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. Understand operations/properties of functions.

2. Develop, use vectors/polar/parametric equations in problem situations.

3. Develop, solve, use: matrices with algebraic situations/relationships between functions.

4. Understand, apply to areas the foundations of: limit, rate of change, area under a curve.

5. Defend reasonableness of solutions from real-world scenarios.

Geometry & Measurement:

1. Develop, analyze graphs/linear and nonlinear relationships/expressions.

2. Apply properties of figures and graphs using coordinates/transformations, polynomial, rational, radical, and transcendental functions.

3. Determine, interpret, extend conic sections, maximum/minimum points using computers/real-world scenarios.

Patterns, Relations, & Functions:

1. Represent, develop, model real situations using linear and nonlinear functions, matrices.

2. Develop, use geometric/arithmetic sequences and series; circular, sine, and cosine functions through real-world situations.

3. Solve, verify trigonometric identities/equations graphically & analytically.

4. Develop connections, investigate: trigonometric, logarithmic, exponential funtions, polar coordinates, complex numbers and limits.

Statistics and Probability:

1. Use curve fitting, interpret data to: identify patterns, trends, make predictions, etc.

2. Apply analyze central tendencey and variability.

3. Design a statistical experiment.

4. Describe normal curve; interpret descrete probability distributions.

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, pictoral, 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.