### 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
Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic) of non-linear and

Recognize and describe errors in data collection and analysis as well as identifying representations of data as being accurate or misleading.

Use technology tools to identify and describe patterns in data using non-linear and transcendental functions that approximate data as well as using those

Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely to effectively communicate reasoning in the process of

### 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
Understand the hierarchy of the complex number system and relationships between the elements, properties and operations.
Connect numeric, analytic, graphical and verbal representations of both real and complex numbers.
Use appropriate technology (including graphing calculators and computer spreadsheets) to solve problems, recognize patterns and collect and analyze data.
Understand the capabilities and limitations of technology when performing operations, graphing, and solving equations involving complex numbers.
State Performance Indicator
Describe any number in the complex number system.

Compute with all real and complex numbers.

Use the number system, from real to complex, to solve equations and contextual problems

### 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
Understand and apply properties of rational exponents and perform basic operations to simplify algebraic expressions.
Understand, analyze, transform and generalize mathematical patterns, relations and functions using properties and various representations.
Analyze and apply various methods to solve equations, absolute values, inequalities, and systems of equations over complex numbers.
Graph and compare equations and inequalities in two variables. Identify and understand the relationships between the algebraic and geometric properties of the graph.
Use mathematical models involving equations and systems of equations to represent, interpret and analyze quantitative relationships, change in various contexts,
State Performance Indicator
Add, subtract and multiply polynomials; divide a polynomial by a lower degree polynomial.

Solve quadratic equations and systems, and determine roots of a higher order polynomial.

Add, subtract, multiply, divide and simplify rational expressions including those with rational and negative exponents.

Use the formulas for the general term and summation of finite arithmetic and both finite and infinite geometric series.

Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions

Combine functions (such as polynomial, rational, radical and absolute value expressions) by addition, subtraction, multiplication, division, or by composition

Identify whether a function has an inverse, whether two functions are inverses of each other, and/or explain why their graphs are reflections over the line y = x.

Solve systems of three linear equations in three variables.

Graph the solution set of two or three linear or quadratic inequalities.

Identify and/or graph a variety of functions and their transformations.

Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the

Interpret graphs that depict real-world phenomena.

Solve contextual problems using quadratic, rational, radical and exponential equations, finite geometric series or systems of equations.

Solve problems involving the binomial theorem and its connection to Pascals Triangle, combinatorics, and probability.

### 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
Understand the trigonometric functions and their relationship to the unit circle.
Know and use the basic identities of sine, cosine, and tangent as well as their reciprocals.

Graph all six trigonometric functions and identify their key characteristics.
Know and use the Law of Sines to find missing sides and angles of a triangle, including the ambiguous case.
Use trigonometric concepts, properties and graphs to solve problems.

State Performance Indicator
Exhibit knowledge of unit circle trigonometry.

Match graphs of basic trigonometric functions with their equations.

Describe and articulate the characteristics and parameters of parent trigonometric functions to solve contextual problems.

### 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
Describe, interpret, and apply quantitative data.
Evaluate and critique various ways of collecting data and using information based on data published in the media.
Use data and statistical thinking to draw inferences, make predictions, justify conclusions and identify and explain misleading uses of data.
Develop an understanding of probability concepts in order to make informed decisions.
State Performance Indicator
Compute, compare and explain summary statistics for distributions of data including measures of center and spread.

Compare data sets using graphs and summary statistics.

Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data.

Apply the characteristics of the normal distribution.

Determine differences between randomized experiments and observational studies.

Find the regression curve that best fits both linear and non-linear data (using technology such as a graphing calculator) and use it to make predictions.

Determine/recognize when the correlation coefficient measures goodness of fit.

Apply probability concepts such as conditional probability and independent events to calculate simple probability.

Disclaimer: This website provides a reference tool for browsing academic standards and locating associated resources. We are not the originator of these academic standards. Although we strive to maintain accuracy, there may be revisions, updates, or errors within the text and structure of the information displayed. In case of any discrepancy, please respect the originator's published version (http://www.tn.gov/education/article/mathematics-standards) as the definitive record.