7th Grade Honors Unit 5 Exponents
Enduring understanding (Big Idea): Students will learn the properties of exponents and how to use numbers written in powers of tens to
solve problems. Students will learn the Pythagorean Theorem and how to solve problems using Pythagorean Theorem.
Essential Questions: How can you represent very large and very small numbers? How can you simplify expressions involving exponents?
What are the characteristics of exponential functions? Why is the Pythagorean Theorem useful? How can patterns help you simplify expressions
involving zero and negative exponents? Why should you use powers of ten to write and organize numbers? How do properties of exponents make
problems solving easier? Why should you use properties of exponents to simplify a power raised to a power or a product raised to a power? How
are the properties of dividing powers and multiplying powers similar? Why should you graph exponential functions?
BY THE END OF THIS UNIT:
Students will know…
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Students will be able to…
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Zero and negative exponents
Rules for multiplying and dividing powers
The Pythagorean Theorem
Scientific Notation
Vocabulary:
 Scientific Notation
Unit Resources
Learning Task:

Concept Byte 10-1 Distance and Midpoint Formula
Performance Task:

Pages 79-80 in Teacher resources
CMP2 Resources:

8th Grade CMP2 Looking For Pythagoras (All
Investigations)
Write numbers in scientific notation
Define and use zero and negative exponents
Multiply powers with the same base
Divide powers
Solve for lengths of missing sides of right triangles
Solve problems using the Pythagorean Theorem
Simplify expressions involving zero and nonnegative exponents
Write numbers in scientific and standard notation and compare their values
Raise a power to a power
Raise a product to a power
To divide powers with the same base
To raise a quotient to a power
Graph and evaluate exponential functions
Mathematical Practices in Focus:
12345678-
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
Standards
Chapter and Section
Suggested Homework
Standard 8.EE.1
7-1
Problems 1-4, Exs. 9-27 odd, 28-48 even, 50-66
Standard 8.EE.3
7-2
Problems 1-3, Exs. 11-23 odd, 24-34 even, 35-59
Standard 8.EE.4
7-3
Problems 1-4, Exs. 8-24 even, 25-31,32-40 even, 41-48, 54-69
Standard 8.EE.4
7-4
Problems 1-5, Exs 10-28 even, 30-43, 46-66
Standard 8.EE.4
7-5
Part 1 Problems 1-2, Exs. 8-26 even, 27-29, 70-86
Part 2 Problems 3-4 Exs. 30-46 even, 47-55, 59,61,62, 65-67
Standard 8.F.3
7-6
Problems 1-3 Exs. 8-25, 26-38 even, 39-52
Standard 8.G.7, 8.EE.2
10-1
Problems 1-3, Exs. 6-19, 20-28 even, 29-40
Standard 6.NS.6
Investigation 1
Coordinate Grids
Standard 8.EE.2
Investigation 2
Squaring Off
8th Grade CMP2 Looking
For Pythagoras
Investigation 1
8th Grade CMP2 Looking
For Pythagoras
Investigation 2
1.1: ACE 1-7, 26-28, 30, 35, 36
1.2: ACE 8-14, 29, 31, 37
1.3: ACE 15-25, 32-34, 38, 39
2.1: ACE 1-3, 42, 47-48
2.2: ACE 4-34
2.3: ACE 35-41, 43-46, 49-53
Common Core
Investigations
1.2 Cube Roots
Common Core Investigations
1.2: ACE 40-52
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
Standards 8.EE.2; 8.G.6;
8.G.7; 8.G.8
8th Grade CMP2 Looking
For Pythagoras
Investigation 3
3.1:ACE 1-14
3.2:ACE 18-23, 26
3.3:ACE 24. 27-35
3.4:ACE 15-17, 25
Standards 8.NS.1; 8.NS.2;
8.EE.2; 8.G.7
8th Grade CMP2 Looking
For Pythagoras
Investigation 4
4.1:ACE 1. 2. 13-16
4.2:ACE 3-9. 17-25,
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Understand and Apply the Pythagorean Theorem
Standard 8.G.6: Explain a proof of the Pythagorean Theorem and its converse.
Concepts and Skills to Master
• Know that in a right triangle a² + b² = c² (the Pythagorean Theorem).
• Understand and explain a proof of the Pythagorean Theorem.
• Understand and explain a proof of the converse of the Pythagorean Theorem.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand the relationship between a and a2, b and b2, c and c2.
 Understand the relationship between squares and square roots.
Academic Vocabulary
right triangle, leg, hypotenuse, square, Pythagorean Theorem
Suggested Instructional Strategies
Resources
 Textbook Correlation
 Consider introducing this with an application regarding
o Looking for Pythagoras (CMP2)
distance.

