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Common Core: Math
Subject: Math
212 Results

 Simultaneous equations and their solutions are the focus of Topic D. Students begin by comparing the constant speed of two individuals to determine which has greater speed (8.EE.C.8c). Students...

 In Topic C, students know that the slope of a line describes the rate of change of a line. Students first encounter slope by interpreting the unit rate of a graph (8.EE.B.5). In general, students...

 In Topic B, students work with constant speed, a concept learned in Grade 6 (6.RP.A.3), but this time with proportional relationships related to average speed and constant speed. These relationships...

 In Topic A, students begin by transcribing written statements using symbolic notation. Then, students write linear and nonlinear expressions leading to linear equations, which are solved using...

 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...

 In Topic B, students’ understanding of integer exponents is expanded to include the concept of magnitude as a measurement. Students learn to estimate how big or how small a number is using magnitude...

 In Topic A, students begin by learning the precise definition of exponential notation where the exponent is restricted to being a positive integer. In Lessons 2 and 3, students discern the structure...

 Student Outcomes Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or...

 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 calculate the decimal expansion of pi using basic properties of area. Students estimate the value of expressions such as pi2.