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 Georgia performance standards SIXTH GRADE ALGEBRA Students will investigate relationships between two quantities. They will write and solve proportions and simple one-step equations that result from problem situations. M6A1. Students will understand the concept of ratio and use it to represent quantitative relationships. M6A2. Students will consider relations between varying quantities. a. Analyze and describe patterns arising from function rules, tables, and graphs. b. Use manipulatives or draw pictures to solve problems involving proportional relationships. c. Use proportions (a/b=c/d) to describe relationships and solve problems, including percent problems. d. Describe proportional relationships mathematically using y = kx, where k is the constant of proportionality. e. Graph proportional relationships in the form y = kx and describe characteristics of the graphs. f. In a proportional relationship expressed as y = kx, solve for one quantity given values of the other two. Given quantities may be whole numbers, decimals, or fractions. Solve problems using the relationship y = kx. g. Use proportional reasoning (a/b=c/d and y = kx) to solve problems. M6A3. Students will evaluate algebraic expressions, including those with exponents, and solve simple one-step equations using each of the four basic operations. Process Standards Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards. See below for specific standards. SEVENTH GRADE ALGEBRA Students will demonstrate an understanding of linear relations and fundamental algebraic concepts. M7A1. Students will represent and evaluate quantities using algebraic expressions. a. Translate verbal phrases to algebraic expressions. b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate. c.Add and subtract linear expressions. M7A2. Students will understand and apply linear equations in one variable. a. Given a problem, define a variable, write an equation, solve the equation, and interpret the solution. b. Use the addition and multiplication properties of equality to solve one- and two step linear equations. M7A3. Students will understand relationships between two variables. a. Plot points on a coordinate plane. b. Represent, describe, and analyze relations from tables, graphs, and formulas. c. Describe how change in one variable affects the other variable. d. Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x). Process Standards The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need. See below for specific standards. EIGHTH GRADE ALGEBRA Students will use linear algebra to represent, analyze and solve problems. They will use equations, tables, and graphs to investigate linear relations and functions, paying particular attention to slope as a rate of change M8A1. Students will use algebra to represent, analyze, and solve problems. a. Represent a given situation using algebraic expressions or equations in one variable. b. Simplify and evaluate algebraic expressions. c. Solve algebraic equations in one variable, including equations involving absolute values. d. Interpret solutions in problem contexts. M8A2. Students will understand and graph inequalities in one variable. a. Represent a given situation using an inequality in one variable. b. Use the properties of inequality to solve inequalities. c. Graph the solution of an inequality on a number line. d. Interpret solutions in problem contexts. M8A3. Students will understand relations and linear functions. a. Recognize a relation as a correspondence between varying quantities. b. Recognize a function as a correspondence between inputs and outputs where the output for each input must be unique. c. Distinguish between relations that are functions and those that are not functions. d. Recognize functions in a variety of representations and a variety of contexts. e. Use tables to describe sequences recursively and with a formula in closed form. f. Understand and recognize arithmetic sequences as linear functions with whole number input values. g. Interpret the constant difference in an arithmetic sequence as the slope of the associated linear function. h. Identify relations and functions as linear or nonlinear. i. Translate among verbal, tabular, graphic, and algebraic representations of functions. M8A4. Students will graph and analyze graphs of linear equations. a. Interpret slope as a rate of change. b. Determine the meaning of the slope and y-intercept in a given situation. c. Graph equations of the form y = mx + b. d. Graph equations of the form ax + by = c. e. Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship. f. Solve problems involving linear relationships. M8A5. Students will understand systems of linear equations and use them to solve problems. a. Given a problem context, write an appropriate system of linear equations. b. Solve systems of equations graphically and algebraically, using technology as appropriate. c. Interpret solutions in problem contexts. Process Standards The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need. See below for specific standards. ALL GRADES Process Standards P1. Students will solve problems (using appropriate technology). a. Build new mathematical knowledge through problem solving. b. Solve problems that arise in mathematics and in other contexts. c. Apply and adapt a variety of appropriate strategies to solve problems. d. Monitor and reflect on the process of mathematical problem solving. P2. Students will reason and evaluate mathematical arguments. a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof. P3. Students will communicate mathematically. a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely. P4. Students will make connections among mathematical ideas and to other disciplines. a. Recognize and use connections among mathematical ideas. b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. c. Recognize and apply mathematics in contexts outside of mathematics. P5. Students will represent mathematics in multiple ways. a. Create and use representations to organize, record, and communicate mathematical ideas. b. Select, apply, and translate among mathematical representations to solve problems. c. Use representations to model and interpret physical, social, and mathematical phenomena.