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

 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...

 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...

 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 use factors of a number to simplify a square root.

 Student Outcomes Students find the positive solutions for equations of the form x2 = p and x3 = p.

 Student Outcomes Students know that for most integers n, n is not a perfect square, and they understand the square root symbol. Students find the square root of small perfect squares. Students...

 Student Outcomes Students know that the positive square root and cube root exists for all positive numbers and is unique. Students solve simple equations that require them to find the square or cube...

 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 learn a realworld application of linear equations with respect to the conversion of temperatures from Celsius to Fahrenheit and Fahrenheit to Celsius.

 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 any nonvertical line is the graph of a linear equation in the form of y = mx + b, where b is a constant. Students write the equation that represents the graph of...