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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Topic 8H
Big Idea(s)
Pythagorean Theorem
Pythagorean Theorem
Converse and the Pythagorean Theorem
Distance on the Coordinate Plane
Understand and apply the Pythagorean Theorem.
What enduring understandings are
essential for application to new
situations within or beyond this
content?
Essential Question(s)
What questions will provoke and
sustain student engagement while
focusing learning?
Enduring Standard(s)
Which standards provide
endurance beyond the course,
leverage across multiple
disciplines, and readiness for the
next level?
How do models help solve math problems?
Why is the Pythagorean Theorem considered to be the most important
mathematical equation?
Enduring Understandings
 The Pythagorean Theorem can be used both algebraically and
geometrically to solve problems involving right triangles.
 There is a relationship between the Pythagorean Theorem and the
distance formula.
 Both the Pythagorean Theorem and distance formula can be used
to find missing side lengths in a coordinate plane and real-world
situation.
 How to solve simple and complex linear and literal equations with
one solution.
 Finding the square root of a number is the inverse operation of
squaring that number.
 Finding the cube root of a number is the inverse operation of
cubing that number.
 Right triangles have a special relationship among the side lengths
which can be represented by a model and a formula.
 Pythagorean Triples can be used to construct right triangles.
 How to simplify radicals and solve quadratic equations.
Standards for Mathematical Practice
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.
Curriculum and Instruction
2014-2015
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Standards for Mathematical Content
Geometry
Understand and apply the Pythagorean Theorem.
8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse.
Supporting Standard(s)
Which related standards will be
incorporated to support and
enhance the enduring standards?
Instructional Outcomes
Standards for Mathematical Content
Geometry
Understand and apply the Pythagorean Theorem.
8.G.B.7 Apply the Pythagorean Theorem to determine unknown side
lengths in right triangles in real-world and mathematical problems in
two and three dimensions.
8.G.B.8 Apply the Pythagorean Theorem to find the distance between
two points in a coordinate system.
Essential Vocabulary
I can…
 explain a proof of the Pythagorean Theorem and its converse.
 identify the parts of a right triangle.
 use a^2+b^2=c^2.
 determine the hypotenuse of a right triangle given it’s legs.
 determine a missing leg of a right triangle, given the
hypotenuse and a leg.
 determine the unknown side lengths in right triangles in realworld and mathematical problems (2D and 3D) using the
Pythagorean Theorem.
 use the Pythagorean Theorem to find the distance between
two points in the coordinate plane.
Students who demonstrate understanding can…
 explain a proof of the Pythagorean Theorem and its converse.
 determine the unknown side lengths in right triangles in realworld and mathematical problems (2D and 3D) using the
Pythagorean Theorem.
 use the Pythagorean Theorem to find the distance between
two points in the coordinate plane.
Essential Vocabulary
What vocabulary must students
know to understand and
communicate effectively about
this content?
converse - The interchanging of the "if" and "then" parts of a
conditional statement.
What must students learn by the
end of the unit?
Performance Expectations
What must students be able to do
by the end of the unit to
demonstrate their mastery of the
instructional outcomes?
Pythagorean Theorem - "The theorem that relates the three sides of a
right triangle: a^2 + b^2 = c^2".
right triangle - A triangle in which one angle is a right angle. The
relation between the sides and angles of a right triangle is the basis for
trigonometry.
Curriculum and Instruction
2014-2015
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FAYETTE COUNTY PUBLIC SCHOOLS
District Curriculum Map for Mathematics: Grade 8
Supporting Vocabulary
Triangle Inequality Theorem
hypotenuse
leg
Common Core Glossary
http://www.corestandards.org/Math/Content/mathematicsglossary/glossary/
Curriculum and Instruction
2014-2015
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Subject and Grade Level
Unit Title
Summative Assessment of
Learning
Mathematics 8H
Pythagorean Theorem
In what way will students meet the
performance expectations to
demonstrate mastery of the
standards?
Instructional Outcomes
How will the instructional outcomes
be sequenced into a
progression of learning?
Learning Activities
What well-designed progression of
learning tasks will intellectually
engage students
in challenging content?
Formal Formative Assessments
What is the evidence to show
students have learned the lesson
objective and are progressing
toward mastery of the instructional
outcomes?
Integration Standards
What standards from other
disciplines will enrich the learning
experiences for the students?
Resources
Resources
What resources will be utilized to
enhance student learning?
Curriculum and Instruction
2014-2015
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