Further Mathematics - Senior Secondary 1 - Calculating and Processing Devices I

Calculating and Processing Devices I

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TERM: 3RD TERM

WEEK 3

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Calculating and Processing Devices I
Focus: i) Abacus
ii) Decimal and Binary Systems

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

  1. Understand the concept and history of the abacus as a calculating device.
  2. Learn how to use the abacus to perform basic arithmetic operations.
  3. Demonstrate proficiency in converting between the decimal and binary number systems using the abacus.
  4. Solve problems involving the binary system using an abacus and calculators.

INSTRUCTIONAL TECHNIQUES:
• Direct instruction
• Guided practice
• Question and answer
• Hands-on demonstration
• Peer collaboration

INSTRUCTIONAL MATERIALS:
• Abacus
• Four-figure tables
• Slide rules
• Calculators
• Computers
• Whiteboard and markers
• Worksheets with problems on decimal and binary systems

PERIOD 1 & 2: Introduction to the Abacus

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of the abacus, explaining its origin and historical significance.

Students listen attentively and ask questions for clarification.

Step 2 - Structure of the Abacus

Demonstrates the structure of the abacus (beads, rods, and their placement). Explains how each rod represents a place value (ones, tens, hundreds, etc.).

Students observe and take notes on the structure of the abacus.

Step 3 - Basic Operations

Demonstrates simple addition and subtraction using the abacus. Explains how to move beads to represent numbers and perform calculations.

Students follow the demonstration and practice simple operations.

Step 4 - Practice

Provides practice problems for students to solve using the abacus, guiding them through the steps.

Students solve problems individually or in pairs using their abacuses.

NOTE ON BOARD:
The abacus consists of several rods, with each rod representing a place value. The beads are moved up or down to represent numbers. The number of beads moved corresponds to the value of the number.

EVALUATION (5 exercises):

  1. What is the abacus used for?
  2. How does the abacus represent numbers?
  3. Show the number 345 on the abacus.
  4. What are the place values represented by the first three rods of the abacus?
  5. Perform the following calculation on the abacus: 25 + 17.

CLASSWORK (5 questions):

  1. Show the number 578 on the abacus.
  2. Perform the following subtraction on the abacus: 99 - 46.
  3. What does each bead on the abacus represent?
  4. How do you use the abacus for addition?
  5. Perform 123 + 876 on the abacus.

ASSIGNMENT (5 tasks):

  1. Practice showing numbers on the abacus from 100 to 999.
  2. Perform the addition 458 + 367 on the abacus.
  3. Explain how subtraction is performed on the abacus.
  4. Practice using the abacus for multiplication (e.g., 5 × 12).
  5. Research the history of the abacus and summarize its significance.

 

PERIOD 3 & 4: Decimal and Binary Systems

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Decimal and Binary Systems

Reviews the decimal system (base 10) and introduces the binary system (base 2). Explains the basic difference between the two systems.

Students take notes on the decimal and binary systems and ask questions.

Step 2 - Converting Between Decimal and Binary

Demonstrates how to convert decimal numbers into binary and vice versa. Explains the process of repeated division by 2 for conversion from decimal to binary.

Students observe and follow along with the conversion process, taking notes.

Step 3 - Solving Problems Using Binary

Guides students in solving binary system problems using calculators and computers. Students will also use the abacus to practice binary calculations.

Students solve binary problems with teacher guidance. They use calculators and computers for practice.

Step 4 - Practice

Provides students with problems that require them to convert decimal numbers to binary and solve binary calculations.

Students practice solving the problems individually or in pairs.

NOTE ON BOARD:

  • Decimal System (Base 10): Uses digits 0-9. Each place value represents a power of 10.
  • Binary System (Base 2): Uses digits 0 and 1. Each place value represents a power of 2.
  • Conversion Method (Decimal to Binary):
  1. Divide the decimal number by 2.
  2. Record the remainder.
  3. Repeat the process with the quotient until the quotient is 0.
  4. Read the remainders from bottom to top to get the binary equivalent.

EVALUATION (5 exercises):

  1. Convert 13 (decimal) to binary.
  2. Convert 25 (decimal) to binary.
  3. Convert 10101 (binary) to decimal.
  4. Convert 11010 (binary) to decimal.
  5. Solve the binary addition: 1101 + 1011.

CLASSWORK (5 questions):

  1. Convert 12 (decimal) to binary.
  2. Convert 1010 (binary) to decimal.
  3. Convert 27 (decimal) to binary.
  4. Perform binary subtraction: 1011 - 110.
  5. Solve the binary multiplication: 101 × 11.

ASSIGNMENT (5 tasks):

  1. Convert 45 (decimal) to binary.
  2. Convert 11100 (binary) to decimal.
  3. Perform binary division: 10010 ÷ 101.
  4. Convert the following decimal numbers to binary: 5, 8, 14.
  5. Research the use of binary numbers in computer systems and explain why binary is important.