NCTM Standards
Pennsylvania Standards
Academic Standards
- NCTM Standards Addressed in the Lab Activity:
- Algebra Standard for Grades 9-12
Represent and analyze mathematical situations and structures using algebraic symbols
- understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;
- use symbolic algebra to represent and explain mathematical relationships;
- Geometry Standard for Grades 9-12
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
- establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others;
- Reasoning and Proof Standard for Grades 9-12
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- recognize reasoning and proof as fundamental aspects of mathematics;
- make and investigate mathematical conjectures;
- develop and evaluate mathematical arguments and proofs;
- select and use various types of reasoning and methods of proof
- Communication Standard for Grades 9-12
- organize and consolidate their mathematical thinking through communication;
- communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
- analyze and evaluate the mathematical thinking and strategies of others;
- use the language of mathematics to express mathematical ideas precisely
- Trigonometry Grades 9-12
- apply trigonometry to problem situations involving triangles;
- explore periodic real-world phenomena using the sine and cosine functions; and so that, in addition, college-intending students can—
- understand the connection between trigonometric and circular functions;
- use circular functions to model periodic real-world phenomena;
- apply general graphing techniques to trigonometric functions;
- solve trigonometric equations and verify trigonometric identities;
- understand the connections between trigonometric functions and polar coordinates, complex numbers, and series
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- Pennsylvania Standards Addressed in the Lab Activity:
- 2.1 Numbers, Number Systems and Number Relationships
> Use operations (e.g., opposite, reciprocal absolute value, raising to a power, finding roots, finding logarithms).
- 2.3 Measurement and Estimation
> Measure and compare angles in degrees and radians.
- 2.4 Mathematical Reasoning and Connections
> Use direct proofs, indirect proofs or proof by contradiction to validate conjectures
> Construct valid arguments from stated facts.
- 2.5 Mathematical Problem Solving and Communication
> Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results.
> Present mathematical procedures and results clearly, systematically, succinctly and correctly.
- 2.10 Trigonometry
> Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem.
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- Academic Standards for Reading, Writing, Speaking and Listening Addressed in the Lab Activity:
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- 1.1 Learning to Read Independently
- Locate various texts, media and traditional resources for assigned and independent projects before reading
- Understand the meaning of and apply key vocabulary across the various subject areas
- 1.4 Types of Writing
- Write complex informational pieces (e.g., research papers, analyses, evaluations, essays)
- Use precise language and specific detail
- Use primary and secondary sources
- 1.6 Speaking and Listening
Listen to others
- Ask clarifying questions
- Synthesize information, ideas and opinions to determine relevancy
- Take notes
- Speak using skills appropriate to formal speech situations
- Use a variety of sentence structures to add interest to a presentation
- Pace the presentation according to audience and purpose
- Adjust stress, volume and inflection to provide emphasis to ideas or to influence the audience
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- Contribute to discussions
- Ask relevant, clarifying questions
- Respond with relevant information or opinions to questions asked
- Listen to and acknowledge the contributions of others
- Adjust tone and involvement to encourage equitable participation
- Facilitate total group participation
- Introduce relevant, facilitating information, ideas and opinions to enrich the discussion
- Paraphrase and summarize as needed
- Participate in small and large group discussions and presentations
- Organize and participate in informal debate around a specific topic
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