Mathematics - Junior Secondary 1 - Number base

Number base

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TERM: 2ND TERM

WEEK 3

Class: Junior Secondary School 1
Age: 12 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Number Base
Focus: Counting in Base Two, Conversion to Binary, Addition & Subtraction of Binary Numbers

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

  1. Count in base two (binary system).
  2. Convert base ten (decimal) numbers to binary.
  3. Perform addition and subtraction of 2- and 3-digit binary numbers.
  4. Understand place values in base two.
  5. Apply binary operations to real-life technology applications.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided discovery
• Individual practice
• Peer learning
• Real-life integration

INSTRUCTIONAL MATERIALS:
• Flashcards (binary place value)
• Binary conversion charts
• Counters or coins
• Worksheets
• Interactive board/Whiteboard
• Number base app or game (optional)

 

PERIOD 1: Counting in Base Two

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Explains base two system using "0" and "1", compares with base ten.

Pupils listen and ask questions.

Step 2 – Explanation

Demonstrates how counting works in base two: 0, 1, 10, 11, 100, etc.

Pupils follow along.

Step 3 – Practice

Uses flashcards or counters to guide counting.

Pupils count in base two aloud.

Step 4 – Note Taking

Writes examples, pupils copy and practice.

Pupils copy and recite.

NOTE ON BOARD:

  • Binary is base 2: only uses digits 0 and 1
  • Examples:
    • 0 = 0
    • 1 = 1
    • 10 (binary) = 2 (decimal)
    • 11 (binary) = 3
    • 100 (binary) = 4

EVALUATION:
Write the next 5 binary numbers after:

  1. 101
  2. 111
  3. 1000
  4. 1001
  5. 1010

CLASSWORK:
Convert to binary:

  1. 2
  2. 3
  3. 5
  4. 6
  5. 7

ASSIGNMENT:

  1. Count in base two from 0 to 20
  2. Write the binary for 8, 9, 10, 12, 15
  3. Write 4 rules of binary system
  4. Convert 14 to binary
  5. Convert 13 to binary

 

PERIOD 2 & 3: Conversion of Base 10 to Binary

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Recaps base 10 and introduces conversion to binary using division by 2.

Pupils answer recap questions.

Step 2 – Demonstration

Shows step-by-step conversion of base 10 numbers to binary.

Pupils follow and ask questions.

Step 3 – Practice

Pupils convert numbers with teacher’s guidance.

Practice in pairs.

Step 4 – Note Taking

Teacher writes methods and examples on board.

Pupils copy into notebooks.

NOTE ON BOARD:
To convert:

  • Divide number by 2, record remainders
  • Arrange remainders from bottom to top
    Example:
    Convert 10:
    10 ÷ 2 = 5 R0
    5 ÷ 2 = 2 R1
    2 ÷ 2 = 1 R0
    1 ÷ 2 = 0 R1
    Binary = 1010

EVALUATION:
Convert to binary:

  1. 4
  2. 6
  3. 9
  4. 12
  5. 15

CLASSWORK:
Convert 8, 10, 14, 16, 18 to binary.

ASSIGNMENT:

  1. Convert 20, 22, 25, 30, 32 to binary.
  2. Explain the steps you used for any two.
  3. Create your own 3-digit binary number and convert it to base 10.
  4. Practice 3 binary conversions using a calculator (if available).
  5. List 3 devices that use binary.

 

PERIOD 4 & 5: Binary Addition & Subtraction

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 – Introduction

Teaches basic rules of binary addition and subtraction.

Pupils listen and take note.

Step 2 – Demonstration

Works out sample additions like 101 + 10, and subtractions like 110 – 10.

Pupils follow and ask questions.

Step 3 – Group Work

Gives exercises to solve in groups.

Pupils solve and discuss.

Step 4 – Summary

Revises rules and corrects mistakes.

Pupils take correction.

NOTE ON BOARD:
Binary Addition Rules:
0 + 0 = 0
1 + 0 = 1
1 + 1 = 10
1 + 1 + 1 = 11

Binary Subtraction Rules:
0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
0 – 1 = borrow from next digit

EVALUATION (solve):

  1. 101 + 11
  2. 110 – 10
  3. 111 + 1
  4. 1001 – 1
  5. 1010 + 10

CLASSWORK:

  1. 111 + 101
  2. 110 – 11
  3. 1011 – 100
  4. 100 + 100
  5. 1000 – 11

ASSIGNMENT:

  1. Solve 5 binary additions and 5 subtractions
  2. Convert your answers to base 10
  3. Create 3 binary problems of your own
  4. Convert 3 base ten numbers to binary and add them

State 3 reasons why binary is important in technology