (Base 2): Uses two digits (0, 1). It is fundamental in computer systems.
Quaternary (Base 4): Uses four digits (0, 1, 2, 3).
Quinary (Base 5): Uses five digits (0, 1, 2, 3, 4).
Octal (Base 8): Uses eight digits (0, 1, 2, 3, 4, 5, 6, 7).
Duodecimal (Base 12): Uses twelve digits (0-9, A, B). (e.g., in measuring time and dozens).
Hexadecimal (Base 16): Uses sixteen digits (0-9, A, B, C, D, E, F). Also used in computing.

The base of a number is usually written as a subscript. For example, 1011₂ means 1011 in base 2.

Conversion from Base 10 to Other Bases

To convert a number from base 10 to another base, the number is repeatedly divided by the new base, and the remainders are recorded. The remainders, read from bottom to top, form the number in the new base.

Example: Convert 25₁₀ to base 2.

25 ÷ 2 = 12 R 1

12 ÷ 2 = 6 R 0

6 ÷ 2 = 3 R 0

3 ÷ 2 = 1 R 1

1 ÷ 2 = 0 R 1

Reading the remainders from bottom up: 11001₂. Therefore, 25₁₀ = 11001₂.

Conversion from Other Bases to Base 10

To convert a number from another base to base 10, multiply each digit by its place value (which is a power of the base) and then sum the results.

Example: Convert 1101₂ to base 10.

1101₂ = (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

= (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1)

= 8 + 4 + 0 + 1

= 13₁₀

Therefore, 1101₂ = 13₁₀.

Conversion of Numbers with Decimal Fraction to Base 10

For numbers with decimal fractions in other bases, the digits after the decimal point are multiplied by negative powers of the base, starting from -1.

Example: Convert 10.11₂ to base 10.

10.11₂ = (1 × 2¹) + (0 × 2⁰) + (1 × 2⁻¹) + (1 × 2⁻²)

= (1 × 2) + (0 × 1) + (1 × ¹/₂) + (1 × ¹/₄)

= 2 + 0 + 0.5 + 0.25

= 2.75₁₀

Therefore, 10.11₂ = 2.75₁₀.

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 asks them to state the number system they commonly use. The teacher then introduces the topic “NUMBER BASES” and explains that numbers can be represented in different bases.
Pupils’ Activity: Pupils respond by saying “Base 10” or “Decimal system.” They listen attentively to the teacher’s introduction.
Learning Point: Pupils are introduced to the concept of number bases.

Step 2: Explanation of Decimal Base (Base 10)

Time: 5 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the decimal base (Base 10), its digits (0-9), and how place value works in this system, using an example like 345₁₀.
Pupils’ Activity: Pupils listen and take notes, asking questions for clarification where needed.
Learning Point: Pupils understand the structure of the familiar base 10 system.

Step 3: Introduction to Other Number Bases

Time: 5 minutes
Teaching Skill: Questioning/Guidance
Teacher’s Activity: The teacher guides pupils to identify other number bases by asking if they know of other ways numbers are counted (e.g., days of the week, computer language). The teacher then lists and explains examples like binary, octal, and hexadecimal bases, emphasizing their unique digits.
Pupils’ Activity: Pupils mention other bases they might know (e.g., base 2, base 8). They observe the chart and note the digits used in different bases.
Learning Point: Pupils identify various number bases beyond base 10.

Step 4: Conversion from Base 10 to Other Bases

Time: 10 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates the step-by-step process of converting a base 10 number to another base (e.g., base 2) using repeated division and collecting remainders. The teacher then provides one or two practice questions for pupils to solve.
Pupils’ Activity: Pupils observe the demonstration, ask questions, and practice solving conversion problems in their notebooks.
Learning Point: Pupils learn to convert numbers from base 10 to other bases.

Step 5: Conversion from Other Bases to Base 10

Time: 10 minutes
Teaching Skill: Demonstration/Practice
Teacher’s Activity: The teacher demonstrates how to convert a number from another base (e.g., base 2 or base 5) back to base 10 by multiplying each digit by the power of its base. The teacher provides another example for pupils to attempt.
Pupils’ Activity: Pupils pay attention to the teacher’s explanation and work through the practice problems.
Learning Point: Pupils learn to convert numbers from other bases to base 10.

Step 6: Conversion of Numbers with Decimal Fractions to Base 10

Time: 5 minutes
Teaching Skill: Demonstration
Teacher’s Activity: The teacher demonstrates how to convert a number with a decimal fraction from another base (e.g., base 2) to base 10, explaining the use of negative powers for the fractional part.
Pupils’ Activity: Pupils observe the demonstration and ask questions for clarification.
Learning Point: Pupils understand how to convert numbers with decimal fractions to base 10.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define a number base.
Mention three number bases other than base 10.
Convert 37₁₀ to base 5.
Convert 123₄ to base 10.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson on number bases and assigns homework:
1. Convert 49₁₀ to base 2.
2. Convert 10110₂ to base 10.
3. Convert 11.01₂ to base 10.
Pupils’ Activity: Pupils listen to the summary and copy the homework assignment.
Learning Point: Pupils consolidate their learning and prepare for further practice.

Lesson Keywords

Decimal Base – A number system that uses ten unique digits (0-9).
Binary Base – A number system that uses two unique digits (0 and 1).
Place Value – The value of a digit based on its position in a number.
Base – The number of unique digits used in a number system, including zero.
Conversion – The process of changing a number from one base to another.

Differentiation

For pupils who grasp concepts quickly, challenge them with conversions involving larger numbers or more complex bases like hexadecimal. For those who need more support, provide additional guided practice with simpler conversions and use visual aids more frequently.

Note for teachers using this lesson plan

Ensure pupils understand the concept of place value thoroughly before moving to conversions. Emphasize the importance of writing the base as a subscript. Encourage pupils to show all their working steps for conversion problems.