 Explore various proofs of the Pythagorean Theorem and
discuss the logic within each.
Investigations 3

MARS Tasks (HS):
E04: Proofs Of The Pythagorean Theorem
E08: Pythagorean Triples

MARS Problem Solving Lesson (HS):Proofs of the
Pythagorean Theorem

Texas Instrument 8.G.6 Lessons
 CMP2 Resources
Sample Formative Assessment Tasks
Skill-based Task
Problem Task
Explain the logical reasoning behind a proof of the Pythagorean
Theorem.
Investigate the historical context of one of the proofs of the
Pythagorean Theorem and present the proof in context to the class.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Understand and Apply the Pythagorean Theorem
Standard 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions.
Concepts and Skills to Master
• Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other two sides.
• Use the Pythagorean Theorem to solve problems in real-world contexts, including three-dimensional contexts.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
•Solve an equation using squares and square roots.
• Use rational approximations of irrational numbers to express answers.
Academic Vocabulary
right triangle, leg, hypotenuse, Pythagorean Theorem, square, square root,
Suggested Instructional Strategies
Resources
 Textbook Correlation
 Find and solve right triangles in career situations
o Looking for Pythagoras (CMP2)
such as construction.
 Investigations 3 and 4
o Foundations of Algebra
 Chapter 10-1
 Texas Instrument 8.G.7 Lessons
 CMP2 Resources
Sample Formative Assessment Tasks
Skill-based Task
If the height of a cone is 10 meters and the radius is 6
meters, what is the slant height?
Problem Task
TVs are measured along their diagonal to find their dimension.
How does a 52-inch HD (wide-screen) TV compare to a
traditional 52-inch (full screen) TV?
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Understand and apply the Pythagorean Theorem.
Standard 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Concepts and Skills to Master
• Calculate the distance between two points in a coordinate system using the Pythagorean Theorem.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
•Use the Pythagorean Theorem to solve for the hypotenuse of a right triangle.
Academic Vocabulary
right triangle, distance formula, leg, hypotenuse, Pythagorean Theorem, square, square root, ,
Suggested Instructional Strategies
Resources
 Textbook Correlation
 Overlap a map with a coordinate grid and use the
o Looking for Pythagoras (CMP2)
Pythagorean Theorem to find the distance between two
 Investigations 3
locations.
 Investigate the relationship between the Pythagorean
 Texas Instrument 8.G.8 Lessons
Theorem and the distance formula.
 Use the Pythagorean Theorem to explore and categorize
 CMP2 Resources
triangles and quadrilaterals on a coordinate system.
Sample Formative Assessment Tasks
Skill-based task
Using the Pythagorean Theorem, find the distance between
(4,2) and (7,10).
Problem Task
List 3 coordinate pairs that are 5 units away from the origin in
the first quadrant. Describe how to find the points and justify
your reasoning. (Note: Points on the axes are not in the
quadrant.)
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Define, evaluate, and compare functions.
Standard 8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of
functions that are not linear.
Concepts and Skills to Master
 Distinguish between linear and non-linear functions given their algebraic expression, a table, or a graph.
 Recognize that functions written in the form y = mx + b are linear and that every linear function can be written in the form y
= mx + b.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Generate and plot ordered pairs from an equation.
 Understand linear slope as a constant rate of change.
Academic Vocabulary
collinear, linear, nonlinear
Suggested Instructional Strategies
Resources
 Examine constant and non-constant rates of
 Textbook Correlation
change in tables of values.
o Algebra 1 Foundations
 Chapter 7-6
 Explore growing patterns, generated from a
 Grapher
variety of contexts to explore linear and
 CMP2 Resources
nonlinear relationships.
 Line Plotter
 MARS Concept Assessment Task Lessons (MS):
A05: Baseball Jerseys; A17: Linear Graphs, A19: Meal Out
 MARS Concept Formative Assessment Lessons (MS):
Modeling Situations With Linear
 Texas Instrument 8.F.3 Lessons
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Expressions and Equations: Work with radicals and integer exponents.
Standard 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For
1
1
example: 3² x3−5 = 3−3 = =
3³
27
Concepts and Skills to Master
 Know the properties of integer exponents.
 Apply the properties of integer exponents to simplify and evaluate numerical expressions.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand exponents as repeated multiplication. (6.EE.1)
 Compute fluently with integers (add, subtract, and multiply).
Academic Vocabulary
exponent, base, power, integer
Suggested Instructional Strategies
Resources
 Use repeated multiplication and division to
 Textbook Correlation
informally derive the exponent rules.
 Foundations of Algebra
 Chapter 7-1
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 Have students examine equivalent numerical
expressions with exponents.
Sample Formative Assessment Tasks
Skill-based Task
Simplify
57
( ( (2)²)²)² −50 2−2 * 4
3
MARS AssessmentTask (HS):
E06: “Ponzi” Pyramid Schemes
 Texas Instrument 8.EE.1 Lessons
 CMP2 Resources
Problem Task
Explain why 35 * 32 = 37 and not 97 .
5
Write three expressions equivalent to 32 * 92 .
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Expressions and Equations: Work with radicals and integer exponents.
Standard 8.EE.2:Use square root and cube root symbols to represent solutions to equations of the form x 2 = 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.
Concepts and Skills to Master
 Evaluate the square roots of small, perfect squares and cube roots of small perfect cubes.
 Represent the solutions to equations using square root and cube root symbols.
 Understand that all non-perfect square roots and cube roots are irrational.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Understand and use inverse operations to solve equations.
Academic Vocabulary
square, square root, , cube, cube root, , radical
Suggested Instructional Strategies
Resources
 Textbook Correlation
 Use the geometric representations of square area and
o Looking for Pythagoras (CMP2)
cube volumes and their relation to the side length.
 Use the idea of inverse operations to introduce the
concept of roots.
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Investigations 2, 3, and 4
Foundations of Algebra
 Chapter 10-1
Squares, Square Roots and Exponential Expressions
MARS Formative Assessment Lesson (MS):
The Pythagorean Theorem: Square Areas
CMP2 Resources
Texas Instrument 8.EE.2 Lessons
Sample Formative Assessment Tasks
Skill-based Task
If a square has an area of 9/16 square inches, what is the length of a side?
If a cube has a volume of 0.125 cubic meters, what are the dimensions of
the cube?
Problem Task
Is the square root of a number always smaller than the number itself? Explain.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title:Work with radicals and integer exponents.
Standard 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 ×
8
9
10 and the population of the world as 7 × 10 , and determine that the world population is more than 20 times larger.
Concepts and Skills to Master
• Estimate numbers as a product of a single digit and a power of ten.
• Compare numbers expressed as a product of a single digit and a power of ten by a scale factor.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
• Understand properties of integer exponents.
• Use and understand powers of ten and place value.
• Estimate and round numbers.
Academic Vocabulary
powers of ten, estimate
Suggested Instructional Strategies
Resources
 Textbook Correlation
• Use large and small real-life numbers (e.g. national debt).
 Foundations of Algebra
• Use base 10 blocks.
 Chapter 7-2
• Write numbers as repeated multiplication or as the value
 MARS AssessmentTask (MS):
of a power of 10.(e.g. 7∙103→7∙1000 𝑜𝑟
A02: 100 People ; A03: A Million Dollars
7000 →7∙1000→7∙(10∙10∙10))
 Texas Instrument 8.EE.3 Lessons

