Exponents and Scientific Notation

Lesson 11

Math

Unit 1

8th Grade

Lesson 11 of 15

Objective


Define and write numbers in scientific notation.

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.

Foundational Standards

  • 4.NBT.A.1
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  1. Define and understand a number written in scientific notation as a product of 2 factors, where the first factor is a number greater than or equal to 1 and less than 10 (has only one digit to the left of the decimal point), and the second factor is a power of 10 (integer powers only).
  2. Understand scientific notation as an efficient, abbreviated way to communicate about very large and very small numbers.
  3. Write numbers in scientific notation into standard form and vice versa.

Tips for Teachers


  • There are a few common misconceptions that may arise when it comes to scientific notation. One is confusing the power of 10 as representing the number of 0’s and not place values. Show students examples where this pattern does not hold up. Another is confusing the negative power of 10 as indicating a negative value. Remind students of what negative exponents mean and have them re-write them as fractions with a numerator 1. Lastly, students may not write the first factor as a number between 1 and 10. Show students examples such as $${35\times10^3}$$ and ask them to write it into scientific notation. 
  • Some real-world contexts that involve scientific notation may be new or unfamiliar to students (celestial objects, subatomic particles, geography of unfamiliar locations, etc.). To the extent possible, provide additional information around these contexts both in and out of math class to support conceptual understanding. 
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Anchor Problems

25-30 minutes


Problem 1

What is the number? Write each number below in standard form.

a.   $${30,000\times10^{-1}}$$

b.   $${3\times10^3}$$

c.   $${0.3\times10^4}$$

Guiding Questions

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Student Response

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References

MARS Formative Assessment Lesson for Grade 8 Estimating Length Using Scientific Notation

Estimating Length Using Scientific Notation from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Aug. 4, 2017, 1:07 p.m..

Problem 2

Write each number described below in scientific notation.

a.   The distance from the earth to the sun is 92,955,807 miles.

b.   The mass of a grain of salt is approximately 0.0000000585 kilograms.

Guiding Questions

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Student Response

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Problem 3

Match each number in column A to a number in column B. One number in each column is missing, which must be written in to create the remaining pairs.

Column A: Scientific Notation Column B: Standard Form
A. $$2.8\times10^{-4}$$ i. $$280,000$$
B. $$2.8\times10^4$$ ii.             
C. $$2.8\times 10^5$$ iii. $$28,000$$
D.                 iv. $$0.00028$$
E. $$2.8\times10^6$$ v. $$0.0000028$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Complete the table below. Then use the letters to order the values from least to greatest.

  Decimal Notation Scientific Notation
A 0.001  
B   $$3\times10^{-2}$$
C 3,000,000,000  
D 600  
E   $$7\times10^5$$
F 20  
G   $$7\times10^{-4}$$
H   $$2\times10^{-1}$$

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.

Next

Compare numbers written in scientific notation.

Lesson 12
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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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