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Common Core: Math
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 Student Outcomes Students apply knowledge of geometry to writing and solving linear equations.

 Student Outcomes Students write rules to express functions related to geometry. Students review what they know about volume with respect to rectangular prisms and further develop their conceptual...

 Topic A begins by demonstrating the need for a precise definition of dilation instead of “same shape, different size” because dilation will be applied to geometric shapes that are not polygons. ...

 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...

 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...

 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...

 Throughout Topic A, on the definitions and properties of the basic rigid motions, students verify experimentally their basic properties and, when feasible, deepen their understanding of these...

 Topic B is a critical foundation to the understanding of congruence. All the lessons of Topic B demonstrate to students the ability to sequence various combinations of rigid motions while...

 In Topic C, on the definition and properties of congruence, students learn that congruence is just a sequence of basic rigid motions. The fundamental properties shared by all the basic rigid motions...

 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...

 Topic B begins with the definition of similarity and the properties of similarities. In Lesson 8, students learn that similarities map lines to lines, change the length of segments by factor r, and...

 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...

 In Topic B, students apply their knowledge of volume from previous grade levels (5.MD.C.3, 5.MD.C.5) to the learning of the volume formulas for cones, cylinders, and spheres (8.G.C.9). First,...

 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...

 Grade 8 Module 5: Examples of Functions from Geometry In the first topic of this 15 day module, students learn the concept of a function and why functions are necessary for describing geometric...

 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...

 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...