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. Demonstrate an understanding of reason for the impossible division by zero.

2. Develop and understanding of integers and their properties.

3. Demonstrate an understanding of special numbers (palindromes, triangular, etc.).

4. Develop an understanding of the coordinate plane.

5. Extend understanding of integers to real numbers.

6. Evaluate choices through estimation.

7. Estimate to validate solutions using fractions, decimals, percents, squares, etc.

8. Solve problems using percentages and proportions.

Geometry and Measurement:

1. Develop, extend concepts of area, volume, through hands-on activities.

2. Identify, label parts of right triangle, polygons.

3. Develop transformational and coordinate geometry; models of the Pythagorean Theorum.

4. Develop, extend understanding of real-world measurements and measurement devices.

Patterns, Relations, and Functions:

1. Demonstrate an understanding of patterns through models (areas., number, etc.).

2. Develop an understanding of table, graphs, and equations to solve problem situations involving growth and decay, interest.

3. Use standard and invented symbols to explain function relationships.

Statistics and Probability:

1. Further interpret, extend information in graphs.

2. Predict, and develop: models, central tendencies, statistical conclusions, misuses of data.

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.