Grade Level: 8
Subject: Mathematics
Standard(s): (bold the priority standards)
Unit Topic: Radicals and Integer Exponents
Explanations and Examples:
Length of Unit: 3 Weeks
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.1 Integer (positive and negative) exponents are further used to
generate equivalent numerical expressions when multiplying, dividing or
raising a power to a power. Using numerical bases and the laws of
exponents, students generate equivalent expressions.
8.EE.2 Use square root and cube root symbols to
represent solutions to equations of the form x2 = p
and x3 = p, where p is a positive rational number.
Evaluate square roots of small perfect squares and
cube roots of small perfect cubes. Know that √2 is
irrational.
8.EE.2 Students recognize that squaring a number and taking the square
root √ of a number are inverse operations; likewise, cubing a number and
taking the cube root 3 are inverse operations. This understanding is used to
solve equations containing square or cube numbers. Equations may
include rational numbers such as x2 = 1 /4, x2 = 4 /9 or x3 = 1/8 (NOTE:
Both the numerator and denominators are perfect squares or perfect
cubes.) Students recognize perfect squares and cubes, understanding that
non-perfect squares and non-perfect cubes are irrational. Students
understand that in geometry a square root is the length of the side of a
square and a cube root is the length of the side of a cube. The value of p
for square root and cube root equations must be positive.
1Retrieved
from www.corestandards.org, p.3, Introduction: Common Core State Standards for Mathematics.
Revised 6/2013
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 times 108 and the population of
the world as 7 times 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
Page 2 of 7
8.EE.3 Students express numbers in scientific notation. Students compare
and interpret scientific notation quantities in the context of the situation. If
the exponent increases by one, the value increases 10 times. Students
understand the magnitude of the number being expressed in scientific
notation and choose an appropriate corresponding unit. For example, 3 x
108 is equivalent to 30 million, which represents a large quantity.
Therefore, this value will affect the unit chosen.
8.EE.4 Students use laws of exponents to multiply or divide numbers
written in scientific notation. Additionally, students understand scientific
notation as generated on various calculators or other technology.
Revised 6/2013
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.
Students can convert decimal forms to scientific notation and apply rules of
exponents to simplify expressions. In working with calculators or
spreadsheets, it is important that students recognize scientific notation.
Students should recognize that the output of 2.45E+2 3 is 2.45 x 1023 and
3.5E-4 is 3.5 x 10-4. Students enter scientific notation using E or EE
(scientific notation), * (multiplication), and ^ (exponent) symbols.
Concepts:(What students need to
Skills:(What students need to be able to do) Blooms / DOK Levels:
know)
 Apply
 2/1
 Integers
 Generate
 1/3
 Exponents
 Evaluate
 4/3
 Square root
 Estimate
 2/2
 Cube root
 Express
 1/2
 Solution
 Perform
 2/1
 Equation
 Choose
 1/3
 Rational number
 Interpret
 4/4
 Perfect Cubes
 Perfect Squares
 Irrational
 Power of 10
 Operations
 Scientific Notation
 Decimal Expansion
Essential Questions: (Open-ended questions that the students
Corresponding Big Ideas: (Foundational understandings that
should be able to answer by the end of the unit)
students need to discovered by the end of the unit)
 How is equivalency shown in Algebra?
 Large numbers that have factors that are repeated can
be written as a product of powers.
 Why is it helpful to write numbers in different ways?

Scientific notation allows for easy recognition of the
 How are square and cube roots related?
magnitude of values for comparison purposes.
 How can you develop and use the properties of integer

Mathematical operations can be performed efficiently
exponents?
on numbers written in scientific notation.
 How do you add, subtract, multiply, and divide using scientific
 Students become much more adept at learning new
notation?
concepts when they are provided opportunities to
 How do you estimate and compare irrational numbers?
interact with the content from different vantage points.
 What are the similarities and differences between a number
 Calculations involving expressions with exponents can
written in scientific notation and the calculator notation of the
be solve more efficiently by using properties of powers.
number shown on a screen?
Page 3 of 7
Revised 6/2013

What is the difference between an exact value and an
approximate value?
Vocabulary:
Mathematical Practices:
Resources:
(Practices in bold are to be emphasized in the
 Integers
 Engage NY
unit.)
http://www.engageny.org/sites/default/files
 Exponents
/resource/attachments/g8-m1-module Square Root
1.
Make
sense
of
problems
and
persevere
in
overview-and-assessments.pdf
 Cube Root
solving
them.

