Academic Standard

Mathematical Processes
Initiative: 
Tennessee Diploma Project
Set: 
Mathematics
Type: 
Standard
Code: 
1
Grade range: 
9 to 12
Conceptual StrandThe Mathematical Process Standards are embedded in the content standards to reap the learning benefits gained from attention to them. These standards exemplify best teaching practices in mathematical instruction and mirror the NCTM Process Standards as well as the Common Core Mathematical Practices.Guiding QuestionWhat is the role of the mathematical processes standards in formative instruction?
 
Elements within this Standard
 
Course Level Expectation
Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.
Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the
Develop inductive and deductive reasoning to independently make and evaluate mathematical arguments and construct appropriate proofs; include various types of
Move flexibly between multiple representations (contextual, physical written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to
Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms,
Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between
Use technologies appropriately to develop understanding of abstract mathematical ideas, to facilitate problem solving, and to produce accurate and reliable models.
Check For Understanding
Check solutions after making reasonable estimates in appropriate units of quantities encountered in contextual situations.
Determine position using spatial sense with two and three-dimensional coordinate systems.
Comprehend the concept of length on the number line.
Recognize that a definition depends on undefined terms and on previous definitions.
Use technology, hands-on activities, and manipulatives to develop the language and the concepts of geometry, including specialized vocabulary (e.g. graphing
Use inductive reasoning to write conjectures and/or conditional statements.
Recognize the capabilities and the limitations of calculators and computers in solving problems.
Understand how the similarity of right triangles allows the trigonometric functions sine, cosine, and tangent to be defined as ratio of sides.
Expand analysis of units of measure to include area and volume.
Use visualization, spatial reasoning, and geometric modeling to solve problems.
Identify and sketch solids formed by revolving two-dimensional figures around lines.
Connect the study of geometry to the historical development of geometry.
Use proofs to further develop and deepen the understanding of the study of geometry (e.g. two-column, paragraph, flow, indirect, coordinate).
Identify and explain the necessity of postulates, theorems, and corollaries in a mathematical system.
State Performance Indicator
Give precise mathematical descriptions or definitions of geometric shapes in the plane and space.
Determine areas of planar figures by decomposing them into simpler figures without a grid.
Use geometric understanding and spatial visualization of geometric solids to solve problems and/or create drawings.
Use definitions, basic postulates, and theorems about points, lines, angles, and planes to write/complete proofs and/or to solve problems.