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Common Core: Math
Subject: Math
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 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...

 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,...

 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...

 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...

 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. ...

 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...

 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...

 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...

 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...

 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 determine the distance between two points on a coordinate plane using the Pythagorean Theorem.

 Student Outcomes Students explain a proof of the converse of the Pythagorean Theorem. Students apply the theorem and its converse to solve problems.

 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 the volume formula for a sphere as it relates to a right circular cylinder with the same diameter and height. Students apply the formula for the volume of a sphere to...

 Student Outcomes Students know the volume formulas for cones and cylinders. Students apply the formulas for volume to realworld and mathematical problems.

 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...

 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...