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Common Core: Math
Subject: Math
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 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...

 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...

 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...

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

 Student Outcomes Students use factors of a number to simplify a square root.

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

 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 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 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 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 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...

 Student Outcomes Students know that two equations in the form of ax + by = c and a'x + b'y = c' graph as the same line when a'/a = b'/b = c'/c and at least one of a or b is nonzero. Students know...

 Student Outcomes Students know that any constant rate problem can be described by a linear equation in two variables where the slope of the graph is the constant rate. Students compare two different...

 Student Outcomes Students write the equation of a line given two points or the slope and a point on the line. Students know the traditional forms of the slope formula and slopeintercept equation.