and and Place value in binary numbers for JSS 1

Class: JSS 1
Term: First Term
Week: 9
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:

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

Previous Lesson: Meaning of base-ten numeral and binary number
Topic: Conversion Of Base-Ten Numerals To Binary Numbers
Subject Matter: Place value in binary numbers

Specific Objectives

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

Cognitive Domain

• Convert base ten numerals to binary numbers using the continuous division method.
• Identify the place value of digits in binary numbers.
• Identify computing binary digits (bits).

Affective Domain

• Appreciate the importance of binary numbers in computing.
• Demonstrate patience and accuracy in performing number conversions.

Psychomotor Domain

• Perform step-by-step conversion of base ten numbers to binary.
• Check the accuracy of binary conversions by converting back to base ten.

Reference Materials

The following resources were used in planning this lesson:

• 2025 Revised 9 Years Basic Education Curriculum
• Relevant State Unified Scheme of Work
• A suitable Mathematics textbook for JSS 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.

Rationale for the Lesson

This lesson is essential as it introduces students to binary numbers, which are fundamental to computer science and digital technology. Understanding how to convert between base ten and binary helps students grasp the underlying principles of how computers process information. It also builds foundational mathematical skills in number representation and systems.

Prerequisite/Previous Knowledge

Students should have a good understanding of base ten (decimal) numbers, basic division, and remainders.

Lesson Content/Board Summary

Conversion of Base-Ten Numerals to Binary Numbers

What are Binary Numbers?

Binary numbers are numbers expressed in base 2. This means they only use two digits: 0 and 1. These digits are called “bits” (binary digits).

Binary numbers are very important in computers because computers use electrical signals that are either ON (represented by 1) or OFF (represented by 0).

Place Value in Binary Numbers

Just like base ten numbers have place values like units, tens, hundreds (powers of 10), binary numbers have place values that are powers of 2.

For example, in a binary number like (1011_2):

1. The rightmost digit is the (2^0) place (units, which is 1).
2. The next digit to the left is the (2^1) place (twos, which is 2).
3. The next is the (2^2) place (fours, which is 4).
4. The next is the (2^3) place (eights, which is 8).

So, (1011_2 = (1 times 2^3) + (0 times 2^2) + (1 times 2^1) + (1 times 2^0))

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

( = 8 + 0 + 2 + 1 = 11_{10})

Conversion from Base Ten to Binary (Continuous Division Method)

To convert a base ten number to a binary number, we use the continuous division method:

1. Divide the base ten number by 2.
2. Write down the remainder (which will be either 0 or 1).
3. Divide the quotient from the previous step by 2.
4. Repeat steps 2 and 3 until the quotient becomes 0.
5. Read the remainders from bottom to top to get the binary number.

Checking Binary Conversion

To check if a binary conversion is correct, convert the binary number back to base ten using its place values (powers of 2).

1. Multiply each binary digit by its corresponding power of 2.
2. Sum up all the products.
3. The sum should be equal to the original base ten number.

Worked Examples

Example 1: Convert (25_{10}) to binary.

Solution:

1. (25 div 2 = 12) remainder (1)
2. (12 div 2 = 6) remainder (0)
3. (6 div 2 = 3) remainder (0)
4. (3 div 2 = 1) remainder (1)
5. (1 div 2 = 0) remainder (1)

Reading the remainders from bottom to top: (11001_2)

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

Example 2: Convert (42_{10}) to binary.

Solution:

1. (42 div 2 = 21) remainder (0)
2. (21 div 2 = 10) remainder (1)
3. (10 div 2 = 5) remainder (0)
4. (5 div 2 = 2) remainder (1)
5. (2 div 2 = 1) remainder (0)
6. (1 div 2 = 0) remainder (1)

Reading the remainders from bottom to top: (101010_2)

Answer: (42_{10} = 101010_2)

Example 3: Check the conversion of (25_{10}) to (11001_2).

Solution:

(11001_2 = (1 times 2^4) + (1 times 2^3) + (0 times 2^2) + (0 times 2^1) + (1 times 2^0))

( = (1 times 16) + (1 times 8) + (0 times 4) + (0 times 2) + (1 times 1))

( = 16 + 8 + 0 + 0 + 1)

( = 25_{10})

The check confirms the conversion is correct.

Teaching Methods/Instructional Techniques

Discussion, Demonstration, Guided Practice, Question and Answer, Explanation, Video Presentation, Problem Solving

Instructional Procedures

Step 1: Introduction

Time: 5 minutes

Teaching Skill: Recalling/Engaging

Teacher’s Activity: The teacher greets the students and asks them to recall what they know about number bases, specifically base ten. The teacher then introduces the concept of binary numbers (base 2) as used in computers.

