Georgia State Standards for Mathematics: Grade 7

GA.M7N. Numbers 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 rational numbers and use them in computation.

M7N1.a. Find the absolute value of a number and understand it as the distance from zero on a number line.

M7N1.b. Compare and order rational numbers, including repeating decimals.

M7N1.c. Add, subtract, multiply, and divide positive and negative rational numbers.

M7N1.d. Solve problems using rational numbers.

GA.M7G. Geometry: Students will further develop and apply their understanding of plane and solid geometric figures through the use of constructions and transformations. Students will explore the properties of similarity and further develop their understanding of 3-dimensional figures.

M7G1. Students will construct plane figures that meet given conditions.

M7G1.a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

M7G1.b. Recognize that many constructions are based on the creation of congruent triangles.

M7G2. Students will demonstrate understanding of transformations.

M7G2.a. Demonstrate understanding of translations, dilations, rotations, reflections, and relate symmetry to appropriate transformations.

M7G2.b. Given a figure in the coordinate plane, determine the coordinates resulting from a translation, dilation, rotation, or reflection.

M7G3. Students will use the properties of similarity and apply these concepts to geometric figures.

M7G3.a. Understand the meaning of similarity, visually compare geometric figures for similarity, and describe similarities by listing corresponding parts.

M7G3.b. Understand the relationships among scale factors, length ratios, and area ratios between similar figures. Use scale factors, length ratios, and area ratios to determine side lengths and areas of similar geometric figures.

M7G3.c. Understand congruence of geometric figures as a special case of similarity: The figures have the same size and shape.

M7G4. Students will further develop their understanding of three-dimensional figures.

M7G4.a. Describe three-dimensional figures formed by translations and rotations of plane figures through space.

M7G4.b. Sketch, model, and describe cross-sections of cones, cylinders, pyramids, and prisms.

GA.M7A. Algebra: Students will demonstrate an understanding of linear relations and fundamental algebraic concepts.

M7A1. Students will represent and evaluate quantities using algebraic expressions.

M7A1.a. Translate verbal phrases to algebraic expressions.

M7A1.b. Simplify and evaluate algebraic expressions, using commutative, associative, and distributive properties as appropriate.

M7A1.c. Add and subtract linear expressions.

M7A2. Students will understand and apply linear equations in one variable.

M7A2.a. Given a problem, define a variable, write an equation, solve the equation, and interpret the solution.

M7A2.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.

M7A3.a. Plot points on a coordinate plane.

M7A3.b. Represent, describe, and analyze relations from tables, graphs, and formulas.

M7A3.c. Describe how change in one variable affects the other variable.

M7A3.d. Describe patterns in the graphs of proportional relationships, both direct (y = kx) and inverse (y = k/x).

GA.M7D. Data Analysis and Probability: Students will demonstrate understanding of data analysis by posing questions, collecting data, analyzing the data using measures of central tendency and variation, and using the data to answer the questions posed. Students will understand the role of probability in sampling.

M7D1. Students will pose questions, collect data, represent and analyze the data, and interpret results.

M7D1.a. Formulate questions and collect data from a census of at least 30 objects and from samples of varying sizes.

M7D1.b. Construct frequency distributions.

M7D1.c. Analyze data using measures of central tendency (mean, median, and mode), including recognition of outliers.

M7D1.d. Analyze data with respect to measures of variation (range, quartiles, interquartile range).

M7D1.e. Compare measures of central tendency and variation from samples to those from a census. Observe that sample statistics are more likely to approximate the population parameters as sample size increases.

M7D1.f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line graphs, circle graphs, and line plots introduced earlier, and using box-and-whisker plots and scatter plots.

M7D1.g. Analyze and draw conclusions about data, including a description of the relationship between two variables.

GA.M7P. 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.

M7P1. Students will solve problems (using appropriate technology).

M7P1.a. Build new mathematical knowledge through problem solving.

M7P1.b. Solve problems that arise in mathematics and in other contexts.

M7P1.c. Apply and adapt a variety of appropriate strategies to solve problems.

M7P1.d. Monitor and reflect on the process of mathematical problem solving.

M7P2. Students will reason and evaluate mathematical arguments.

M7P2.a. Recognize reasoning and proof as fundamental aspects of mathematics.

M7P2.b. Make and investigate mathematical conjectures.

M7P2.c. Develop and evaluate mathematical arguments and proofs.

M7P2.d. Select and use various types of reasoning and methods of proof.

M7P3. Students will communicate mathematically.

M7P3.a. Organize and consolidate their mathematical thinking through communication.

M7P3.b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

M7P3.c. Analyze and evaluate the mathematical thinking and strategies of others.

M7P3.d. Use the language of mathematics to express mathematical ideas precisely.

M7P4. Students will make connections among mathematical ideas and to other disciplines.

M7P4.a. Recognize and use connections among mathematical ideas.

M7P4.b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

M7P4.c. Recognize and apply mathematics in contexts outside of mathematics.

M7P5. Students will represent mathematics in multiple ways.

M7P5.a. Create and use representations to organize, record, and communicate mathematical ideas.

M7P5.b. Select, apply, and translate among mathematical representations to solve problems.

M7P5.c. Use representations to model and interpret physical, social, and mathematical phenomena.

GA.M7RC. Reading Across the Curriculum: Reading across curriculum content develops both academic and personal interests in students. As students read, they develop both content and contextual vocabulary. They also build good habits for reading, researching, and learning. The Reading Across the Curriculum standard focuses on the academic and personal skills students acquire as they read in all areas of learning.

M7RC1. Students will enhance reading in all curriculum areas by:

M7RC1.a. Reading in All Curriculum Areas: Read a minimum of 25 grade-level appropriate books per year from a variety of subject disciplines and participate in discussions related to curricular learning in all areas; Read both informational and fictional texts in a variety of genres and modes of discourse; Read technical texts related to various subject areas.

M7RC1.b. Discussing books: Discuss messages and themes from books in all subject areas; Respond to a variety of texts in multiple modes of discourse; Relate messages and themes from one subject area to messages and themes in another area; Evaluate the merit of texts in every subject discipline; Examine author's purpose in writing; Recognize the features of disciplinary texts.

M7RC1.c. Building vocabulary knowledge: Demonstrate an understanding of contextual vocabulary in various subjects; Use content vocabulary in writing and speaking; Explore understanding of new words found in subject area texts.

M7RC1.d. Establishing context: Explore life experiences related to subject area content; Discuss in both writing and speaking how certain words are subject area related; Determine strategies for finding content and contextual meaning for unknown words.