Livingston County Schools
Eighth Math Unit 5
The Pythagorean Theorem
Unit Overview
Students understand the Pythagorean Theorem and its converse and can explain why the Pythagorean thm holds. Apply the Pythagorean thm
to find distance between points on the coordinate plane. Students apply volume formula for cones, cylinders, and spheres.
Length of unit: 20 days
KY Core Academic
Standard
8.G.6 Explain a proof of
the Pythagorean
Theorem and it’s
converse.
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.
Learning Target
K
97. Define key vocabulary: square
root, Pythagorean Theorem, right
triangle, legs a & b, hypotenuse,
sides, right angle, converse, base,
height, proof.
X
98. Be able to identify the legs and
hypotenuse of a right triangle.
X
99. Explain a proof of the
Pythagorean Theorem.
X
100. Explain a proof of the
converse of the Pythagorean
Theorem.
101. Recall the Pythagorean
theorem and its converse.
Reasoning Targets
102. Solve basic mathematical
Pythagorean theorem problems
and its converse to find missing
lengths of sides of triangles in two
and three-dimensions.
103. Apply Pythagorean theorem
in solving real-world problems
R
S
P
Critical
Vocabulary
Pythagorean
Theorem, legs,
hypotenuse,
right triangle,
converse, proof
Texts/Resources/Activities
Pythagorean
Theorem, legs,
hypotenuse,
right triangle,
converse, proof
Crosswalk Lesson 31
Crosswalk Lesson 29
Lesson 4-8 p. 196
Pythagorean Theorem
X
X
X
X
8.G.8 Apply the
Pythagorean Theorem to
find the distance
between two points in a
coordinate system.
dealing with two and threedimensional shapes.
104. Recall the Pythagorean
Theorem and its converse.
X
Reasoning Targets
105. Determine how to create a
right triangle from two points on a
coordinate graph.
106. Use the Pythagorean
Theorem to solve for the distance
between the two points.
8.G.9 Know the formulas 107. Identify and define vocabulary:
for the volumes of cones, cone, cylinder, sphere, radius,
diameter, circumference, area,
cylinders, and spheres
volume, pi, base, height .
and use them to solve
real-world and
mathematical problems. 108. Know formulas for volume of
cones, cylinders, and spheres.
Reasoning Targets
109. Compare the volume of cones,
cylinders, and spheres.
110. Determine and apply
appropriate volume formulas in
order to solve mathematical and
real-world problems for the given
shape.
111. Given the volume of a cone,
cylinder, or sphere, find the radii,
height, or approximate for π.
Common Assessments Developed (Proposed Assessment Dates):
X
Pythagorean
Theorem, legs,
hypotenuse,
right triangle,
converse, proof
Crosswalk Lesson 30
cone, cylinder,
sphere, radius,
diameter,
circumference,
area,
volume, pi,
base, height
Crosswalk Lesson 32
Lesson 8-5, 8-6, 8-9
Volume of Cylinder, Cones,
Spheres
X
X
X
X
X
X
HOT Questions: