Meaning of base-ten numeral and binary number for JSS 1

Class: JSS 1
Term: First Term
Week: 8
Age: 12 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: NUMBER AND NUMERATION
Focal competence: Observing patterns in binary representation and understanding binary significance in computers
Key competencies/values: Tolerance
Skills:

• Familiarizing with how computing/basic programming works by first converting everything to binary
• Identifying patterns in binary representation

Previous Lesson: Counting in group of twos
Topic: Conversion Of Base-Ten Numerals To Binary Numbers
Subject Matter: Meaning of base-ten numeral, Meaning of binary number, Converting numbers from Base-ten to Binary

Specific Objectives

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

Cognitive Domain

• Define base-ten numeral.
• Define binary number.
• Convert base-ten numerals to binary numbers using the continuous division method.
• Identify simple patterns in binary representation.

Affective Domain

• Appreciate the importance of binary numbers in computer systems.
• Show patience and precision when performing number base conversions.

Psychomotor Domain

• Demonstrate the step-by-step process of converting base-ten numbers to binary.
• Write binary representations of given base-ten numbers.

Social Domain

• Collaborate effectively in group activities to solve conversion problems.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• New General Mathematics for Junior Secondary Schools 1
• The HeadTeacher Scheme of work

Instructional Materials

The teacher will teach this lesson with the aid of:

• Flash cards with worked examples of base-ten to binary conversion
• Videos on how to convert numbers from base-ten to binary using the continuous division method
• Whiteboard and markers
• Charts showing place values in base-ten and binary systems

Rationale for the Lesson

This lesson is crucial for students to understand different number systems, especially the binary system which is fundamental to how computers process information. It builds a foundation for future studies in computer science and logical reasoning, enabling students to appreciate the mathematical basis of digital technology.

Prerequisite/Previous Knowledge

Students should have a basic understanding of whole numbers, place values in the base-ten system, and the concept of division with remainders.

Lesson Content/Board Summary

Conversion Of Base-Ten Numerals To Binary Numbers

Meaning of Base-Ten Numeral

The base-ten numeral system, also known as the decimal system, is the number system we use every day. It has a base of 10 and uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The value of each digit depends on its position, which represents powers of 10.

For example, in the number 345:

1. 5 is in the units place ((5 times 10^0)).
2. 4 is in the tens place ((4 times 10^1)).
3. 3 is in the hundreds place ((3 times 10^2)).

Meaning of Binary Number

The binary number system is a base-2 system. It uses only two digits: 0 and 1. Binary numbers are very important in computing because computers understand and process information using electrical signals that are either ‘on’ (represented by 1) or ‘off’ (represented by 0). The value of each digit depends on its position, which represents powers of 2.

For example, in the binary number (101_2):

1. 1 is in the units place ((1 times 2^0)).
2. 0 is in the twos place ((0 times 2^1)).
3. 1 is in the fours place ((1 times 2^2)).

Converting Numbers from Base-Ten to Binary

To convert a base-ten numeral to a binary number, we use the continuous division method. This involves repeatedly dividing the base-ten number by 2 and recording the remainders. The binary number is then formed by reading the remainders from bottom to top.

Steps for Conversion:

1. Divide the base-ten number by 2.
2. Record the remainder (which will be either 0 or 1).
3. Take the quotient from the division and divide it by 2 again.
4. Continue this process until the quotient becomes 0.
5. Read the remainders from the last one obtained to the first one obtained to get the binary number.

Example 1: Convert (13_{10}) to a binary number.

Solution:

Step 1: Divide 13 by 2.

(13 div 2 = 6) remainder (1)

Step 2: Divide the quotient (6) by 2.

(6 div 2 = 3) remainder (0)

Step 3: Divide the quotient (3) by 2.

(3 div 2 = 1) remainder (1)

Step 4: Divide the quotient (1) by 2.

(1 div 2 = 0) remainder (1)

Step 5: Read the remainders from bottom to top.

The remainders are 1, 1, 0, 1.

Answer: (13_{10} = 1101_2)

Example 2: Convert (25_{10}) to a binary number.

Solution:

Step 1: Divide 25 by 2.

(25 div 2 = 12) remainder (1)

Step 2: Divide the quotient (12) by 2.

(12 div 2 = 6) remainder (0)

Step 3: Divide the quotient (6) by 2.

(6 div 2 = 3) remainder (0)

Step 4: Divide the quotient (3) by 2.

(3 div 2 = 1) remainder (1)

Step 5: Divide the quotient (1) by 2.

(1 div 2 = 0) remainder (1)

Step 6: Read the remainders from bottom to top.

The remainders are 1, 1, 0, 0, 1.

Answer: (25_{10} = 11001_2)

Checking Method (Binary to Base-Ten)

To check your conversion, convert the binary number back to base-ten by multiplying each digit by the corresponding power of 2 and summing the results.