Pupils’ Activity: Students respond to questions about base ten numbers and listen attentively to the introduction of binary numbers.

Learning Point: Introduction to binary numbers

Step 2: Explanation of Binary Numbers and Place Value

Time: 8 minutes

Teaching Skill: Explaining/Illustrating

Teacher’s Activity: The teacher explains that binary numbers use only 0 and 1. Using flashcards, the teacher illustrates the place values in binary numbers (powers of 2: (2^0, 2^1, 2^2), etc.) and shows how to interpret a simple binary number like (101_2).

Pupils’ Activity: Students observe the flashcards, listen to the explanation, and ask questions for clarification on binary digits and place values.

Learning Point: Binary digits and place values

Step 3: Introduction to Continuous Division Method

Time: 7 minutes

Teaching Skill: Demonstrating/Explaining

Teacher’s Activity: The teacher introduces the continuous division method for converting base ten numbers to binary. The teacher plays a short video demonstrating this method, pausing to explain each step clearly.

Pupils’ Activity: Students watch the video, pay attention to the steps of continuous division, and note down key instructions.

Learning Point: Continuous division method

Step 4: Worked Example 1 (Conversion)

Time: 6 minutes

Teaching Skill: Modelling/Guiding

Teacher’s Activity: The teacher works through Example 1 ((25_{10}) to binary) on the board, explaining each division by 2 and how to record the remainders. The teacher guides students to read the remainders from bottom to top.

Pupils’ Activity: Students follow along, copy the example, and participate in identifying the remainders and the final binary number.

Learning Point: Converting (25_{10}) to binary

Step 5: Worked Example 2 (Conversion)

Time: 6 minutes

Teaching Skill: Guiding/Practicing

Teacher’s Activity: The teacher presents Example 2 ((42_{10}) to binary) and guides students to attempt the steps. The teacher provides support and corrects errors as students work through the problem.

Pupils’ Activity: Students actively participate in solving the second example, performing divisions and identifying remainders with teacher guidance.

Learning Point: Converting (42_{10}) to binary

Step 6: Explaining the Checking Method

Time: 5 minutes

Teaching Skill: Explaining/Verifying

Teacher’s Activity: The teacher explains how to check the conversion by converting the binary number back to base ten using place values. The teacher demonstrates Example 3 (checking (11001_2)).

Pupils’ Activity: Students listen and observe how to check their conversions, understanding the importance of verification.

Learning Point: Checking binary conversions

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. Convert (13_{10}) to a binary number.
2. What are the only two digits used in binary numbers?
3. State the place value of the digit ‘1’ in (1010_2).
4. Convert (101_2) back to base ten.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Binary conversion assessment

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 binary numbers, conversion, and checking methods into their notebooks.

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

Learning Point: Recording lesson notes

Step 9: Conclusion

Time: 2 minutes

Teaching Skill: Summarising/Reinforcing

Teacher’s Activity: The teacher briefly recaps the main points of the lesson, emphasizing the continuous division method for conversion and the importance of binary numbers in technology. The teacher encourages students to practice more conversions at home.

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

Learning Point: Reinforcement of binary conversion

Continuous Assessment/Further Study

Type: Homework

Instruction: Convert the following base ten numbers to binary and check your answers:

1. (19_{10})
2. (37_{10})
3. (50_{10})
4. What is the base ten equivalent of (1110_2)?
5. Explain why binary numbers are important in computers.

Lesson Keywords

• Binary Numbers – A number system that uses only two digits, 0 and 1.
• Base Ten (Decimal) – The standard number system we use, with ten digits (0-9).
• Bit – A single binary digit (0 or 1).
• Place Value – The value of a digit based on its position in a number.
• Conversion – The process of changing a number from one base to another.

Differentiation

For weaker learners, provide additional simple examples and one-on-one guidance during the continuous division process. Use a multiplication table to help them with basic division. For faster learners, challenge them with larger base ten numbers or introduce the concept of converting binary to other bases like base 4 or base 8.

Suggested Lesson Videos

For further understanding, search on YouTube for: convert base 10 to binary jss1 maths

Teacher Guide for Using This Lesson Plan

Before the lesson, ensure you have prepared flashcards showing binary place values and a short, clear video demonstrating the continuous division method. Set up your projector or screen for the video. During the lesson, start by reviewing base ten to ensure students have a solid foundation. When teaching the continuous division method, go slowly, explaining each step of division and remainder recording. Encourage students to participate actively by calling on them to provide remainders. Emphasise the importance of reading the remainders from bottom to top. For the checking method, clearly show how powers of 2 are used. Allow students to copy the Board Summary notes after the main teaching and practice activities to consolidate their learning. Pay attention to common errors such as incorrect division or reading remainders from top to bottom. Provide extra practice problems for those struggling and challenge advanced learners with more complex conversions.