Home›Lesson Plans›Mathematics›Expressions & Equations · Grade 8

Scientific Notation: Writing the Huge and the Tiny

Students learn scientific notation — a compact way to write very large or very small numbers as a number between 1 and 10 times a power of 10 — so they can handle everything from the distance to stars to the size of atoms.

Grade 8Numbers50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Write a number in scientific notation.
  • ✓Convert to and from standard form.
  • ✓Understand positive and negative exponents.
  • ✓Compare numbers in scientific notation.
Essential Question

The Sun is 150,000,000,000 meters away, and an atom is 0.0000000001 meters wide. How can we write such numbers without so many zeros?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Notation Converter

Project this and change the coefficient and the power of 10. Watch the standard-form number grow huge or shrink tiny as the exponent changes.

🔬 Change the power of 10 — huge or tiny?Try it
Coefficient: 3.2
Power of 10: 4

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Too Many Zeros

5 min

150,000,000,000 — is there a shorter way to write this?

👩‍🏫 Teacher Moves

  • Show a huge and a tiny number.
  • Ask for a shorter way.
  • Set the goal: scientific notation.

🎒 Student Actions

  • Count the zeros.
  • Wish for a shortcut.
  • Predict the method.
2

I Do — a × 10ⁿ

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Write a number as a × 10ⁿ.
  • Show a from 1 to 10.
  • Explain positive vs. negative exponents.

🎒 Student Actions

  • Write the form.
  • Set the coefficient.
  • Use the exponent.
3

We Do — Convert Together

13 min

Class drives the Notation Converter.

👩‍🏫 Teacher Moves

  • Change coefficient and exponent.
  • Convert both directions.
  • Move the decimal to check.

🎒 Student Actions

  • Set the values.
  • Convert both ways.
  • Check the decimal.
4

You Do — On Your Own

12 min

Students convert numbers.

👩‍🏫 Teacher Moves

  • Assign standard ↔ scientific.
  • Include very small numbers.
  • Compare two values.

🎒 Student Actions

  • Convert numbers.
  • Handle small ones.
  • Compare values.
5

Close — Close

5 min

One conversion.

👩‍🏫 Teacher Moves

  • Give a number to convert.
  • Show the exponent.
  • Hand out the exit ticket.

🎒 Student Actions

  • Convert it.
  • State the exponent.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
8.EE.3

Use numbers expressed as a single digit times a power of 10 to estimate very large or small quantities.

CCSS
8.EE.4

Perform operations with numbers in scientific notation.

CCSS
8.EE.1

Know and apply the properties of integer exponents.

SMP
MP.6

Attend to precision when moving the decimal.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Move the decimal with arrows.
  • Sentence frame: “___ × 10 to the ___.”
  • Count places to the decimal.

Support & Access

IEP / 504
  • Start with positive exponents.
  • Use a decimal-place chart.
  • Count zeros together.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply numbers in scientific notation.
  • Order several values.
  • Estimate real quantities (star distances).
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Notation Converter
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

scientific notationa × 10ⁿ form for big/small numberscoefficientthe number from 1 to 10 in frontexponentthe power of 10power of 1010 raised to a numberstandard formthe ordinary way to write a numberpositive exponentmakes a number largernegative exponentmakes a number smallerdecimala point separating whole and part
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Write 45,000 in scientific notation.
4.5 × 10⁴.
QUESTION 2
What does a negative exponent (like 10⁻³) mean?
A very small number — move the decimal to the left (10⁻³ = 0.001).
QUESTION 3
Write 3.2 × 10³ in standard form.
3,200.

Going deeper? Operations in sci notation.

Have students multiply and divide numbers in scientific notation by combining the coefficients and adding/subtracting the exponents. A printable operations sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Scientific NotationFlip
Card 1
Term
Tap to flip →
Meaning
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Nice work!

Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Scientific NotationQuiz
Score: 0
1 / 6
Question 1
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Nice work!

Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Scientific NotationPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: coefficient, decimal, exponent, negative exponent, positive exponent, power of 10, scientific notation, standard form
  1. 10 raised to a number
  2. makes a number larger
  3. the ordinary way to write a number
  4. the number from 1 to 10 in front
  5. a point separating whole and part
  6. the power of 10
  7. a × 10ⁿ form for big/small numbers
  8. makes a number smaller

Part B · Show what you learned

  1. Write 45,000 in scientific notation.
  2. What does a negative exponent (like 10⁻³) mean?
  3. Write 3.2 × 10³ in standard form.
Answer key — Part A: 1) power of 10 · 2) positive exponent · 3) standard form · 4) coefficient · 5) decimal · 6) exponent · 7) scientific notation · 8) negative exponent
Part B: 1) 4.5 × 10⁴. 2) A very small number — move the decimal to the left (10⁻³ = 0.001). 3) 3,200.