enVision Mathematics Topic 7
8th Grade; March – April (3 weeks); 4th Quarter
Embedded Files
Topic Title(s):
Understand and Apply the Pythagorean Theorem
Prepared Graduates:
MP3. Construct viable arguments and critique the reasoning of others.
MP7. Look for and make use of structure.
MP8. Look for and express regularity in repeated reasoning.
Standard(s):
4. Geometry
The highlighted evidence outcomes are the priority for all students, serving as the essential concepts and skills. It is recommended that the remaining evidence outcomes listed be addressed as time allows, representing the full breadth of the curriculum.
Students Can (Evidence Outcomes):
8.G.B. Geometry: Understand and apply the Pythagorean Theorem.
Explain a proof of the Pythagorean Theorem and its converse. (CCSS: 8.G.B.6)
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (CCSS: 8.G.B.7)
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (CCSS: 8.G.B.8)
Think of the Pythagorean Theorem as not just a formula, but a formula that only holds true under certain conditions. (Entrepreneurial Skills: Inquiry/Analysis)
Construct a viable argument about why a proof of the Pythagorean Theorem is valid. (MP3)
Test to see if a triangle is a right triangle by applying the Pythagorean Theorem. (MP7)
Use patterns to recognize and generate Pythagorean triples. (MP8)
Inquiry Questions
What is the relationship between the Pythagorean Theorem and its converse? In what ways is each useful?
Is it always possible to use the Pythagorean Theorem to find the distance between points on the coordinate plane? How do you know?
Coherence Connections
This expectation represents major work of the grade.
In Grades 6 and 7, students solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
In Grade 8, this expectation connects with radicals and integer exponents, square roots, and solving simple equations in the form x2 = p.
In high school, students (a) prove and apply trigonometric identities, (b) prove theorems involving similarity, (c) define trigonometric ratios and solve problems involving right triangles, (d) translate between the geometric description and the equation for a conic section, and (e) use coordinates to prove simple geometric theorems algebraically.
Academic Vocabulary & Language Expectations:
Hypotenuse, leg, Pythagorean Theorem, proof, Converse of the Pythagorean Theorem
Assessments:
Instructional Resources & Notes:
enVision Mathematics Topic 7
Let's Investigate! Tasks
Let's Investigate! Building The Right Way (TE) (relates to Lesson 7-2)
Tier 1 Intervention & Supports (i-Ready Tools for Instruction):
Tier 1 Intervention: Use the Pythagorean Theorem to Find Distance
enVision Mathematics 6-8 & Number Worlds Connections (for SVVSD Special Education teachers only)
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