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Mathematics Lesson Note – JSS 2 (Week 10)

Term: Third Term

Week: 10

Class: JSS 2

Subject: Mathematics

Duration: 40 minutes

Theme: Algebra and Number Work

Topic: Notation and Standard Form

Sub-topic: Introduction to Scientific Notation

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Performance Objectives

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

1. Define notation and standard form.

2. Convert large and small numbers to standard form.

3. Convert numbers from standard form back to ordinary notation.

4. Solve simple problems using standard form.

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Previous Knowledge

Students are already familiar with place values, indices, and basic multiplication and division of numbers.

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Instructional Materials

• Number chart

• Scientific calculator

• Flash cards with large and small numbers

• Chalkboard and marker

• Printed table of powers of 10

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✨ Set Induction (Classroom Warm-Up)

Teacher: “Imagine a scientist tells you the mass of the sun is 1,989,000,000,000,000,000,000,000,000 kg. Can you write that on your exam paper without missing a zero? “

Pupils: (Laughing) “No, that’s too long!”

Teacher: “That’s why we use something called standard form. It helps us write numbers quickly and clearly.”

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Lesson Development

Step 1: Explanation of Key Terms

Notation is a system of symbols or signs used to represent numbers or quantities.

Standard Form (also called Scientific Notation) is a way of writing numbers that are very large or very small in the form:

a×10na \times 10^na×10n

Where:

• $1\le a<10$

• $n$ is an integer (positive or negative)

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Step 2: Converting to Standard Form

✅ Examples of Large Numbers:

Example 1:
Write 45,000,000 in standard form.

Solution:

45,000,000=4.5×10745,000,000 = 4.5 \times 10^745,000,000=4.5×107

Explanation: Move decimal 7 places to the left.

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✅ Examples of Small Numbers:

Example 2:
Write 0.00067 in standard form.

Solution:

0.00067=6.7×10−40.00067 = 6.7 \times 10^{-4}0.00067=6.7×10−4

Explanation: Move decimal 4 places to the right.

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Step 3: Converting from Standard Form

Example 3:
Convert 3.2×1063.2 \times 10^63.2×106 to ordinary number.

Solution:
Move decimal 6 places to the right:

3.2×106=3,200,0003.2 \times 10^6 = 3,200,0003.2×106=3,200,000

Example 4:
Convert 5.4×10−35.4 \times 10^{-3}5.4×10−3 to ordinary number.

Solution:
Move decimal 3 places to the left:

5.4×10−3=0.00545.4 \times 10^{-3} = 0.00545.4×10−3=0.0054

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‍ Teacher–Pupil Interaction

Teacher: “Chika, can you try converting 76,000 to standard form?”

Chika: “Yes, ma. I think it’s 7.6 × 10⁴.”

Teacher: “Well done, you moved the decimal 4 places.”

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Class Activity

Write the following in standard form:

1. 8,000,000

2. 0.00032

3. 74,300

4. 0.0098

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Real-Life Applications

• Scientists use standard form to express distances between stars or size of microscopic bacteria.

• Bankers use it for large currency figures.

• Engineers use it in formulas and measurements.

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Summary

• Notation helps represent numbers efficiently.

• Standard form = a×10na \times 10^na×10n

• Decimal point moves left for large numbers, right for small numbers.

• Powers of 10 are key.

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Evaluation Questions

1. What is standard form?

2. Convert 390,000 to standard form.

3. Convert 0.00021 to standard form.

4. Convert 4.2×1054.2 \times 10^54.2×105 to ordinary number.

5. Why is standard form useful in science?

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✅ Assignment

Write the following in standard form:

1. 560,000

2. 0.000045

3. 7.2 million

4. 0.00389

5. 102,000,000

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‍♀️ 10 FAQs for Reinforcement

1. What is another name for standard form?
   → Scientific Notation.

2. What does the power of 10 represent?
   → The number of decimal places moved.

3. Is the number in front of the 10 always less than 10?
   → Yes, between 1 and 9.9.

4. Can standard form be used for small numbers?
   → Yes, with negative powers.

5. What is 1×1001 \times 10^01×100?
   → 1

6. How do you write 1 billion in standard form?
   → 1×1091 \times 10^91×109

7. Can a number like 32.5 be in standard form?
   → No, it must be < 10.

8. What is 6.2×10−26.2 \times 10^{-2}6.2×10−2 in ordinary form?
   → 0.062

9. Why do scientists prefer standard form?
   → It saves space and prevents error.

10. Is this standard form: 15×10315 \times 10^315×103?
    → No, 15 is greater than 10.

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