Grade 8
Unit 1 Table of Contents
Pythagorean Theorem
Section
Page Number
Unit Description
Unit Standards
Unit Essential Questions
Unit Proficiencies (Learning Targets)
Unit Vocabulary and Language Support
Sample Unit Calendar and Possible Supporting Materials
Student Proficiencies Handout
Unit Assessments and Rubric/Commentary
2
2
3
3
4
6
8
10
1|Page
This Unit Developed by:
Grade 8
Content Unit 1
Unit Title:
Stage 1
Unit
Description:
Standards:
Dates of Unit:
Weeks 1-9
Pythagorean Theorem
Identify Desired Results
Students explore two main ideas: The Pythagorean Theorem and square roots. They will also understand and apply
the concepts of area, volume, distance, irrational numbers, and scientific notation.
8.G.6 - Explain a proof of the Pythagorean Theorem and its 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.
8.G.8 - Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.NS.1 - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal
expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which
repeats eventually into a rational number.
8.NS.2 - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately
on a number line diagram, and estimate the value of expressions (e.g., π2)
8.EE.1 - Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 35 = 3-3 = 1/33 = 1/27.
8.EE.2 - Use square root and cube root symbols to represent solutions to equations of the formx2 = 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
8.G.9 - Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical
problems.
8.G.5 - Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created
when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
2|Page
This Unit Developed by:
Essential
Question(s):
Proficiencies
(Learning Targets)
How can the Pythagorean Theorem be used to solve problems?
Proficiency #1 – “I can apply the properties of exponents to write equivalent expressions (8.EE.1).”
Proficiency #2 – “I can write really big and small numbers in standard form and scientific notation (8.EE.3).”
Proficiency #3 – “I can perform operations using numbers in scientific notation (8.EE.4).”
Proficiency #4 – “I can explain a proof of the Pythagorean Theorem and its converse (8.G.6).”
Proficiency #5 – “I can apply the Pythagorean Theorem to find the distance between two points in a coordinate system (8.G.8).”
Proficiency #6 – “I can apply the Pythagorean Theorem to determine unknown sides in right triangles (8.G.7).”
Proficiency #7 – “I can use square root and cube root symbols to represent solutions to equations (8.EE.2).”
Proficiency #8 – “I can identify whether numbers are rational or irrational (8.NS.1).”
Proficiency #9 – “I can approximate irrational numbers (8.NS.2).”
Proficiency #10 – “I know and can use the formulas for volume of cones, cylinders, and spheres (8.G.9).”
Proficiency #11 – “I can justify angle sums and measures for triangles and transversals (8.G.5).”
Proficiency #12 – “I know and can use the definitions of the vocabulary words associated with this unit (see Student Proficiencies
Handout).”
3|Page
This Unit Developed by:
Stage 2
Determine Assessment Evidence
Academic Language Function(s):

Academic Language (What language will students need to sound like experts?)
Academic Language Stems:
Easy for Beginners
Academic Vocabulary:
Area
Cone
Coordinate Grid
Cylinder
Exponent
Parallel
Perpendicular
Sphere
Volume
30-60-90 Triangle
45-45-90 Triangle
Hypotenuse
Irrational
Legs
Rational
Right Triangle
Scientific Notation
Square Number
Square Root
Transversal
Assessment
Tools:
 Goals Rubric
 Assessment Checklist
4|Page
This Unit Developed by:
Medium for Intermediate
Difficult for Advanced and Fluent
Student Name
B = Beginning
5|Page
This Unit Developed by:
D = Developing
P = Proficient
M=Mastery
I know and can use the
definitions of the vocabulary
words associated with this
unit (see Student
Proficiencies Handout)
I can justify angle sums and
measures for triangles and
transversals (8.G.5)
I know and can use the
formulas for volume of
cones, cylinders, and
spheres (8.G.9)
I can approximate irrational
numbers (8.NS.2)
I can identify whether
numbers are rational or
irrational (8.NS.1)
I can use square root and
cube root symbols to
represent solutions to
equations (8.EE.2)
I can apply the Pythagorean
Theorem to determine
unknown sides in right
triangles (8.G.7)
I can apply the Pythagorean
Theorem to find the
distance between two
points in a coordinate
system (8.G.8)
I can explain a proof of the
Pythagorean Theorem and
its converse (8.G.6).
