8th Grade Mathematics
UNIT 1: EXPONENTS
Unit/ Topic Length:
This five-week unit focuses on exponential expressions and scientific notation.
Students build upon their foundation with exponents as they explore how zero and
negative exponents are defined and prove the properties (laws) of integer
exponents. Having established the properties of integer exponents, students express
the magnitude of a positive number through the use of scientific notation and
compare their relative magnitudes. They make calculations with very large
quantities, such as the U.S. national debt, the number of stars in the universe, and
the distance between planets; and very small quantities, such as the mass of
subatomic particles.
Essential Question: Why are quantities represented in multiple ways?
Key Ideas
 The exponent in an exponential
term tells us how many times the
base is to be multiplied.
 An exponent can have any value,
positive or negative.
 The value of any number to the
zero power is equal to one, except
if the base is zero.
 The value of any number raised to
a negative integer power can be
expressed with either a negative
exponent or the multiplicative
inverse (reciprocal) of the number
raised to the positive integer
exponent.
 The inverse operation of any
exponent is its root (i.e. the inverse
operation of squaring a number is
to take the square root)
 Positive powers of 10 are very
large numbers, and negative
powers of 10 are very small
numbers.
 We can use scientific notation as a
means of estimating and
comparing very small and very
large quantities.
Guiding/Focus Questions:
1. What is the relationship between a base
and its exponent?
2. How can we prove that x0 = 1 and
1
x-1 = ?
x
3. How can we prove that
a. xa · xb = xa+b?
xa
b.
= xa-b?
xb
c. (xa)b = xab?
4. When a number is written in scientific
notation, what do we notice about the
relationship between the decimal places
in the given number and the power of
10?
5. How does scientific notation help us
compare large and small quantities?
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8th Grade Mathematics
NYS Common Core Standards for Mathematics Assessed:
Mathematical Content
8.EE.1 Know and apply the properties of integer exponents to generate equivalent
numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.
8.EE.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.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.
Mathematical Practices
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Content






Exponential Notation
Numbers Raised to the Zeroth Power
Negative Exponents
Laws of Exponents
Scientific Notation
Operations with Scientific Notation
Skills
 Simplify expressions with integer
exponents
 Write equivalent numerical and
symbolic expressions using the laws
of exponents
 Express large and small numbers in
scientific notation
 Estimate and compare numbers
written in scientific notation
 Add, subtract, multiply, and divide
numbers written in scientific
notation
 Determine appropriate units for
various measurements
Vocabulary/ Key Terms
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8th Grade Mathematics
base, exponent, power, whole number, integer, scientific notation
ASSESSMENT EVIDENCE
Initial Assessment

Unit Readiness Test
Formative Assessments:
 Quizzes
 Exit Slips
 Checks for Understanding
 Short- and Extended-Response questions used throughout the unit.
 Reflections
 Formative Assessment Tasks
Summative Assessments:
1. Unit test
2. Performance Tasks
 Properties of Exponents
 Scientific Notation
TEACHING PLAN
Teaching and Learning Activities:
1. Administer the Unit Readiness Test.
Students who demonstrate weakness in evaluating numerical and exponential expressions
will be given remediation.
2. Instruction follows the Launch-Explore-Summarize flow.
3. Use the guiding/focus questions to focus each lesson.
Lesson 1: Simplifying Exponential Expressions (4 days)
 Calculate values of exponential expressions with integer exponents
Lesson 2: Product Laws of Exponents (2 days)
 Multiplying Expressions with the Same Base
 Multiplying Expressions with the Same Exponents
Lesson 3: Quotient Laws of Exponents (2 days)
 Dividing Expressions with the Same Base
 Dividing Expressions with the Same Exponents
Lesson 4: Power to a Power Law (2 days)
 Raise a power to a power [e.g. (23)4]
4. Administer Performance Task 1
Lesson 5: Writing Numbers in Scientific Notation (4 days)
 Use numbers expressed in scientific notation to estimate very large or
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8th Grade Mathematics
very small quantities, and to express how many times as much one is than
the other.
Lesson 6: Adding and Subtracting with Scientific Notation (3days)
 Perform addition and subtraction with numbers expressed in scientific
notation, including problems where both decimal and scientific notation
are used.
Lesson 7: Multiplying and Dividing with Scientific Notation (3 days)
 Perform multiplication and division with numbers expressed in scientific
notation, including problems where both decimal and scientific notation
are used.
5. Administer Performance Task 2
6. Use the essential question as a post-assessment.
7. Administer the unit test.
Resources:
 Connected Math Project 3 (CMP3)
Unit: Growing, Growing, Growing: Exponential Functions (Investigation 5)
 NYS Common Core Math Module 1: Integer Exponents and Scientific Notation
 Impact Mathematics Course 3
 Integrated Algebra Textbook
 MathXL (Pearson’s online homework, tutorial, and assessment system)
 Scientific Calculators
CALENDAR
Time
Spent on
Standard
15 days
Standards
8.EE.1
Topics To Cover
CMP3 Unit:
Growing,
Growing,
Growing
(Investigation 5)
 Overview of the unit
 Exponents
o Zero
o Negative
 Evaluating Exponential
Expressions
 Properties/Laws of Exponents
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8th Grade Mathematics
10 days
8.EE.3
8.EE.4.
 Scientific notation
 Operations with scientific
notation
5