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 NCTM Standards NCTM Standards 2000 Addressed Within the InterMath Patterns Unit: Grades 6-8 GEOMETRY STANDARD Instructional programs from pre-kindergarten through grade 12 should enable all students to-- Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. In grades 6-8 all students should precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. Apply transformations and use symmetry to analyze mathematical situations. In grades 6-8 all students should describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling. Use visualization, spatial reasoning, and geometric modeling to solve problems. In grades 6-8 all students should draw geometric objects with specified properties such as side lengths or angle measures; use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume; and recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. MEASUREMENT STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- Understand measurable attributes of objects and the units, systems, and processes of measurement. In grades 6-8 all students should understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. Apply appropriate techniques, tools, and formulas to determine measurements. In grades 6-8 all students should select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision; develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes; and solve simple problems involving scale factors, using ratio and proportion. PROBLEM SOLVING STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- build new mathematical knowledge through problem solving; solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. REASONING AND PROOF STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures; develop and evaluate mathematical arguments and proofs; select and use various types of reasoning and methods of proof. COMMUNICATION STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely. CONNECTIONS STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics. REPRESENTATION STANDARD Instructional programs from prekindergarten through grade 12 should enable all students to-- create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena.