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Subjects
Grades
Resource Type
Common Core: Math
CCLS  Math: 8.G.7
 Category
 Geometry
 SubCategory
 Understand And Apply The Pythagorean Theorem.
 State Standard:
 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions.
18 Results

 In Topic D, students learn that radical expressions naturally arise in geometry, such as the height of an isosceles triangle or the lateral length of a cone. The Pythagorean Theorem is applied to...

 Topic C revisits the Pythagorean Theorem and its applications, now in a context that includes the use of square roots and irrational numbers. Students learn another proof of the Pythagorean Theorem...

 Optional Topic E is an application of systems of linear equations (8.EE.C.8b). Specifically, a system that generates Pythagorean triples. First, students learn that a Pythagorean triple can be...

 It is recommended that students have some experience with the lessons in Topic D from Module 2 before beginning these lessons. In Lesson 13 of Topic C, students are presented with a general proof...

 Optional Topic D begins the learning of Pythagorean Theorem. Students are shown the “square within a square” proof of the Pythagorean Theorem. The proof uses concepts learned in previous topics of...

 Student Outcomes Using square roots, students determine the position of the bottom of a ladder as its top slides down a wall at a constant rate.

 Student Outcomes Students know how to compute the average rate of change in the height of water level when water is poured into a conical container at a constant rate.

 Student Outcomes Students know how to determine the volume of a figure composed of combinations of cylinders, cones, and spheres.

 Student Outcomes Students know that truncated cones and pyramids are solids obtained by removing the top portion above a plane parallel to the base. Students find the volume of truncated cones.

 Student Outcomes Students use the Pythagorean Theorem to determine an unknown dimension of a cone or a sphere. Students know that a pyramid is a special type of cone with triangular faces and a...

 Student Outcomes Students apply the Pythagorean Theorem to real world and mathematical problems in two dimensions.

 Student Outcomes Students know that the Pythagorean Theorem can be interpreted as a statement about the areas of similar geometric figures constructed on the sides of a right triangle. Students...

 Student Outcomes Students know that a Pythagorean triple can be obtained by multiplying any known triple by a common whole number. Students use this method to generate Pythagorean triples. Students...

 Student Outcomes Students illuminate the converse of the Pythagorean Theorem through computation of examples and counterexamples. Students apply the theorem and its converse to solve problems.

 Student Outcomes Students use the Pythagorean theorem to determine missing side lengths of right triangles.

 Grade 8 Module 7: Introduction to Irrational Numbers Using Geometry Module 7 begins with work related to the Pythagorean Theorem and right triangles. Before the lessons of this module are presented...

 Grade 8 Module 3: Similarity In Module 3, students learn about dilation and similarity and apply that knowledge to a proof of the Pythagorean Theorem based on the AngleAngle criterion for similar...

 Grade 8 Module 2: The Concept of Congruence In this module, students learn about translations, reflections, and rotations in the plane and, more importantly, how to use them to precisely define the...