Academic standards list

Geometry — Mathematics

Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

Mathematical Processes

 
Standard 1 — Mathematical Processes
 
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?
 
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.
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.
 

Number and Operations

 
Standard 2 — Number and Operations
 
Conceptual StrandThe Number and Operations Standard describes deep and fundamental understanding of, and proficiency with, counting, numbers, and arithmetic, as well as an understanding of number systems and their structures.Guiding QuestionHow do students develop number sense that allows them to naturally decompose numbers, use particular numbers as referents, solve problems using the relationships among operations and knowledge about the base-ten system, estimate a reasonable result for a problem, and have a disposition to make sense of numbers, problems, and results?
 
Course Level Expectation
Establish the relationships between the real numbers and geometry; explore the importance of irrational numbers to geometry.
Explore vectors as a numeric system, focusing on graphic representations and the properties of the operation.
Establish an ability to estimate, select appropriate units, evaluate accuracy of calculations and approximate error in measurement in geometric settings.
 
State Performance Indicator
Analyze, apply, or interpret the relationships between basic number concepts and geometry (e.g. rounding and pattern identification in measurement, the
 
Perform operations on vectors in various representations.
 

Algebra

 
Standard 3 — Algebra
 
Conceptual StrandThe Algebra Standard emphasizes relationships among quantities, including functions, patterns, ways of representing mathematical relationships, and the analysis of change.Guiding QuestionHow does algebra encompass the relationships among quantities, the use of symbols, the modeling of phenomena, and the mathematical study of change?
 
Course Level Expectation
Use analytic geometry tools to explore geometric problems involving parallel and perpendicular lines, circles, and special points of polygons.
Explore the effect of transformations on geometric figures and shapes in the coordinate plane.
 
State Performance Indicator
Use algebra and coordinate geometry to analyze and solve problems about geometric figures (including circles).
 
Use coordinate geometry to prove characteristics of polygonal figures.
 
Describe algebraically the effect of a single transformation (reflections in the x- or y-axis, rotations, translations, and dilations) on two-dimensional
 

Geometry and Measurement

 
Standard 4 — Geometry and Measurement
 
Conceptual StrandGeometry studies geometric shapes and structures and their characteristics and relationships. Understanding what a measurable attribute is and becoming familiar with the units and processes that are used in measuring attributes are the major emphasis of this standard.Guiding QuestionHow can students make and explore conjectures about geometry and reason carefully about geometric ideas while expanding their understanding of precision in measurement?
 
Course Level Expectation
Develop the structures of geometry, such as lines, angles, planes, and planar figures, and explore their properties and relationships.
Describe the properties of regular polygons, including comparative classification of them and special points and segments.
Develop an understanding of the tools of logic and proof, including aspects of formal logic as well as construction of proofs.
Develop geometric intuition and visualization through performing geometric constructions with straightedge/compass and with technology.
Extend the study of planar figures to three-dimensions, including the classical solid figures, and develop analysis through cross-sections.
Generate formulas for perimeter, area, and volume, including their use, dimensional analysis, and applications.
Apply the major concepts of transformation geometry to analyzing geometric objects and symmetry.
Establish processes for determining congruence and similarity of figures, especially as related to scale factor, contextual applications, and transformations.
Develop the role of circles in geometry, including angle measurement, properties as a geometric figure, and aspects relating to the coordinate plane.
Develop the tools of right triangle trigonometry in the contextual applications, including the Pythagorean Theorem, Law of Sines and Law of Cosines.
State Performance Indicator
Differentiate between Euclidean and non-Euclidean geometries.
 
Define, identify, describe, and/or model plane figures using appropriate mathematical symbols (including collinear and non-collinear points, lines, segments,
 
Identify, describe and/or apply the relationships and theorems involving different types of triangles, quadrilaterals and other polygons.
 
Analyze different types and formats of proofs.
 
Describe solids and/or surfaces in three-dimensional space when given two-dimensional representations for the surfaces of three-dimensional objects.
 
Use various area of triangle formulas to solve contextual problems (e.g., Herons formula, the area formula for an equilateral triangle, and A = ab sin C).
 
Compute the area and/or perimeter of triangles, quadrilaterals and other polygons when one or more additional steps are required (e.g. find missing dimensions
 
Solve problems involving area, circumference, area of a sector, and/or arclength of a circle.
 
Use right triangle trigonometry and cross-sections to solve problems involving surface areas and/or volumes of solids.
 
Identify, describe, and/or apply transformations on two and three dimensional geometric shapes.
 
Use basic theorems about similar and congruent triangles to solve problems.
 
Solve problems involving congruence, similarity, proportional reasoning and/or scale factor of two similar figures or solids.
 
Identify, analyze and/or use basic properties and theorems of circles to solve problems (including those relating right triangles and circles).
 
Use properties of right triangles to solve problems (such as involving the relationship formed when the altitude to the hypotenuse of a right triangle is drawn).
 
Determine and use the appropriate trigonometric ratio for a right triangle to solve a contextual problem.
 

Data, Probability and Statistics

 
Standard 5 — Data, Probability and Statistics
 
Conceptual StrandThe Data Analysis and Probability Standard recommends that students formulate questions that can be answered using data and addresses what is involved in gathering and using the data wisely. The basic concepts and applications of probability are also addressed, with an emphasis on the way that probability and statistics are related.Guiding QuestionHow do students experiences with the collection and analysis of data enable them to reason statistically and understand the various purposes of surveys, observational studies, and experiments?
 
Course Level Expectation
Analyze, interpret, employ and construct accurate statistical graphs.
 
Develop the basic principles of geometric probability.
 
State Performance Indicator
Use area to solve problems involving geometric probability (e.g. dartboard problem, shaded sector of a circle, shaded region of a geometric figure).
 
 
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