Lesson Plan: Number Base (Expansion and Conversion to Base Ten)

Subject: Mathematics

Class: JSS 1

Term: Second Term

Week: 4

Age: 10–12 years

Topic: Number Base

Sub-topic: Expansion and Conversion to Base Ten

Duration: 40 minutes

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Behavioural Objectives

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

1. Explain the concept of number bases.
2. Identify the decimal (denary) system as base ten.
3. Expand numbers in different bases using expanded notation.
4. Convert numbers from other bases to base ten.

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Keywords

• Number base
• Decimal system
• Denary system
• Expanded notation
• Conversion

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Set Induction

The teacher asks students:

• “What system do we use to count numbers every day?”
• “Can you think of any numbering system different from what we normally use?”

This introduces students to the concept of number bases.

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Entry Behaviour

Students have learned how to count and write numbers in the decimal system (base 10). They are also familiar with place values.

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Learning Resources and Materials

• Place value charts
• Flashcards with numbers in different bases
• Whiteboard and marker

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Building Background/Connection to Prior Knowledge

The teacher reminds students that the decimal system uses digits 0–9. The teacher writes the number 345 and asks:

• “What does the digit 3 represent?”
• “What about the digits 4 and 5?”

This helps students recall place value, which is essential for understanding number 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

• Number base conversion charts
• Example problems on the board
• Worksheets for practice

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Content (Explanation in List Format)

1. Meaning of Number Base

• A number base is a system of counting that uses a fixed number of digits.
• The decimal system (base ten) is the most commonly used system.
• Other bases include base two (binary), base five, base eight (octal), and base sixteen (hexadecimal).

2. Decimal (Denary) System (Base 10)

• The decimal system uses digits 0–9.
• Each digit has a place value based on powers of 10.
• Example: 345₁₀ = 3 × 10² + 4 × 10¹ + 5 × 10⁰
  • 3 is in the hundreds place (10² = 100),
  • 4 is in the tens place (10¹ = 10),
  • 5 is in the ones place (10⁰ = 1).
  • 345₁₀ = 300 + 40 + 5

3. Expansion of Numbers in Other Bases

• Just like base 10, numbers in other bases have place values.
• The place values are determined by powers of the base.
• Example in base 5: 243₅
  • 2 × 5² + 4 × 5¹ + 3 × 5⁰
  • 2 × 25 + 4 × 5 + 3 × 1
  • 50 + 20 + 3 = 73₁₀

4. Conversion from Other Bases to Base 10

• 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 2 to Base 10)

Convert 1101₂ to base 10.

• 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰
• 1 × 8 + 1 × 4 + 0 × 2 + 1 × 1
• 8 + 4 + 0 + 1 = 13₁₀

Example 2 (Base 8 to Base 10)

Convert 75₈ to base 10.

• 7 × 8¹ + 5 × 8⁰
• 7 × 8 + 5 × 1
• 56 + 5 = 61₁₀

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

1. The decimal system is also called ______.
   a) base ten
   b) base eight
   c) base five
   d) base two

2. The number 243₅ is equivalent to ______ in base 10.
   a) 73
   b) 83
   c) 93
   d) 103

3. The base two system is also called ______.
   a) octal
   b) binary
   c) hexadecimal
   d) decimal

4. The number 1101₂ in base 10 is ______.
   a) 12
   b) 13
   c) 14
   d) 15

5. The number 75₈ in base 10 is ______.
   a) 58
   b) 61
   c) 65
   d) 71

6. The number 543₆ in base 10 is ______.
   a) 187
   b) 195
   c) 203
   d) 215

7. What is the place value of the 3 in 345₁₀?
   a) 10²
   b) 10³
   c) 10¹
   d) 10⁰

8. The digits in base 5 are ______.
   a) 0–9
   b) 0–4
   c) 0–5
   d) 0–7

9. The expanded form of 56₈ is ______.
   a) 5 × 8¹ + 6 × 8⁰
   b) 5 × 8² + 6 × 8¹
   c) 5 × 8⁰ + 6 × 8¹
   d) 5 × 8¹ + 6 × 8²

10. In base 2, the digit that does not exist is ______.
    a) 0
    b) 1
    c) 2
    d) None

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Class Activity Discussion (10 FAQs with Answers)

1. What is a number base?

   • A system of counting that uses a fixed number of digits.

2. What is the decimal system?

   • It is base ten and uses digits 0–9.

3. What are the first four digits in base five?

   • 0, 1, 2, 3, 4.

4. How do we convert from other bases to base ten?

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

5. What is base two commonly used for?

   • Computers and digital systems.

6. How do you write 101₂ in base ten?

   • 1 × 2² + 0 × 2¹ + 1 × 2⁰ = 5₁₀.

7. Why do we use number bases?

   • For different counting and computational systems.

8. What is the base of the octal system?

   • Base eight.

9. What is the highest digit in base seven?

   • 6.

10. Which base is commonly used in computer programming?

    • Base two (binary) and base sixteen (hexadecimal).

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Presentation Steps

1. Teacher revises the previous topic.
2. Teacher introduces number bases.
3. Teacher demonstrates expansion and conversion.
4. Students practice examples in groups.
5. Teacher reviews students’ answers and provides corrections.

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Conclusion

• The teacher summarizes the lesson and gives additional exercises.
• Students explain their solutions to number base problems.
• The teacher marks students’ work and provides feedback.

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Addition and Subtraction of Approximations (JSS 1 Mathematics Lesson Note)