Lesson Plan: Converting Numbers from One Base to Another

Subject: Mathematics

Class: JSS 1

Term: Second Term

Week: 5

Age: 10–12 years

Topic: Number System

Sub-topic: Converting Numbers from One Base to Another

Duration: 40 minutes

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Behavioural Objectives

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

1. Explain the two-stage process of converting numbers between different bases.
2. Convert numbers from any base to base ten.
3. Convert numbers from base ten to other bases.
4. Convert numbers directly between two non-decimal bases using the two-stage method.

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Keywords

• Number system
• Base conversion
• Decimal system
• Place value
• Two-stage method

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Set Induction

The teacher asks students:

• “Can you think of different number systems we have studied?”
• “What do we do when we need to switch between number systems?”
• “How do computers store numbers?”

This engages students and introduces them to base conversion.

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Entry Behaviour

Students already understand number bases and can convert numbers between base ten and other bases.

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Learning Resources and Materials

• Place value charts
• Flashcards with base conversion steps
• Worksheets for practice

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Building Background/Connection to Prior Knowledge

The teacher reminds students how to convert numbers from other bases to base ten and how to convert numbers from base ten to other bases.

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Embedded Core Skills

• Critical thinking
• Logical reasoning
• Problem-solving

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Learning Materials

• Lagos State Scheme of Work
• Essential Mathematics for JSS 1
• New General Mathematics for Junior Secondary Schools

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Instructional Materials

• Base conversion charts
• Example problems on the board
• Worksheets for class activities

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Content (Explanation in List Format)

1. Meaning of Base Conversion

• Base conversion is the process of changing a number from one base to another.
• The most common method is the two-stage method:
  1. Convert the number to base ten.
  2. Convert the result to the required base.

2. Converting from Any Base to Base Ten

• Identify the place values in the given base.
• Multiply each digit by its place value.
• Add the results to get the decimal (base ten) equivalent.

Example 1 (Base 5 to Base 10)

Convert 243₅ to base 10.

• 2 × 5² + 4 × 5¹ + 3 × 5⁰
• 2 × 25 + 4 × 5 + 3 × 1
• 50 + 20 + 3 = 73₁₀

Example 2 (Base 7 to Base 10)

Convert 321₇ to base 10.

• 3 × 7² + 2 × 7¹ + 1 × 7⁰
• 3 × 49 + 2 × 7 + 1 × 1
• 147 + 14 + 1 = 162₁₀

3. Converting from Base Ten to Another Base

• Divide the base ten number by the required base.
• Record the remainder.
• Continue dividing until you get 0 as the quotient.
• Read the remainders from bottom to top to get the converted number.

Example 3 (Base 10 to Base 2)

Convert 13₁₀ to base 2.

• 13 ÷ 2 = 6 remainder 1
• 6 ÷ 2 = 3 remainder 0
• 3 ÷ 2 = 1 remainder 1
• 1 ÷ 2 = 0 remainder 1
• Reading from bottom to top: 13₁₀ = 1101₂

Example 4 (Base 10 to Base 5)

Convert 73₁₀ to base 5.

• 73 ÷ 5 = 14 remainder 3
• 14 ÷ 5 = 2 remainder 4
• 2 ÷ 5 = 0 remainder 2
• Reading from bottom to top: 73₁₀ = 243₅

4. Converting Directly Between Two Non-Decimal Bases

• First, convert the number to base ten.
• Then, convert the base ten number to the required base.

Example 5 (Base 5 to Base 2 via Base 10)

Convert 243₅ to base 2.

1. Convert 243₅ to base ten (as seen earlier): 73₁₀.
2. Convert 73₁₀ to base 2:
   • 73 ÷ 2 = 36 remainder 1
   • 36 ÷ 2 = 18 remainder 0
   • 18 ÷ 2 = 9 remainder 0
   • 9 ÷ 2 = 4 remainder 1
   • 4 ÷ 2 = 2 remainder 0
   • 2 ÷ 2 = 1 remainder 0
   • 1 ÷ 2 = 0 remainder 1
   • Reading from bottom to top: 243₅ = 1001001₂

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Evaluation (10 Fill-in-the-Blank Questions with Options)

1. The process of changing a number from one base to another is called ______.
   a) multiplication
   b) conversion
   c) subtraction
   d) division

2. The number 243₅ is equivalent to ______ in base 10.
   a) 70
   b) 73
   c) 75
   d) 80

3. The first step in converting a number from one base to another is to convert it to ______.
   a) base 8
   b) base 5
   c) base 10
   d) base 2

4. The number 1101₂ in base 10 is ______.
   a) 11
   b) 12
   c) 13
   d) 14

5. The number 162₁₀ in base 7 is ______.
   a) 321₇
   b) 312₇
   c) 231₇
   d) 123₇

6. The number 1001001₂ in base 5 is ______.
   a) 243₅
   b) 342₅
   c) 423₅
   d) 234₅

7. What is the remainder when 73 is divided by 5?
   a) 0
   b) 3
   c) 4
   d) 5

8. The base of the binary system is ______.
   a) 1
   b) 2
   c) 3
   d) 4

9. The highest digit in base 5 is ______.
   a) 5
   b) 4
   c) 6
   d) 3

10. Which number is written as 1001₂?
    a) 5
    b) 8
    c) 9
    d) 7

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Class Activity Discussion (10 FAQs with Answers)

1. What is base conversion?

   • Changing a number from one base to another.

2. Why do we convert numbers?

   • To work with different number systems.

3. What is the first step in converting between bases?

   • Convert the number to base ten.

4. What is the second step?

   • Convert from base ten to the required base.

5. How do we convert to base ten?

   • Multiply each digit by its place value and sum the results.

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Number Bases (Expansion and Conversion) – JSS 1 Mathematics Lesson Note