For example, to check (1101_2):

(1101_2 = (1 times 2^3) + (1 times 2^2) + (0 times 2^1) + (1 times 2^0))

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

(= 8 + 4 + 0 + 1 = 13_{10})

This confirms the conversion is correct.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Video Presentation, Individual Practice

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Engaging/Activating prior knowledge

Teacher’s Activity: The teacher greets the students and asks them about the number system they use daily. The teacher then introduces the idea that computers use a different number system and asks students if they know what it is called.

Pupils’ Activity: Students respond to the greeting and discuss the everyday number system (base-ten). Some may mention binary numbers or computers.

Learning Point: Everyday number system

Step 2: Meaning of Base-Ten Numeral

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher explains the meaning of a base-ten numeral, emphasizing its base of 10 and the digits used (0-9). The teacher uses examples to illustrate place values (units, tens, hundreds).

Pupils’ Activity: Students listen attentively, ask questions for clarity, and identify digits and place values in base-ten numbers.

Learning Point: Base-ten numeral definition

Step 3: Meaning of Binary Number

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher introduces the binary number system, explaining its base of 2 and the two digits (0 and 1). The teacher highlights its importance in computers and shows simple binary numbers on flash cards or the board.

Pupils’ Activity: Students listen, observe the flash cards, and understand the concept of a base-2 system.

Learning Point: Binary number definition

Step 4: Introduction to Conversion Method

Time: 7 minutes

Teaching Skill: Demonstration/Instruction

Teacher’s Activity: The teacher explains that base-ten numbers can be converted to binary. The teacher introduces the continuous division by 2 method and shows a short video demonstrating the process step-by-step.

Pupils’ Activity: Students watch the video, pay attention to the steps, and ask questions about the continuous division method.

Learning Point: Continuous division method

Step 5: Worked Example 1

Time: 6 minutes

Teaching Skill: Guided Practice

Teacher’s Activity: The teacher guides students through the first example of converting (13_{10}) to binary, writing each step clearly on the board and ensuring students understand how to record remainders and read the final answer.

Pupils’ Activity: Students follow along with the teacher, perform the divisions in their notebooks, and write down the remainders.

Learning Point: First conversion example

Step 6: Worked Example 2 and Checking

Time: 6 minutes

Teaching Skill: Guided Practice/Reinforcement

Teacher’s Activity: The teacher guides students through a second example, converting (25_{10}) to binary. The teacher also briefly demonstrates how to check the answer by converting the binary back to base-ten.

Pupils’ Activity: Students work through the second example in their notebooks and observe the checking method.

Learning Point: Second conversion example

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

1. What is a base-ten numeral?
2. What are the two digits used in the binary number system?
3. Convert (10_{10}) to a binary number.
4. Explain how you would check your binary conversion.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Understanding conversion process

Step 8: Note-Taking

Time: 4 minutes

Teaching Skill: Guided Writing

Teacher’s Activity: The teacher guides pupils/students to copy the essential Board Summary notes on the meaning of base-ten, binary, and the conversion steps into their notebooks.

Pupils’ Activity: Pupils/students copy the notes carefully into their notebooks.

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 3 minutes

Teaching Skill: Summarizing

Teacher’s Activity: The teacher briefly summarizes the key concepts of base-ten and binary numbers and the importance of the continuous division method for conversion. The teacher encourages students to practice more at home.

Pupils’ Activity: Students listen to the summary and prepare for the next lesson.

Learning Point: Lesson recap and reinforcement

Continuous Assessment/Further Study

Type: Homework

Instruction: Convert the following base-ten numerals to binary numbers and show your working clearly:

1. (15_{10})
2. (21_{10})
3. (30_{10})
4. (42_{10})
5. What is the significance of binary numbers in computers?

Lesson Keywords

• Base-ten numeral – Our everyday number system with base 10.
• Decimal system – Another name for the base-ten numeral system.
• Binary number – A number system with base 2, using only digits 0 and 1.
• Continuous division – A method for converting base-ten numbers to other bases by repeatedly dividing.
• Remainder – The amount left over after a division.

Differentiation

For weaker learners, provide additional flash cards with simpler base-ten numbers (e.g., 5, 7, 9) for conversion and offer one-on-one guidance during practice. For faster learners, challenge them with larger base-ten numbers or introduce the concept of converting binary back to base-ten as an extension activity.

Suggested Lesson Videos

Search on YouTube for: “Convert Base 10 to Binary JSS 1 Maths”

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure all instructional materials, especially flash cards and the video on base-ten to binary conversion, are ready. Begin by engaging students with their prior knowledge of numbers. Clearly explain the concepts of base-ten and binary systems, emphasizing why binary is important for computers. When demonstrating the continuous division method, go step-by-step, explaining each division and remainder. Encourage students to participate actively in the guided practice sessions. During the note-taking phase (Step 8), ensure students copy the Board Summary accurately. Pay close attention to common errors such as reading remainders from top to bottom instead of bottom to top, or incorrect division. Provide immediate feedback and support to correct misconceptions. The evaluation questions should directly assess the specific objectives, ensuring students can define the terms and perform conversions.