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

Scientific Notation

Eighth graders learn a compact way to write enormous and tiny numbers, as a value between 1 and 10 multiplied by a power of ten, and to convert back to standard form.

Grade 8Scientific Notation50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Assign or share this lesson

Copy link works with Canvas, Schoology, Moodle and any other LMS — paste it in as a resource or assignment.

Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define scientific notation.
  • ✓Use the a × 10ⁿ form.
  • ✓Convert to & from standard.
  • ✓Read the exponent.
Essential Question

Scientists work with numbers as huge as the distance to a star and as tiny as the width of an atom. How can we write such numbers without endless zeros?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

Notation Check

Project this and answer each question about writing numbers in scientific notation — read the explanation after each one.

🔢 Check what you know about scientific notationTry it
Answer each question about scientific notation.
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

Hook — Too Many Zeros

5 min

The distance to the Sun is about 150,000,000 km. Is there a shorter way to write that?

👩‍🏫 Teacher Moves

  • Show a huge number.
  • Ask for a shortcut.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Notation Check

12 min

Students answer questions about scientific notation.

👩‍🏫 Teacher Moves

  • Send students to the Notation Check.
  • Answer each question.
  • Read the why.

🎒 Student Actions

  • Answer.
  • Check.
  • Read it.
3

Modify — Convert Both Ways

13 min

Students convert numbers to and from the form.

👩‍🏫 Teacher Moves

  • Write a big number in the form.
  • Expand one back to standard.
  • Check the exponent.

🎒 Student Actions

  • Write.
  • Expand.
  • Check.
4

Create — Sort by Size

15 min

Students compare numbers in the notation.

👩‍🏫 Teacher Moves

  • Write five numbers in the form.
  • Order them by size.
  • Use the exponents to decide.

🎒 Student Actions

  • Write.
  • Order.
  • Use.
5

Reflect — Power of Ten

5 min

Students reflect on what the exponent tells them.

👩‍🏫 Teacher Moves

  • What does a positive exponent mean?
  • What does a negative exponent mean?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
8.EE.A.3

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

CCSS
8.EE.A.4

Perform operations with numbers expressed in scientific notation, including problems where both forms are used.

CCSS
8.EE.A.1

Know and apply the properties of integer exponents to generate equivalent expressions.

CCSS
MP.6

Attend to precision.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Number + power-of-ten cards.
  • Sentence frame: “Move the decimal ___ places.”
  • Convert one number at a time.

Support & Access

IEP / 504
  • Start with large numbers only.
  • Count decimal moves out loud.
  • Add negative exponents after mastering positives.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply and divide in scientific notation.
  • Compare numbers across many exponents.
  • Estimate real quantities (atoms, distances).
Materials

What to gather

  • 📽️Projector / board
  • 🔢Place-value / digit cards
  • 💻Notation Check
  • 🧮Calculators
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

scientific notationa way to write numbers as a value between 1 and 10 times a power of 10standard formthe ordinary way of writing a number, like 3,400power of ten10 raised to an exponent, like 10³ = 1,000exponentthe small number that tells how many times to multiply the basecoefficientthe number (a) in a × 10ⁿ, at least 1 and less than 10basethe number being raised to a power; here it is 10large numbera number greater than 1, with a positive exponentsmall numbera number between 0 and 1, with a negative exponent
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
What form does scientific notation use?
A number between 1 and 10 multiplied by a power of ten (a × 10ⁿ).
QUESTION 2
Write 52,000 in scientific notation.
5.2 × 10⁴.
QUESTION 3
What does a negative exponent tell you about the number?
That it is a small number, between 0 and 1.

Create: sort by size.

Have students write five numbers in scientific notation and order them from smallest to largest, using the exponents to compare. A printable scientific-notation worksheet is in the Mathematics 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
0

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
0%

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: base, coefficient, exponent, large number, power of ten, scientific notation, small number, standard form
  1. the small number that tells how many times to multiply the base
  2. the number (a) in a × 10ⁿ, at least 1 and less than 10
  3. a number greater than 1, with a positive exponent
  4. a number between 0 and 1, with a negative exponent
  5. 10 raised to an exponent, like 10³ = 1,000
  6. the number being raised to a power; here it is 10
  7. a way to write numbers as a value between 1 and 10 times a power of 10
  8. the ordinary way of writing a number, like 3,400

Part B · Show what you learned

  1. What form does scientific notation use?
  2. Write 52,000 in scientific notation.
  3. What does a negative exponent tell you about the number?
Answer key — Part A: 1) exponent · 2) coefficient · 3) large number · 4) small number · 5) power of ten · 6) base · 7) scientific notation · 8) standard form
Part B: 1) A number between 1 and 10 multiplied by a power of ten (a × 10ⁿ). 2) 5.2 × 10⁴. 3) That it is a small number, between 0 and 1.