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Common Core: 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...

 The problemsolving material in Topic D provides students with further applications of percent and exposure to problems involving population, mixtures, and counting, in preparation for later topics...

 In Topic B, students create algebraic representations and apply their understanding of percent from Topic A to interpret and solve multistep word problems related to markups or markdowns, simple...

 In Topic B, students use linear equations and inequalities to solve problems. They continue to use bar diagrams from earlier grades where they see fit but will quickly discover that some problems...

 To begin this module, students will generate equivalent expressions using the fact that addition and multiplication can be done in any order with any grouping and will extend this understanding to...

 In Topic C, students problemsolve with rational numbers and draw upon their work from Grade 6 with expressions and equations (6.EE.A.2, 6.EE.A.3, 6.EE.A.4, 6.EE.B.5, 6.EE.B.6, 6.EE.B.7). They...

 In Topic C, students extend their reasoning about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers, such as a speed of ½ mile per ¼ hour...

 In Topic B, students learn that the unit rate of a collection of equivalent ratios is called the constant of proportionality and can be used to represent proportional relationships with equations of...

 In Topic H, students use their prior knowledge from Module 1 to contruct tables of independent and dependent values in order to analyze equations with two variables from reallife contexts. They...

 In Topic G, students are introduced to the fact that equations have a structure similar to some grammatical sentences. Some sentences are true: “George Washington was the first president of the...

 Students write and evaluate expressions and formulas in Topic F. They use variables to write expressions and evaluate those expressions when given the value of the variable (6.EE.A.2). From there,...

 In Topic E, students express operations in algebraic form. They read and write expressions in which letters stand for and represent numbers (6.EE.A.2). They also learn to use the correct...

 In Topic D, students become comfortable with new notations of multiplication and division and recognize their equivalence to the familiar notations of the prior grades. The expression 2 × b is...

 Students represent letters with numbers and numbers with letters in Topic C. In past grades, students discovered properties of operations through example (1.OA.B.3, 3.OA.B.5). Now, they use letters...

 In Topic B, students experience special notations of operations. They determine that 3x = x + x + x is not the same as x3, which is x times x times x. Applying their prior knowledge from Grade 5,...

 To begin this module, students are introduced to important identities that will be useful in solving equations and developing proficiency with solving problems algebraically. In Topic A, students...