Mathematical Reasoning

1.1 Analyze problems by identifying relationships, distinguishing relevant from irreverent information, sequencing and prioritizing information, and observing patterns.

1.2 Determine when and how to break a problem into simpler parts.

2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and apply them in other circumstances.

6.0 PROBLEM SOLVING

6.1 Make Decisions About How to Approach
- id relationships, distinguish relevant from irrelevant info; sequence and prioritize info; observe patterns
- determine when and how to break problem into simpler parts
- solve multi-step problems

6.2 Apply a Variety of Strategies, Skills, & Concepts to Solve
- organize info ~ eliminate possibilities; guess and check; develop a matrix; create models or lists; number sentences; key words
- choose focus ~ solve related; break into smaller parts; act out; use manipulatives; work backwards; guess & check
- use estimation to verify reasonableness of answer
- use calculator & determine if effective & efficient
- use technology

7.0 REASONING, COMMUNICATION & CONNECTIONS

7.1 Use Reasoning to Develop, Analyze, Justify & Validate Thinking
- indicate the advantages of exact & approximate solutions
- give answers to a specified degree of accuracy
- make precise calculations and interpret the validity of the results
- locate a flaw in a mathematical argument

7.2 Express Math Thinking Orally, Graphically, & in Writing
- restate or summarize problem
- use variety of methods (words, numbers, charts…) to explain reasoning
- communicate reasonable solutions clearly & logically; support solution w/ evidence in both verbal & symbolically

7.3 Understand Multiple Representations of Same Concept
-recognize relationship between concrete and symbols
- translate written problems into symbols
- translate data from one representation to another
- understand relationship between operations

7.4 Move Beyond a Problem by Generalizing to Other Situations
-develop generalizations of results & extend to other circumstances
- note method of deriving solution & solve similar problems
- understand & use math in new situations and curricular areas