Teacher Guide: Scientific Notation

@ Learning Objective 5-10 min lesson

Students will: Express numbers in scientific notation, perform operations with numbers in scientific notation, and solve real-world problems involving very large or very small quantities.

Why this matters for FAST: Scientific notation is essential for expressing and computing with very large numbers (like distances in space) and very small numbers (like measurements in chemistry). Students must understand how to convert between standard and scientific notation and perform all four operations.

% Materials Needed

Whiteboard/projector
Student Concept Worksheet
Calculators (optional)
Powers of 10 chart
Place value chart
Real-world examples (space distances, cell sizes)

! Common Misconceptions to Address

Misconception #1: The coefficient can be any number

Students write 45 x 10^6 instead of 4.5 x 10^7. They don't understand that the coefficient must be between 1 and 10 (1 ≤ a < 10).

How to Address:

"In scientific notation, the first number (coefficient) must be at least 1 but less than 10. Think of it as always having exactly ONE digit before the decimal point. If you have 45, that's two digits, so it needs to become 4.5 x 10^1."

Misconception #2: Confusing the direction of decimal movement with positive/negative exponents

Students think moving the decimal right always means positive exponent, regardless of whether the number is large or small.

How to Address:

"For LARGE numbers (like 5,000,000), you move the decimal LEFT and get a POSITIVE exponent. For SMALL numbers (like 0.000005), you move the decimal RIGHT and get a NEGATIVE exponent. Remember: Big number = positive power, Small number = negative power."

Misconception #3: Adding/subtracting without same power of 10

Students add coefficients directly: 3.2 x 10^5 + 4.1 x 10^4 = 7.3 x 10^5 (WRONG!)

How to Address:

"To add or subtract in scientific notation, you MUST have the same power of 10. It's like adding fractions - you need a common denominator. First, rewrite one number to match the other's exponent, then add the coefficients."

$ Lesson Steps

1

Activate Prior Knowledge (1 min)

Review powers of 10: "What is 10^3? 10^-2?" Connect to place value: thousands, hundredths. Show how moving decimal relates to multiplying/dividing by 10.

2

Define Scientific Notation (2 min)

SAY THIS:

"Scientific notation is a way to write very large or very small numbers compactly. The form is a x 10^n, where 'a' (the coefficient) is between 1 and 10, and 'n' is the power of 10."

Scientific Notation Form: a x 10^n

Coefficient (a): Must be 1 ≤ a < 10 (one non-zero digit before decimal)

Exponent (n): Positive for large numbers, negative for small numbers

Example: 6,500,000 = 6.5 x 10^6 | 0.00032 = 3.2 x 10^-4

3

Converting to Scientific Notation (2 min)

Steps to Convert to Scientific Notation

Step	Large Number (93,000,000)	Small Number (0.000047)
1. Place decimal after first non-zero digit	9.3	4.7
2. Count decimal moves	7 places left	5 places right
3. Write with power of 10	9.3 x 10^7	4.7 x 10^-5

4

Operations with Scientific Notation (3 min)

SAY THIS:

"For multiplication and division, work with coefficients and exponents separately. For addition and subtraction, you need the same power of 10 first!"

Operations Rules

Multiplication: (3 x 10^4) x (2 x 10^5) = 6 x 10^9 (multiply coefficients, ADD exponents)

Division: (8 x 10^6) / (2 x 10^2) = 4 x 10^4 (divide coefficients, SUBTRACT exponents)

Addition: 3.2 x 10^5 + 4.1 x 10^5 = 7.3 x 10^5 (SAME exponent required!)

5

Guided Practice (2-3 min)

Work through these together:

Write 4,200,000,000 in scientific notation. (4.2 x 10^9)
Write 0.00000056 in scientific notation. (5.6 x 10^-7)
Multiply: (3 x 10^4) x (5 x 10^3) = 1.5 x 10^8 (adjust: 15 x 10^7 = 1.5 x 10^8)
Which is larger: 8.5 x 10^6 or 2.3 x 10^7? (2.3 x 10^7 because higher exponent)

? Check for Understanding

Quick Exit Ticket (Ask the whole class):

"Which number is written correctly in scientific notation?"

A) 15.2 x 10^4 B) 1.52 x 10^5 C) 0.152 x 10^6 D) 152 x 10^3

Correct answer: B) 1.52 x 10^5. This is the only one where the coefficient is between 1 and 10. All others violate the rule: A has 15.2 (too big), C has 0.152 (too small), D has 152 (way too big).

& IXL Skills to Assign After This Lesson

Recommended IXL Practice:

Convert between standard and scientific notation Compare numbers in scientific notation Multiply numbers in scientific notation Divide numbers in scientific notation Add and subtract in scientific notation Scientific notation word problems

^ Differentiation & Extension

For struggling students: Focus on converting between forms first. Use place value charts. Practice with numbers that have only one or two significant digits. Let them use calculators to verify answers.

For advanced students: Challenge them with multi-step problems involving mixed operations. Have them research real scientific data (planet distances, atomic sizes) and express them in scientific notation.

For home: Send Parent Activity sheet. Families can explore astronomy websites or look up interesting facts about very large/small quantities and practice conversions together.