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MATHEMATICAL ANALYSIS

STANDARD 1: Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Key Idea 1: Abstraction and symbolic representation are used to communicate mathematically.

M1.1a identify independent and dependent variables

M1.1c apply mathematical equations to describe relationships among variables in the natural worldKey Idea 2: Deductive and inductive reasoning are used to reach mathematical conclusions.

M2.1 Use inductive reasoning to construct, evaluate, and validate conjectures and arguments, recognizing that patterns and relationships can assist in explaining and extending mathematical phenomena.

M2.1a interpolate and extrapolate from data

M2.1b quantify patterns and trends

Key Idea 3: Critical thinking skills are used in the solution of mathematical problems.

M3.1 Apply mathematical knowledge to solve real-world problems and problems that arise from the investigation of mathematical ideas, using representations such as pictures, charts, and tables.

M3.1a use appropriate scientific tools to solve problems about the natural world

STANDARD 1 Analysis, Inquiry, and Design

SCIENTIFIC INQUIRY

Key Idea 1: The central purpose of scientific inquiry is to develop explanations of natural phenomenain a continuing, creative process.

S1.1 Formulate questions independently with the aid of references appropriate for guiding the search for explanations of everyday observations.

S1.1a formulate questions about natural phenomena

S1.1b identify appropriate references to investigate a question

S1.1c refine and clarify questions so that they are subject to scientific investigation

S1.2 Construct explanations independently for natural phenomena, especially by proposing preliminary visual models of phenomena.

Key Idea 2: Beyond the use of reasoning and consensus, scientific inquiry involves the testing of proposedexplanations involving the use of conventional techniques and procedures and usually requiring considerable ingenuity.

S2.1 Use conventional techniques and those of their own design to make further observations and refine their explanations, guided by a need for more information.

S2.1a demonstrate appropriate safety techniques

S2.1b conduct an experiment designed by others

S2.1c design and conduct an experiment to test a hypothesis

S2.1d use appropriate tools and conventional techniques to solve problems about the natural world, including: • measuring • observing • describing • classifying • sequencing

Process Skills Based on Standard 4

General Skills

1. Follow safety procedures in the classroom and laboratory
2. Safely and accurately use the following measurement tools: Metric ruler; stopwatch
3. Use appropriate units for measured or calculated values
4. Recognize and analyze patterns and trends
5. Identify cause-and-effect relationships
6. Use indicators and interpret results