Standards

= __Georgia Performance Standards__ =

__**GEOMETRY**__
Students will understand and build plane and solid geometric figures. They will also graph points on the coordinate plane.

**M4G1. Students will define and identify the characteristics of geometric figures through examination and construction.** b. Describe parallel and perpendicular lines in plane geometric figures. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties. d. Compare and contrast the relationships among quadrilaterals.

 **M4G2. Students will understand fundamental solid figures.** b. Describe parallel and perpendicular lines and planes in connection with the rectangular prism.

__**PROCESS STANDARDS**__
Each topic studied in this course should be developed with careful thought toward helping every student achieve the following process standards.

**M4P1. 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.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">**M4P2. Students will reason and evaluate mathematical arguments.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">a. Recognize reasoning and proof as fundamental aspects of mathematics. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">b. Make and investigate mathematical conjectures. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">c. Develop and evaluate mathematical arguments and proofs. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">d. Select and use various types of reasoning and methods of proof.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">**M4P3. Students will communicate mathematically.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">a. Organize and consolidate their mathematical thinking through communication. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">c. Analyze and evaluate the mathematical thinking and strategies of others. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">d. Use the language of mathematics to express mathematical ideas precisely.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">**M4P4. Students will make connections among mathematical ideas and to other disciplines.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">a. Recognize and use connections among mathematical ideas. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">c. Recognize and apply mathematics in contexts outside of mathematics.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">**M4P5. Students will represent mathematics in multiple ways.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">a. Create and use representations to organize, record, and communicate mathematical ideas. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">b. Select, apply, and translate among mathematical representations to solve problems. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">c. Use representations to model and interpret physical, social, and mathematical phenomena.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">__**More GPS Content Standards in Middle Grades that can be applied to the topic of Parallel and Perpendicular lines**__
<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;"> **M7G1. Students will construct plane figures that meet given conditions.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">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.

<span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">**M8G1. Students will understand and apply the properties of parallel and perpendicular lines and understand the meaning of congruence.** <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">a. Investigate characteristics of parallel and perpendicular lines both algebraically and geometrically. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">b. Apply properties of angle pairs formed by parallel lines cut by a transversal. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">c. Understand the properties of the ratio of segments of parallel lines cut by one or more transversals. <span style="font-family: 'Comic Sans MS',cursive; font-size: 120%;">d. Understand the meaning of congruence: that all corresponding angles are congruent and all corresponding sides are congruent.