Grade 8
Unit 1 Table of Contents
Pythagorean Theorem
Section / Page NumberUnit Description / 2
Unit Standards / 2
Unit Essential Questions / 3
Unit Proficiencies(Learning Targets) / 3
Unit Vocabulary and Language Support / 4
Sample Unit Calendar and Possible Supporting Materials / 6
Student Proficiencies Handout / 8
Unit Assessments and Rubric/Commentary / 10
1 | Page
This Unit Developed by:
Grade 8Content Unit 1 / Dates of Unit:
Weeks 1-9
Unit Title: / Pythagorean Theorem
Stage 1 / Identify Desired Results
Unit Description: / 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.
Standards: / 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, 32×3-5= 3-3= 1/33= 1/27.
8.EE.2 - Use square root and cube root symbols to represent solutions to equations of the formx2=pandx3= p, wherepis 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.
Essential Question(s): / How can the Pythagorean Theorem be used to solve problems?
Proficiencies
(Learning Targets) / 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).”
Stage 2 / Determine Assessment Evidence
Academic Language (What language will students need to sound like experts?)
Academic Language Function(s): / Academic Language Stems:
Easy for Beginners
Medium for Intermediate
Difficult for Advanced and Fluent
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
Unit of Study Assessment Checklist
Student Name / Learning I can apply the properties of exponents to write equivalent expressions (8.EE.1). / I can write really big and small numbers in standard form and scientific notation (8.EE.3) / I can perform operations using numbers in scientific notation (8.EE.4) / I can explain a proof of the Pythagorean Theorem and its converse (8.G.6). / I can apply the Pythagorean Theorem to find the distance between two points in a coordinate system (8.G.8) / I can apply the Pythagorean Theorem to determine unknown sides in right triangles (8.G.7) / I can use square root and cube root symbols to represent solutions to equations (8.EE.2) / I can identify whether numbers are rational or irrational (8.NS.1) / I can approximate irrational numbers (8.NS.2) / I know and can use the formulas for volume of cones, cylinders, and spheres (8.G.9) / I can justify angle sums and measures for triangles and transversals (8.G.5) / I know and can use the definitions of the vocabulary words associated with this unit (see Student Proficiencies Handout)B = BeginningD = DevelopingP = ProficientM=Mastery
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).” / Proficiency #1 – “I can apply the properties of exponents to write equivalent expressions (8.EE.1).” / Proficiency #1 – “I can apply the properties of exponents to write equivalent expressions (8.EE.1).” / 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).”Materials – Oregon Focus Stage 3 Companion Text 3-E / Materials – Oregon Focus Stage 3 Companion Text 3-E / Materials – Oregon Focus Stage 3 Companion Text 3-F / Materials – Oregon Focus Stage 3 Companion Text 3-F / 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).” / Proficiency #3 – “I can perform operations using numbers in scientific notation (8.EE.4).” / Proficiency #3 – “I can perform operations using numbers in scientific notation (8.EE.4).” / Assessment for Proficiencies #1-3 / Proficiency #12– “I know and can use the definitions of the vocabulary words associated with this unit (see the back).”
Materials – Oregon Focus Stage 3 Companion Text 3-G / Materials – Oregon Focus Stage 3 Companion Text 3-H / Materials – Oregon Focus Stage 3 Companion Text 3-H / Materials – Assessment #1 / Materials – CMP2 LFP Investigation 1.1
Proficiency #12– “I know and can use the definitions of the vocabulary words associated with this unit (see the back).” / Proficiency #12– “I know and can use the definitions of the vocabulary words associated with this unit (see the back).” / Assessment for Proficiencies #1-3, 12 / Proficiency #7 – “I can use square root and cube root symbols to represent solutions to equations (8.EE.2).” / Proficiency #7 – “I can use square root and cube root symbols to represent solutions to equations (8.EE.2).”
Materials – CMP2 LFP Investigation 1.2 / Materials – CMP2 LFP Investigation 1.3 / Materials – Assessment #2 / Materials – CMP2 LFP Investigation 2.1 / 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).” / Assessment for Proficiencies #1-3, 5, 7 / Proficiency #4 – “I can explain a proof of the Pythagorean Theorem and its converse (8.G.6).” / 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).”
Materials – CMP2 LFP Investigation 2.3 / Materials – Assessment #3 / Materials – CMP2 LFP Investigation 3.1 / Materials – CMP2 LFP Investigation 3.2 / Materials – CMP2 LFP Investigation 3.3
Proficiency #6 – “I can apply the Pythagorean Theorem to determine unknown sides in right triangles (8.G.7).” / Assessment for Proficiencies #4-7, 12 / 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 #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 3.4 / Materials – Assessment #4 / Materials – CMP2 LFP Investigation 4.1 / Materials – CMP2 LFP Investigation 4.2 / Materials – CMP2 LFP Investigation 4.3
Proficiency #6 – “I can apply the Pythagorean Theorem to determine unknown sides in right triangles (8.G.7).” / Assessment for Proficiencies #4-9 / Proficiency #11 – “I can justify angle sums and measures for triangles and transversals (8.G.5).” / Proficiency #11 – “I can justify angle sums and measures for triangles and transversals (8.G.5).” / Proficiency #11 – “I can justify angle sums and measures for triangles and transversals (8.G.5).”
Materials – CMP2 LFP Investigation 4.4 / Materials – Assessment #5 / Materials – CMP2 LFP Common Core Supplement 4.1 / Materials – CMP2 LFP Common Core Supplement 4.2 / Materials – CMP2 LFP Common Core Supplement 4.3
Proficiency #10 – “I know and can use the formulas for volume of cones, cylinders, and spheres (8.G.9).” / Assessment for Proficiencies #4,6,8-12 / Down the road – Assessment for Proficiencies 8,9 one more time and 10,11 two more times. / Proficiency - / Proficiency -
Materials – CMP2 LFP Common Core Supplement 4.4 / Materials – Assessment #6 / Materials – Assessments #7 8 / Materials – / Materials –
Proficiency - / Proficiency - / Proficiency - / Proficiency - / Proficiency -
Materials – / Materials – / Materials – / Materials – / Materials –
1 | Page
This Unit Developed by:
Name ______
Date ______Period_____
My Proficiency Assessment Scores
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 the back).”
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
⧠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
Assessment Place Holder
Name ______
Date ______Period ____
Proficiency #– “I can ...”
Proficiency Score / Percentage / Description4 / 100% / WOW!
I haveshown proficiency and deeper understanding by:
3 / 83% / You got it
I have shown proficiency by:
2 / 67% / Help is needed
I have shown partial understanding by:
1 / 50% / Uh-oh…
I have not yet shown my understanding of the math.
Assessment Place Holder
Name ______
Date ______Period ____
Proficiency #– “I can ...”
Proficiency Score / Percentage / Description4 / 100% / WOW!
I have shown proficiency and deeper understanding by:
3 / 83% / You got it
I have shown proficiency by:
2 / 67% / Help is needed
I have shown partial understanding by:
1 / 50% / Uh-oh…
I have not yet shown my understanding of the math.
1 | Page
This Unit Developed by: