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 multistep and nonroutine 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.

Reasoning and Proof

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 their own thinking;
5. appreciate the pervasive use and power of reasoning as a part of mathematics.

Communication

1. model situations using oral, written, concrete, pictorial, graphical, and algebraic methods;
2. reflect on and clarify their own thinking about mathematical ideas and situations;
3. discuss mathematical ideas and make conjectures and convincing arguments;

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 their 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.

Representations

Number and Operations

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. represent numerical relationships in one - and two - dimensional graphs.
3. compute with whole numbers, fractions, decimals, integers, and rational numbers;
4. develop, analyze, and explain procedures for computation and techniques for estimation;
5. select and use an appropriate method for computing from among mental arithmetic, paper - and - pencil, calculator and computer methods;
6. use computation, estimation, and proportions to solve problems
7. use estimation to check the reasonableness of results.

Algebra

1. describe and represent relationships with tables, graphs, and rules;
2. use patterns and functions to represent and solve problems.

Geometry

Measurement

Data Analysis and Probability

1. In grades 5 - 8, the mathematics curriculum should include exploration of statistics in real - world situations so that students can - systematically collect, organize, and describe data;
2. construct, read, and interpret tables, charts, and graphs;make inferences and convincing arguments that are based on data analysis;
3. evaluate arguments that are based on data analysis;
4. develop an appreciation for statistical methods as powerful means for decision making.

1. I can picture a known quantity and iterate it to estimate a larger unknown.
2. Using mathematics can help solve problems.
3. Using mathematics can be fun.