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 Georgia Peformance Standards SIXTH GRADE Number and Operations Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will apply these concepts and associated skills in real world situations. M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and percents using these concepts to solve problems. a. Use factors and multiples. b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic) c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers. d. Multiply and divide fractions and mixed numbers. e. Use fractions, decimals, and percents interchangeably. f. Solve problems involving fractions, decimals, and percents and justify the process. g. Evaluate expressions using order of operations including exponents. 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 Number and Operations Students will further develop their understanding of the concept of rational numbers and apply them to real world situations. M7N1. Students will understand the meaning of positive and negative numbers including rational numbers and will compute with them. a. Find the absolute value of a number and understand it as the distance from the origin on a number line. b. Compare and order rational numbers including repeating decimals. c. Add, subtract, multiply and divide positive and negative rational numbers. d. Solve problems using rational numbers. 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 Number and Operations Students will understand the numeric and geometric meaning of square root, apply properties of integer exponents and use scientific notation. M8N1. Students will understand different representations of numbers including square roots, exponents, and scientific notation. a. Find square roots of perfect squares. b. Recognize the (positive) square root of a number as a length of a side of a square with a given area. c. Recognize square roots as points and as lengths on a number line. d. Understand that the square root of 0 is 0 and that every positive number has two square roots that are opposite in sign. e. Recognize and use the radical symbol to denote the positive square root of a positive number. f. Estimate square roots of positive numbers. g. Simplify, add, subtract, multiply, and divide expressions containing square roots. h. Distinguish between rational and irrational numbers. i. Simplify expressions containing integer exponents. j. Express and use numbers in scientific notation. k. Use appropriate technologies to solve problems involving square roots, exponents, and scientific notation. 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.