Essential Questions: What are the applications of the Pythagorean Theorem and its converse? What is the relationship among the lengths of the sides of a right triangle? What are the properties of special right triangles and how are these properties used? How can the Pythagorean Theorem be used to solve problems in life? Lesson Plans and Seeds Lesson Plan B.7: Apply the Pythagorean Theorem Lesson Seed B.7: Pythagorean Proof Download Seeds, Plans, and Resources (zip) Unit Overview Content Emphasis By Clusters in Grade 8 Progressions from Common Core State Standards in Mathematics Send Feedback to MSDE’s Mathematics Team
Lesson Plan B.7: Apply the Pythagorean Theorem
Lesson Seed B.7: Pythagorean Proof
Unit Overview
Content Emphasis By Clusters in Grade 8
Progressions from Common Core State Standards in Mathematics
Send Feedback to MSDE’s Mathematics Team
Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
Lesson Plan: 8.G.B.7 Apply the Pythagorean Theorem
Unit/Cluster: Understand and apply the Pythagorean Theorem.
Lesson Topic: Apply the Pythagorean Theorem to real-life situations.
Essential Questions
Focus Standard(s)
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.
It is critical that the Standards for Mathematical Practices are incorporated in ALL lesson activities throughout the unit as appropriate. It is not the expectation that all eight Mathematical Practices will be evident in every lesson. The Standards for Mathematical Practices make an excellent framework on which to plan your instruction. Look for the infusion of the Mathematical Practices throughout this unit.
Coherence of Standards Across-Grade Coherence: Content Knowledge from Earlier Grades
6.EE.A.1: Write and evaluate numerical expressions involving whole-number exponents.
7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
7.G.A.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Within-Grade Coherence: Content from Other Standards in the Same Grade that Provide Reinforcement
8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form x2 = 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.
RIGOR
Procedural Skill Students will use the Pythagorean Theorem and add, subtract, multiply and square root skills.
Conceptual Understanding Students will use their understanding of the Pythagorean Theorem to apply this knowledge while solving real-world problems.
Modeling/Application Students will represent the Pythagorean Theorem in two ways by using equations and drawing examples.
Enduring Understandings:
Student Outcomes
Method for Determining Student Readiness for the Lesson
Learning Experience