ALEX Lesson Plans
 Solution
2.
Reason
abstractly
and
quantitatively.
http://alex.state.al.us/lesson_view.php?id=
 Equation
3.
Construct
viable
arguments
and
critique
the
26292
 Rational Number
reasoning of others.
 PBS.org
 Perfect Cubes
4. Model with mathematics.
http://www.pbs.org/teachers/mathline/con
 Perfect Squares
5. Use appropriate tools strategically.
cepts/space2/activity3.shtm
 Irrational Numbers
6. Attend to precision.

WALCH Education
 Power of 10
7. Look for and make use of structure.
 Center on Disability Studies
 Operations
8. Look for and express regularity in repeated
 Scientific Notation
reasoning.
Assessment for Learning: (How do you know the student has mastered the standards? Include both Pre and Post Assessments)
Pre-Assessment and Scoring Rubric
Radicals and Integer Radicals and Integer
Exponents Pre-Unit Assessment.docx
Exponents Pre-Assessment Scoring Rubric.docx
Post-Assessment and Scoring Rubric
Radicals and Integer Radicals and Integer
Exponents Post-Unit Assessment.docx
Exponents Post-Assessment Scoring Rubric.docx
Engaging Learning Experiences
Task
The Laws of Exponents
http://alex.state.al.us/lesson_vi
ew.php?id=26292
Page 4 of 7
Description: (Standards addressed, Blooms / DOK Levels, links to rubric,
resources, instructional strategies, etc.)
Suggested Length
of Time
Standards Addressed:
8.EE.1 Know and apply the properties of integer exponents to generate
equivalent numerical expressions.
Blooms Level/DOK
5/2
61 – 90 Minutes
Revised 6/2013
The Laws of
Exponents.pdf
Around the World in 0.1345
Seconds Web Quest
http://www.webquest.hawaii.ed
u/kahihi/webquests/math/grade
7/MA7.1.2world/intro.php
The Capacity of the Planets
http://www.pbs.org/teachers/m
athline/concepts/space2/activit
y3.shtm
The Capacity of the
Planets.pdf
Rubric/Resources
Rubric included in attachments on website
Standards Addressed:
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.
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.
Blooms Level/DOK
2/2
Rubric/Resources
Rubric for final project included in Web Quest
Standards Addressed:
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.
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.
Blooms Level/DOK
2/2
Rubric/Resources
Answer Key Attached
60 Minutes
20 Minutes
The Capacity of the
Planets Answer Key.pdf
Page 5 of 7
Revised 6/2013
Exponents and Scientific
Notation Station Rotation
Standards Addressed:
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.
Exponents and
8.EE.2 Use square root and cube root symbols to represent solutions to
Scientific Notation Station Rotation.pdf
equations of the form x2 = p and x3 = p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots
of small perfect cubes. Know that √2 is irrational.
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.
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.
Blooms Level/DOK
3/2
Rubric/Resources
All needed resources and rubrics included in Document
Integer Exponents and
Standards Addressed:
Scientific Notation
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.
Integer Exponents
8.EE.2 Use square root and cube root symbols to represent solutions to
and Scientific Notation.pdf
equations of the form x2 = p and x3 = p, where p is a positive rational
number. Evaluate square roots of small perfect squares and cube roots
of small perfect cubes. Know that √2 is irrational.
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.
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.
Page 6 of 7
60 Minutes
2 – 60 Minute
Classes
Revised 6/2013
Blooms Level/DOK
3/3
Rubric/Resources
All needed resources and rubrics included in attachment
Page 7 of 7
Revised 6/2013