I can perform operations
using numbers in scientific
notation (8.EE.4)
I can write really big and
small numbers in standard
form and scientific notation
(8.EE.3)
Learning I can apply the
properties of exponents to
write equivalent expressions
(8.EE.1).
Unit of Study Assessment Checklist
Stage 3
Plan Learning Experiences and Instruction
SAMPLE UNIT CALENDAR
Proficiency #1 – “I can apply
the properties of exponents
to write equivalent
expressions (8.EE.1).”
Materials – Oregon Focus
Stage 3 Companion Text 3-E
Proficiency #1 – “I can apply
the properties of exponents
to write equivalent
expressions (8.EE.1).”
Materials – Oregon Focus
Stage 3 Companion Text 3-E
Proficiency #1 – “I can apply
the properties of exponents
to write equivalent
expressions (8.EE.1).”
Materials – Oregon Focus
Stage 3 Companion Text 3-F
Proficiency #1 – “I can apply
the properties of exponents
to write equivalent
expressions (8.EE.1).”
Materials – Oregon Focus
Stage 3 Companion Text 3-F
Proficiency #2 – “I can write
really big and small numbers
in standard form and scientific
notation (8.EE.3).”
Materials – Oregon Focus
Stage 3 Companion Text 3-G
Proficiency #2 – “I can write
really big and small numbers
in standard form and
scientific notation (8.EE.3).”
Materials – Oregon Focus
Stage 3 Companion Text 3-G
Proficiency #12– “I know and
can use the definitions of the
vocabulary words associated
with this unit (see the back).”
Proficiency #3 – “I can
perform operations using
numbers in scientific notation
(8.EE.4).”
Materials – Oregon Focus
Stage 3 Companion Text 3-H
Proficiency #12– “I know and
can use the definitions of the
vocabulary words associated
with this unit (see the back).”
Proficiency #3 – “I can
perform operations using
numbers in scientific notation
(8.EE.4).”
Materials – Oregon Focus
Stage 3 Companion Text 3-H
Assessment for Proficiencies
#1-3, 12
Assessment for Proficiencies
#1-3
Materials – CMP2 LFP
Investigation 1.2
Proficiency #5 – “I can apply
the Pythagorean Theorem to
find the distance between
two points in a coordinate
system (8.G.8).”
Materials – CMP2 LFP
Investigation 2.3
Materials – CMP2 LFP
Investigation 1.3
Assessment for Proficiencies
#1-3, 5, 7
Materials – Assessment #2
Proficiency #4 – “I can explain
a proof of the Pythagorean
Theorem and its converse
(8.G.6).”
Proficiency #7 – “I can use
square root and cube root
symbols to represent
solutions to equations
(8.EE.2).”
Materials – CMP2 LFP
Investigation 2.1
Proficiency #4 – “I can explain
a proof of the Pythagorean
Theorem and its converse
(8.G.6).”
Materials – Assessment #3
Materials – CMP2 LFP
Investigation 3.1
Materials – CMP2 LFP
Investigation 3.2
Proficiency #12– “I know and
can use the definitions of the
vocabulary words associated
with this unit (see the back).”
Materials – CMP2 LFP
Investigation 1.1
Proficiency #7 – “I can use
square root and cube root
symbols to represent
solutions to equations
(8.EE.2).”
Materials – CMP2 LFP
Investigation 2.2
Proficiency #5 – “I can apply
the Pythagorean Theorem to
find the distance between
two points in a coordinate
system (8.G.8).”
Materials – CMP2 LFP
Investigation 3.3
6|Page
This Unit Developed by:
Materials – Assessment #1
Proficiency #8 – “I can identify
whether numbers are rational or
irrational (8.NS.1).”
Proficiency #9 – “I can approximate
irrational numbers (8.NS.2).”
Materials – CMP2 LFP
Investigation 4.1
Proficiency #6 – “I can apply
the Pythagorean Theorem to
determine unknown sides in
right triangles (8.G.7).”
Proficiency #6 – “I can apply
the Pythagorean Theorem to
determine unknown sides in
right triangles (8.G.7).”
Materials – CMP2 LFP
Investigation 4.2
Materials – CMP2 LFP
Investigation 4.3
Proficiency #11 – “I can justify
angle sums and measures for
triangles and transversals
(8.G.5).”
