Grade 8
UNIT 1: Integer Exponents & Scientific Notation
Essential Question
Where do I use scientific notation in the real
world?
Vocabulary
Scientific Notation
Order of Magnitude
Exponential Notation
Base, Exponent, Power
Integer
Whole Number
Expanded Form (of decimal numbers)
Square and Cube (of a number)
Equivalent Fractions
Key Concepts

Exponential Notation and Properties of
Integer Exponents

Magnitude and Scientific Notation
*Assessment and Review
Mid-Module Assessment and Review: After
Section A (3 days, included in Unit Instructional
Days)
End-of-Module Assessment and Review: After
Section B (4 days, included in Unit Instructional
Days)
Suggested Number of Days for Entire UNIT: 20
Cross Curricular Connections
Science: Use scientific notation to express
relationships and identify each planet’s distance
from the sun. This can be determined in feet,
yards, or miles. Students can also calculate the
number of atoms in a substance.
Social Studies: Use scientific notation to identify
the number of people who voted in presidential
elections in the United States prior to the 15th
Amendment and after the ratification of the 15th
and 19th Amendments.
Unit Outcome (Focus)
Students’ knowledge of operations on numbers will be expanded to include operations on numbers in integer exponents. Unit 1 also builds on
students’ understanding from previous grades with regard to transforming expressions. Students also build upon their foundation with exponents as
they make conjectures about how zero and negative exponents of a number should be defined and prove the properties of integer exponents. These
properties are codified into three Laws of Exponents. Students explore use of scientific notation and choose appropriately sized units as they represent,
compare, and make calculations with very large quantities.
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2014-2015
UNIT 1
SECTION A: Scientific Notation
Essential Question
Where do I use scientific notation in the real
world?
Comments
In this module, students build upon their
foundation with exponents as they make
conjectures about how zero and negative
exponents of a number should be defined
and prove the properties of integer
exponents (8.EE.1). These properties are
codified into three Laws of Exponents. They
make sense out of very large and very small
numbers, using the number line model to
guide their understanding of the
relationship of those numbers to each
other (8.EE.3)
Archdiocese of New York
Suggested Number of Days for SECTION: 6
Key Concept
Standards for Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
 Exponential Notation
 Multiplication of Numbers in Exponential Form 6. Attend to precision.
8. Look for and express regularity in reasoning.
 Numbers in Exponential Form Raised to a
Power
 Numbers Raised to the Zeroth Power
 Negative Exponents and the Laws of
Exponents
 Proofs of Laws of Exponents
Standard
 Major Standard
 Supporting Standard

Standard
Additional Standard
Priority
No.
 Standard ends at this grade

Fluency Standard

8.EE.1
Know and apply the properties of integer exponents to generate equivalent
(DOK 1)
numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
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2014-2015
UNIT 1
SECTION B: Scientific Notation
Essential Question
Where do I use scientific notation in the
real world?
Comments
Having established the properties of
integer exponents, students learn to
express the magnitude of a positive
number through the use of scientific
notation and to compare the relative
size of two numbers written in
scientific notation (8.EE.3). Students
explore use of scientific notation and
choose appropriately sized units as
they represent, compare, and make
calculations with very large
quantities, such as the U.S. national
debt, the number of stars in the
universe, and the mass of planets;
and very small quantities, such as the
mass of subatomic particles (8.EE.4).
Archdiocese of New York
Key Concept







Suggested Number of Days for SECTION: 7
Standards for Mathematical Practice
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
8. Look for and express regularity in reasoning.
Magnitude
Estimating Quantities
Scientific Notation
Operations with Numbers in Scientific Notation
Efficacy of the Scientific Notation
Choice of Unit
Comparison of Numbers Written in Scientific Notation
and Interpreting Scientific Notation Using Technology .
Standard
 Major Standard
 Supporting Standard

Standard No. Additional Standard
 Standard ends at this grade
 Fluency
Standard
8.EE.3
Use numbers expressed in the form of a single digit times an integer power of 10
(DOK 1)
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.4
(DOK 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.
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Priority


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Resources/Possible Activities
MODELING ACTIVITIES: Challenge students to model and explain: Negative exponents; how squaring a number and taking the square root of a
number are inverse operations; and how cubing a number and taking the cube root 3 are inverse operations.
SCIENTIFIC NOTATION RESEARCH: Have students research three different ways that people use scientific notation in the real world, write a report,
including examples, and present to class.
SIMPLIFY EXPRESSIONS WITH NEGATIVE EXPONENTS: In this lesson students will learn how to simplify expressions involving negative exponents by
applying exponent rules they already know: http://learnzillion.com/lessons/1669-simplify-expressions-with-negativeFACILITATING COMMUNICATION ABOUT MEASUREMENT, EXPONENTS, AND SCIENTIFIC NOTATION VIDEOS AND REFLECTION QUESTIONS such as: The
teacher uses the phrase "double in size" to refer to Alice's change in height. To what other changes in Alice could this phrase refer?
PAN BALANCE – EXPRESSIONS: This interactive pan balance allows numeric or algebraic expressions to be entered and compared. You can "weigh" the
expressions you want to compare by entering them on either side of the balance. Using this interactive tool, you can practice arithmetic and algebraic
skills, and investigate the important concept of equivalence. http://illuminations.nctm.org/ActivityDetail.aspx?ID=10
ONLINE GAMES FOR IDENTIFYING RATIONAL AND IRRATIONAL NUMBERS: Go to www.math-play.com and scroll down main page a bit. Click on 8th
Grade Math Games. Scroll down and click on Rational and Irrational Numbers Game.
PRACTICE CLASSIFYING AND WORKING WITH RATIONAL AND IRRATIONAL NUMBERS: Go to www.toolboxpro.org. Click on Classes, choose Math 7th
Prep from the drop down menu. Near the top is Classifying Rational And Irrational Number Game, and Rational Vs. Irrational Numbers 1 and 2
Practice.
ONLINE EXPONENT GAME WITH KIWI: Practice applying the six rules of exponents by playing a game with Kiwi located at www.math-play.com. Click on
Algebra Games at left and select Exponent Game with Kiwi.
Real-World Scientific Notation: http://www.internet4classrooms.com/grade_level_help/number_real-world_problems_math_eighth_8th_grade.htm
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2014-2015