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 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...

 Updated Modules and Curricular Resources The tables below reflect Mathematics and English Language Arts curricular materials and resources that have been updated. As additional materials are updated...

 In this lesson, students engage in a jigsaw on the evidencebased claims in Chisholm’s speech. • The Summary Writing graphic organizer included in the supporting materials of this lesson was first...

 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....

 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...

 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...

 Student Outcomes Students graph two equations and find the point of intersection. Students identify the point of intersection of the two lines as the solution to the system. Students verify by...

 Student Outcomes Students know that when a system of linear equations has no solution, i.e., no point of intersection of the lines, then the lines are parallel.

 Student Outcomes Students know that since two equations in the form ax + by = c and a'x + b'y = c' graph as the same line when a'/a = b'/b = c'/c, then the system of linear equations has infinitely...

 Student Outcomes Students learn the elimination method for solving a system of linear equations. Students use properties of rational numbers to find a solution to a system, if it exists, through...

 Student Outcomes Students write word problems into systems of linear equations. Students solve systems of linear equations using elimination and substitution methods.

 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 know that a system of linear equations, also known as simultaneous equations, is when two or more equations are involved in the same problem and work must be completed on...

 Authentic Reading Materials CCSSaligned instructional materials include authentic reading materials. Authentic reading materials include published works that are typically encountered by students in...

 This exemplar has been developed to guide middle school students and instructors with Common Core standards for Math. The rational numbers are an arithmetic system that includes 0 as well as...