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The Pythagorean Theorem

Grade Level Grade 8
Resource Type Assessment
Standards Alignment
Common Core State Standards


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8th Grade Math/Science CCSS Unit Plan

The core structure of this unit plan follows OpenUp Resources' Unit 7 on the Pythagorean Theorem and implements the MARS Formative Assessment Lesson 'Finding the Shortest Route: A Schoolyard Problem'. First, students explore the relationship between side lengths and area of squares, as (1) an introduction to rational and irrational numbers, and (2) a geometry guide into our proof of the Pythagorean theorem. Once we prove the Pythagorean Theorem, students work on applying the theorem in a variety of problems, getting started on The Schoolyard Problem. Before taking a final launch into the Formative Assessment Lesson, students learn how to convert rational numbers into repeating decimals, and vice versa, while finally learning what makes a number irrational. Due to the lowered synchronous instructional time commitments permitted by the pandemic, the following unit reflects recommendations from Student Achievement Partners’ 2020–21 Priority Instructional Content in English Language Arts/Literacy and Mathematics.

As per recommendations from SAP, this unit plan does not reduce instructional time on the application of the Pythagorean Theorem to problems (CCSS 8.G.B.7), but eliminates lessons on proving the theorem and its converse (CCSS 8.G.B.6), as well as lessons using the theorem to find the distance between two points on a plane (CCSS 8.G.B.8). Also following recommendations from SAP, this unit integrates irrational numbers (CCSS 8.NS.A) as we explore the square roots that come from the Pythagorean Theorem. 

You can find the full unit plan, as well as a table with all lesson plans, synchronous instruction slides, synchronous assessment slides, and asynchronous assignments: Pythagorean Theorem Unit Plan Site

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Explain a proof of the Pythagorean Theorem and its converse.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
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.
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., ?²).


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