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. Compare algebra of real, rational, and complex numbers with characteristics of matrix algebra system.

2. Expand, extend vectors/linear algebra to higher dimensional situations.

3. Extend relationships between vectors and complex numbers.

4. Use, extend polar/parametric equations to represent problem situations.

5. Develop, generate arguments about limit situations.

Geometry and Measurement:

1. Analyze and formulate interpretations: 3-D objects.

2. Deduce properties, apply transformations, coordinates, and vectors in problem-sloving using technology.

Patterns, Relations, & Functions:

1. Model real world phenomena with a variety of functions.

2. Graph, analyze effects/changes using polar coordiantes, parametrics.

3. Develop, extend 3-D graphics.

4. Understand, analyze the connection between trigonometric and circular functions/complex numbers/series.

5. Extend recursive functions using computers in real-world situations.

6. Demonstrate the relationship between functions (all types) and their inverses.

Statistics & Probability:

1. Apply, transform data to make predictions/interpret situations.

2. Create, interpret, understand discrete probability distributions/random sampling.

3. Extend normal curve and its properties.

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.