STANDARD 1. MATHEMATICS AS PROBLEM SOLVING

1. use problem-solving approaches to investigate and understand mathematical content
   
2. formulate problems from situations within and outside mathematics
   
3. develop and apply a variety of strategies to solve problems, with emphasis on multi-step and non-routine problems
   
4. verify and interpret results with respect to the original problem situation
   
5. generalize solutions and strategies to new problem situations
   
6. acquire confidence in using mathematics meaningfully
   

STANDARD 2. MATHEMATICS AS COMMUNICATION

1. model situations using oral, written, concrete, pictorial, graphical, and algebraic methods
   
2. reflect on and clarify learner's own thinking about mathematical ideas and situations
   
3. develop common understandings of mathematical ideas, including the role of definitions
   
4. use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas
   
5. discuss mathematical ideas and make conjectures and convincing arguments
   
6. appreciate the value of mathematical notation and its role in the development of mathematical ideas
   

STANDARD 3. MATHEMATICS AS REASONING

1. recognize and apply deductive and inductive reasoning
   
2. understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs
   
3. make and evaluate mathematical conjectures and arguments
   
4. validate learner's own thinking
   
5. appreciate the pervasive use and power of reasoning as a part of mathematics
   

STANDARD 4. MATHEMATICAL CONNECTIONS

1. see mathematics as an integrated whole
   
2. explore problems and describe results using graphical, numerical, physical, algebraic, and verbal mathematical models or representations
   
3. use a mathematical idea to further learner's understanding of other mathematical ideas
   
4. apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as art, music, psychology, science, and business
   
5. value the role of mathematics in our culture and society
   

STANDARD 5. NUMBER AND NUMBER RELATIONSHIPS

1. understand, represent, and use numbers in a variety of equivalent forms (integer, fraction, decimal, percent, exponential, and scientific notation) in real-world and mathematical problem situations
   
2. develop number sense for whole numbers, fractions, decimals, integers, and rational numbers
   
3. understand and apply ratios, proportions, and percents in a wide variety of situations
   
4. investigate relationships among fractions, decimals, and percents
   
5. represent numerical relationships in one- and two-dimensional graphs
   
   

STANDARD 6. NUMBER SYSTEMS AND NUMBER THEORY

1. understand and appreciate the need for numbers beyond the whole numbers
   
2. develop and use order relations for whole numbers, fractions, decimals, integers, and rational numbers
   
3. extend learner's understanding of whole number operations to fractions, decimals, integers, and rational numbers
   
4. understand how the basic arithmetic operations are related to one another
   
5. develop and apply number theory concepts (e.g., primes, factors, and multiples) in real-world and mathematical problem situations
   

STANDARD 7. COMPUTATION AND ESTIMATION

1. compute with whole numbers, fractions, decimals, integers, and rational numbers
   
2. develop, analyze, and explain procedures for computation and techniques for estimation
   
3. develop, analyze, and explain methods for solving proportions
   
4. select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods
   
5. use computation, estimation, and proportions to solve problems
   
6. use estimation to check the reasonableness of results
   

STANDARD 8. PATTERNS AND FUNCTIONS

1. describe, extend, analyze, and create a wide variety of patterns
   
2. describe and represent relationships with tables, graphs, and rules
   
3. analyze functional relationships to explain how a change in one quantity results in a change in another
   
4. use patterns and functions to represent and solve problems
   

STANDARD 9. ALGEBRA

1. understand the concepts of variable, expression, and equation
   
2. represent situations and number patterns with tables, graphs, verbal rules, and equations and explore the interrelationships of these representations
   
3. analyze tables and graphs to identify properties and relationships
   
4. develop confidence in solving linear equations using concrete, informal, and formal methods
   
5. investigate inequalities and nonlinear equations informally; apply algebraic methods to solve a variety of real-world and mathematical problems
   

STANDARD 10. STATISTICS

1. systematically collect, organize, and describe data
   
2. construct, read, and interpret tables, charts, and graphs
   
3. make inferences and convincing arguments that are based on data analysis
   
4. evaluate arguments that are based on data analysis
   
5. develop an appreciation for statistical methods as powerful means for decision making
   

STANDARD 11. PROBABILITY

1. model situations by devising and carrying out experiments or simulations to determine probabilities
   
2. model situations by constructing a sample space to determine probabilities
   
3. appreciate the power of using a probability model by comparing experimental results with mathematical expectations
   
4. make predictions that are based on experimental or theoretical probabilities
   
5. develop an appreciation for the pervasive use of probability in the real world
   

STANDARD 12. GEOMETRY

1. identify, describe, compare, and classify geometric figures
   
2. visualize and represent geometric figures with special attention to developing spatial sense
   
3. explore transformations of geometric figures
   
4. represent and solve problems using geometric models
   
5. understand and apply geometric properties and relationships
   
6. develop an appreciation of geometry as a means of describing the physical world
   

STANDARD 13. MEASUREMENT

1. extend learner's understanding of the process of measurement
   
2. estimate, make, and use measurements to describe and compare phenomena
   
3. select appropriate units and tools to measure to the degree of accuracy required in a particular situation
   
4. understand the structure and use of systems of measurement
   
5. extend learner's understanding of the concepts of perimeter, area, volume, angle measure, capacity, and weight and mass
   
6. develop the concepts of rates and other derived and indirect measurements
   
7. develop formulas and procedures for determining measures to solve problems