School Administrative District #4

Unity of purpose

CORE CURRICULUM: SCOPE AND SEQUENCE

Department: Mathematics

CONTENT STANDARD: MATHEMATICAL REASONING

Students will understand and apply concepts of mathematical reasoning. Reasoning is fundamental to the knowing and doing of mathematics. To give more students access to mathematics as a powerful way of making sense of the world, it is essential that an emphasis on reasoning pervade all mathematics. Students need a great deal of time and many experiences to develop their ability to construct and evaluate valid arguments in problem settings and to evaluate the arguments of others.

Performance Indicators: The learner will·

Kindergarten

1.        Review and extend prior learning

2.        Use patterns and relationships to analyze mathematical situations

3.        Demonstrate an initial understanding that multiple paths to a conclusion may exist

Grade 1

1.        Review and extend prior learning

2.        Draw logical conclusions about mathematics by answering questions such as What do you think the answer is? Why do you think that is a good answer? Why isn't that a good answer?

Grade 2

1.        Review and extend prior learning

2.        Distinguish between "important" and "unimportant" mathematical information

3.        Follow logical arguments

á        Describe a simple argument's strengths and weaknesses

Grade 3

1.        Review and extend prior learning

2.        Follow logical arguments

á         Demonstrate an understanding that support for a claim should be based on evidence of various types (e.g., from logical processes, from measurement, or from observation and experimentation)

Grade 4

1.        Review and extend prior learning

2.        Follow logical arguments

á         Justify his/her answers and solution processes

Grade 5

1.        Review and extend prior learning

2.        Follow logical arguments

á         Use models, known facts, properties, and relationships to explain his/her thinking

Grade 6

1.        Review and extend prior learning

2.        Follow logical arguments

á         Demonstrate an initial understanding of deductive and inductive reasoning

á         Demonstrate and justify that multiple paths to a conclusion may exist

Grade 7

1.        Review and extend prior learning

2.        Recognize and apply deductive and inductive reasoning

3.        Understand and apply reasoning processes, with special attention to spatial reasoning and reasoning with proportions and graphs

4.        Follow logical arguments

á         Make and evaluate mathematical conjectures and arguments

Grade 8

1.        Review and extend prior learning

2.        Follow logical arguments

á         Validate his/her own thinking

á         Demonstrate an understanding of the pervasive use and power of reasoning as part of mathematics

Grade 9

1.        Review and extend prior learning

2.        Follow logical arguments

á         Formulate counterexamples

á         Derive properties and other mathematical models

Grade 10

1.        Review and extend prior learning

2.        Follow logical arguments

á         Judge the validity of arguments

3.        Construct simple valid arguments

4.        Construct proofs for mathematical assertions, including indirect proofs and proofs by mathematical induction

Grade 11

1.        Review and extend prior learning

2.        Follow logical arguments

á         Analyze situations where more than one logical conclusion can be drawn from data presented

Grade 12

1.        Review and extend prior learning