CMP2 Resources
Sample Formative Assessment Tasks
Skill-based Task
The mass of the earth is 6×1024kg. The mass of the moon is
7×1022kg. How many times bigger is the mass of the earth than the
mass of the moon?
A proton has 2 x 10 -27 kg mass and an electron has 9×10-14kg mass.
How many times smaller is the electron than the proton?
Problem Task
Provide two (2) original (not teacher-given) real-life situations that could be
illustrated using powers of ten, one that describes a very small number and
one that describes a very large number. Estimate how much larger one is than
the other.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
CORE CONTENT
Cluster Title: Cluster Title: Work with radicals and integer exponents.
Standard 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.
Concepts and Skills to Master
• Add, subtract, multiply and divide with numbers expressed in scientific notation and decimal notation.
• Represent very large and small quantities in scientific notation and use appropriate units.
• Convert between decimal notation and scientific notation.
• Interpret numbers expressed in scientific notation, including numbers generated by technology.
SUPPORTS FOR TEACHERS
Critical Background Knowledge
• Use rules of exponents.
• Understand powers of ten and place value.
Academic Vocabulary
scientific notation, decimal notation, power of ten, units of measure
Suggested Instructional Strategies
Resources
 Textbook Correlation
• Use examples found in science to create authentic reasons
 Foundations of Algebra
to use scientific notation.
 Chapter 7-3, 7-4, 7-5
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MARS AssessmentTask (HS): A18: Giantburgers
MARS Formative AssessmentLesson (MS):
Estimating Length Using Scientific Notation
Scientific Notation (Includes a Smartboard Lesson)
Scientific Notation (WebQuest)
Scientific Notation (Card Game)
Texas Instrument 8.EE.4 Lessons
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes
7th Grade Honors Unit 5 Exponents
Sample Formative Assessment Tasks
Evaluate and express your answers in scientific notation.
• (3×105 )+ (5.54×107 )
• (4.2×10−2 )–(7.4×102 )
Problem Task
Express your age at your last birthday in each of the following
units: years, months, weeks, days, hours, minutes and seconds.
Which values would be useful to write in scientific notation?
Justify your reasoning.
• (3×108 )(500)
Compare your age to that of the 4.5 billion year old earth.
•
30
1.5 𝑥10−4
Multiply 345,328,004 x 234 on your calculator and write the
answer in scientific notation.
Successive pages contain an unpacking of the standards contained in the unit. Standards are listed in alphabetical and numerical order
not suggested teaching order. Teachers must order the standards to form a reasonable unit for instructional purposes