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Common Core: Math
Topic: Common Core Learning Standards
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 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...

 Grade 8 Module 4: Linear Equations In Module 4, students extend what they already know about unit rates and proportional relationships to linear equations and their graphs. Students understand the...

 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 Mathematics Module 1: Integer Exponents and Scientific Notation In Grade 8 Module 1, students expand their basic knowledge of positive integer exponents and prove the Laws of Exponents for...

 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 6: Linear Functions In Grades 6 and 7, students worked with data involving a single variable. Module 6 introduces students to bivariate data. Students are introduced to a function as...

 Algebra I Module 5: A Synthesis of Modeling with Equations and Functions In Module 5, students synthesize what they have learned during the year about functions to select the correct function type in...

 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...

 In Topic B, students learn that to get the decimal expansion of a number (8.NS.A.1), they must develop a deeper understanding of the long division algorithm learned in Grades 6 and 7 (6.NS.B.2, 7.NS....

 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 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 A begins to examine the relationship between two variables using linear functions (8.F.B.4). Linear functions are connected to a context, using the initial value and slope as a rate of change...

 Topic B uses linear functions to model the relationship between two quantitative variables as students move to the domain of Statistics and Probability. Students make scatter plots based on data. ...

 In Topic C, students use linear and nonlinear models to answer questions in context (8.SP.A.1, 8.SP.A.2). They interpret the rate of change and the initial value in context (8.SP.A.3). They use the...

 In Topic D, students examine bivariate categorical data by using twoway tables to determine relative frequencies. They use the relative frequencies calculated from tables to informally assess...

 In Topic A, students learn the notation related to roots (8.EE.A.2). The definition for irrational numbers relies on students’ understanding of rational numbers, that is, students know that rational...

 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. ...

 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 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...

 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 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...

 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...

 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...