Problem-Solving

Students will:

1. Use multiple approaches to investigate and understand mathematical content.

2. Formulate problems from everyday and mathematical situations.

3. Develop and apply strategies to solve a wide variety of problems, including multi-step and non-routine problems.

4. Verify and interpret results with respect to the original problem.

5. Generalize solutions and strategies to new problem situations.

6. Acquire confidence in using mathematics meaningfully.

7. Recognize and formulate problems from within and outside mathematics.

8. Apply the process of mathematical modeling to real-world problem situations.

 Connections

Students will:

1. Link conceptual and procedural knowledge.

2. Relate various representations of concepts or procedures to one another.

3. Recognize and value the relationships among the different topics in mathematics.

4. Use mathematics in other curriculum areas and in daily living.

5. Explore problems and describe results by using graphical, numerical, physical, algebraic, and verbal mathematical models or representations.

6. Apply mathematical thinking and modeling to solve problems that arise in other disciplines.

7. Recognize equivalent representations of the same concept.

8. Relate procedures in one representation to procedures in an equivalent representation.

Content

Number Sense, Estimation, & Computation:

1. Identify common decimal and fraction equivalents between 0-1.

2. Demonstrate an understanding of powers and scientific notation with and without calculator assistance.

3. Demonstrate an understanding of number properties, factors, absolute value, integer, and rational, using models.

4. Formulate strategies to use signed numbers.

5. Validate solutions using estimation.

6. Use fractions, decimal, and percents in estimates.

7. Use estimation to select the best solution.

Geometry and Measurement:

1. Develop ideas of geometric figures and concepts through paper-folding, models, etc.

2. Select appropriate measure and compute length, volume, time, weight, etc.

3. Demonstrate an understanding of the properties of a geometric formulas.

Patterns, Relations, & Functions:

1. Demonstrate an understanding of: graph/table relationships, ordered pairs, direct variation, algebraic expressions, and absolute value, using models.

2. Develop an understanding of ordered pairs using a calculator.

3. Solve linear equations containing one variable.

4. Compare/contrast situations using ratios, proportions, percents in algebraic expressions.

Statistics & Probability:

1. Compile data into tables, charts, and graphs.

2. Calculate probabilities of various types of events.

3. Use Venn diagrams to illustrate situations.

Communications

Students will:

1. Relate physical materials, pictures, and diagrams to mathematical ideas.

2. Reflect on and clarify thinking about mathematical ideas and situations.

3. Relate everyday language to mathematical language and symbols.

4. Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas.

5. Model situations by using oral, written, concrete, pictorial, graphical, and algebraic methods.

6. Develop mathematical ideas, formulate mathematical definitions, and express generalizations discovered through investigations.

7. Ask clarifying and extending questions related to mathematics which students have read or heard about.

8. Appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas.

 Reasoning

Students will: 1. Draw logical conclusions about mathematics.

2. Use models, known facts, properties, and relationships to explain mathematical thinking.

3. Justify solutions and explain solutions' processes.

4. Use patterns and relationships to analyze mathematical situations.

5. Believe that mathematics makes sense.

6. Recognize and apply deductive and inductive reasoning.

7. Make and evaluate mathematical conjectures and arguments.

8. Make and test conjectures.

9. Follow logical arguments.

10. Judge the validity of arguments.