NCTM Standards
NCTM Standards 2000 Addressed Within the InterMath Patterns Unit:
Grades 68
GEOMETRY STANDARD
Instructional programs from prekindergarten through grade 12 should enable all students to
 Analyze characteristics and properties of two and threedimensional geometric shapes and develop mathematical arguments about geometric relationships.
In grades 68 all students should precisely describe, classify, and understand relationships among types of two and threedimensional objects using their defining properties.
 Apply transformations and use symmetry to analyze mathematical situations.
In grades 68 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 68 all students should draw geometric objects with specified properties such as side lengths or angle measures; use twodimensional representations of threedimensional 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 68 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 68 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 morecomplex 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.