Materials – CMP2 LFP
Common Core Supplement 4.1
Down the road – Assessment
for Proficiencies 8,9 one more
time and 10,11 two more
times.
Proficiency #11 – “I can justify
angle sums and measures for
triangles and transversals
(8.G.5).”
Materials – CMP2 LFP
Common Core Supplement 4.2
Proficiency -
Proficiency #11 – “I can justify
angle sums and measures for
triangles and transversals
(8.G.5).”
Materials – CMP2 LFP
Common Core Supplement 4.3
Proficiency -
Materials – Assessment #6
Materials – Assessments #7 & 8
Materials –
Materials –
Proficiency -
Proficiency -
Proficiency -
Proficiency -
Materials –
Materials –
Materials –
Materials –
Proficiency #6 – “I can apply
the Pythagorean Theorem to
determine unknown sides in
right triangles (8.G.7).”
Assessment for Proficiencies
#4-7, 12
Materials – CMP2 LFP
Investigation 3.4
Materials – Assessment #4
Proficiency #6 – “I can apply
the Pythagorean Theorem to
determine unknown sides in
right triangles (8.G.7).”
Materials – CMP2 LFP
Investigation 4.4
Proficiency #10 – “I know and
can use the formulas for
volume of cones, cylinders,
and spheres (8.G.9).”
Assessment for Proficiencies
#4-9
Materials – CMP2 LFP
Common Core Supplement 4.4
Proficiency -
Materials –
Materials – Assessment #5
Assessment for Proficiencies
#4,6,8-12
7|Page
This Unit Developed by:
Name ______________________________
Date ________________________ Period _____
My Proficiency Assessment Scores
1st Try
2nd Try
3rd Try
Proficiency #1 – “I can apply the properties of exponents to write
equivalent expressions (8.EE.1).”
Proficiency #2 – “I can write really big and small numbers in
standard form and scientific notation (8.EE.3).”
Proficiency #3 – “I can perform operations using numbers in
scientific notation (8.EE.4).”
Proficiency #4 – “I can explain a proof of the Pythagorean
Theorem and its converse (8.G.6).”
Proficiency #5 – “I can apply the Pythagorean Theorem to find
the distance between two points in a coordinate system (8.G.8).”
Proficiency #6 – “I can apply the Pythagorean Theorem to
determine unknown sides in right triangles (8.G.7).”
Proficiency #7 – “I can use square root and cube root symbols to
represent solutions to equations (8.EE.2).”
Proficiency #8 – “I can identify whether numbers are rational
or irrational (8.NS.1).”
Proficiency #9
(8.NS.2).”
–
“I can approximate irrational numbers
Proficiency #10 – “I know and can use the formulas for volume
of cones, cylinders, and spheres (8.G.9).”
Proficiency #11 – “I can justify angle sums and measures for
triangles and transversals (8.G.5).”
Proficiency #12– “I know and can use the definitions of the
vocabulary words associated with this unit (see the back).”
8|Page
This Unit Developed by:
Area
Cone
Coordinate Grid
Cylinder
Exponent
Parallel
Perpendicular
Sphere
Volume
30-60-90 Triangle
45-45-90 Triangle
Hypotenuse
Irrational
Legs
Rational
Right Triangle
Scientific Notation
Square Number
Square Root
Transversal
See me if you look at this list and think, “uh, oh…”
⧠ I can add without a calculator
⧠ I can multiply without a calculator
⧠ I can state my answer clearly
⧠ I can plot points on a graph
9|Page
This Unit Developed by:
Assessment Place Holder
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can ...”
10 | P a g e
This Unit Developed by:
Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
11 | P a g e
This Unit Developed by:
Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.
Assessment Place Holder
Name _________________________________
Date _______________________ Period ____
Proficiency # – “I can ...”
12 | P a g e
This Unit Developed by:
Proficiency
Score
4
Percentage
3
83%
2
67%
1
50%
100%
13 | P a g e
This Unit Developed by:
Description
WOW!
I have shown proficiency and deeper understanding by:

You got it 
I have shown proficiency by:

Help is needed
I have shown partial understanding by:

Uh-oh…
I have not yet shown my understanding of the math.