Course Name: 8th Grade Math
Unit # 3
Unit Title: Pythagorean Theorem
Enduring understanding (Big Idea): Students will explore the usage of the Pythagorean Theorem, square roots, and
concepts of area, distance, and irrational numbers.
Essential Questions: Is it appropriate and useful to solve the Pythagorean Theorem in this situation? How do I know this?
How can we use the Pythagorean Theorem to find the length of a line segment? Do I need to find the distance between
two points? How can I estimate the square root of a number? Describe how you can use the Pythagorean Theorem to find
the length of something without directly measuring it. How can you find the length of a square if you know its area?
BY THE END OF THIS UNIT:
Students will know…
Students will be able to…
Pythagorean Theorem: a2 + b2 = c2
Vocabulary:
Hypotenuse
Radical
Legs Radical Expressions
Pythagorean Theorem
Irrational numbers
Real numbers
Square roots
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Relate the area of a square to the side length
Estimate the values of square roots of whole
numbers
Locate irrational numbers on a number line
Develop strategies for finding this distance
between two points on a coordinate grid
Understand and apply the Pythagorean Theorem
Use the Pythagorean Theorem to solve every day
problems
Simplify radical expressions
Unit Resources
Mathematical Practices in Focus:
Learning Task:
 MathematicalReflections
Performance Task:
 Check-Up(s) / Partner Quiz / Unit Test
Project:
 Wheel of Theodorus Project:
Unit Review:
 Looking Back Looking Ahead
1. Make sense of problems and persevere in solving
them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning
of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
CCSS-M Included: 8.NS.1-2, 8.EE.2, 8.G.6-8, 7.NS.2d
Suggested Pacing: 20 Days
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: 8th Grade Math
Unit # 3
Unit Title: Pythagorean Theorem
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:
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Consider introducing this with an application
regarding distance.
Explore various proofs of the Pythagorean
Theorem and discuss the logic within each.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Resources:
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Textbook Correlation
o Looking for Pythagoras (CMP2)
 Investigations 3
MARS Tasks (HS):
E04: Proofs Of The Pythagorean Theorem
E08: Pythagorean Triples
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MARS Problem Solving Lesson (HS):Proofs of
the Pythagorean Theorem
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Texas Instrument 8.G.6 Lessons
CMP2 Resources
Course Name: 8th Grade Math
Unit # 3
Sample Assessment Task:
Skill-based Task
Explain the logical reasoning behind a proof of the
Pythagorean Theorem
Unit Title: Pythagorean Theorem
Problem Task
Investigate the historical context of one of the proofs of the
Pythagorean Theorem and present the proof in context to
the class.
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,
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: 8th Grade Math
Unit # 3
Suggested Instructional Strategies:
Unit Title: Pythagorean Theorem
Resources:
Find and solve right triangles in career situations such as
construction.
Sample 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?
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Textbook Correlation
o Looking for Pythagoras (CMP2)
 Investigations 3 and 4
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Texas Instrument 8.G.7 Lessons
CMP2 Resources
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?
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, ,
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
Course Name: 8th Grade Math
Unit # 3
Suggested Instructional Strategies
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Overlap a map with a coordinate grid and use the
Pythagorean Theorem to find the distance
between two locations.
Investigate the relationship between the
Pythagorean Theorem and the distance formula.
Use the Pythagorean Theorem to explore and
categorize triangles and quadrilaterals on a
coordinate system.
Sample Assessment Tasks
Skill-based task
Using the Pythagorean Theorem, find the distance
between (4,2) and (7,10).
Unit Title: Pythagorean Theorem
Resources
 Textbook Correlation
o Looking for Pythagoras (CMP2)
 Investigations 3
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Texas Instrument 8.G.8 Lessons

MP2 Resources
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.)
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.