Exponents and Scientific Notation

Lesson 10

Math

Unit 1

8th Grade

Lesson 10 of 15

Objective


Write large and small numbers as powers of 10. 

Common Core Standards


Core Standards

  • 8.EE.A.3 — Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
  • 8.EE.A.4 — Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Foundational Standards

  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  1. Represent large numbers as powers of 10 or multiples of powers of 10.
  2. Represent small numbers (<1 and >0) as powers of 10 or multiples of powers of 10. 
  3. Strategize ways to verbally communicate very large or very small numbers to others. 
  4. Compare magnitudes using powers of ten. 
  5. Associate quantities with real-world measurements and examples.

Tips for Teachers


  • This lesson is approaching 8.EE.3 and 8.EE.4 and reviews concepts rooted in powers of 10 that will be important for students to know for scientific notation.
  • The Powers of Ten video is a great introduction to these upcoming lessons on magnitude and scientific notation, although students may have seen it before. It is about 9 minutes long.
  • The MegaPenny Project is a really fun visualization of just how big a million, brillion, trillion, even quadrillion are, as represented in pennies. This can be very helpful to emphasize the difference between a million and a billion.
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Anchor Problems


Problem 1

There are about one million people living in Austin, Texas. There are about ten times as many people living in New York City, NY. Phil says that means there are one billion people living in New York City.

Explain why Phil is incorrect.

Guiding Questions

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Problem 2

Read the following sentences to a peer:

  • Approximately 3,900,000 people live in Los Angeles, CA.
  • The population of the world is approximately 7,900,000,000.
  • A mosquito weighs about 0.0025 grams.
  • The average human cell weighs 0.000000000001 kg.
  • Scientists have estimated that there are approximately 37,200,000,000,000 cells in the human body.

Guiding Questions

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Problem 3

Represent the following numbers as powers of 10 or multiples of powers of 10.

a.   One billion

b.   10,000

c.   0.001

d.   0.00000001

e.   0.00000005

f.   100,000,000

g.   500,000,000

h.   How many times bigger is one billion than 10,000?

Guiding Questions

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Problem Set

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Target Task


Problem 1

A large construction crane weighs one million pounds. A large truck weighs 10,000 pounds. How many times greater is the weight of the crane than the weight of the truck?

Problem 2

Complete the chart below. The first row has been completed for you as an example.

Power of 10 Decimal Notation Place Value

Example of something

measured in this quantity

$${10^2}$$ 100 Hundred Miles traveled between states
$${10^3}$$      
$${10^6}$$      
$${10^9}$$      
$${10^{12}}$$      

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Problems similar to: True or false, a trillion is a million millions.
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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Review of Exponents

Topic B: Properties of Exponents

Topic C: Scientific Notation

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