### 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?

Use mathematical language, symbols, and definitions while developing mathematical reasoning.
Apply and adapt a variety of appropriate strategies to problem solving, including estimation, and reasonableness of the solution.
Develop independent reasoning to communicate mathematical ideas and derive algorithms and/or formulas.
Move flexibly between concrete and abstract representations of mathematical ideas in order to solve problems, model mathematical ideas, and communicate solution
Use mathematical ideas and processes in different settings to formulate patterns, analyze graphs, set up and solve problems and interpret solutions.
Read and interpret the language of mathematics and use written/oral communication to express mathematical ideas precisely.
Recognize the historical development of mathematics, mathematics in context, and the connections between mathematics and the real world.
Use technologies/manipulatives appropriately to develop understanding of mathematical algorithms, to facilitate problem solving, and to create accurate and
State Performance Indicator
Use proportional reasoning to solve mixture/concentration problems.

Generalize a variety of patterns to a symbolic rule from tables, graphs, or words.

Recognize whether information given in a table, graph, or formula suggests a directly proportional, linear, inversely proportional, or other nonlinear relationship.

### 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?

Extend understandings of addition, subtraction, multiplication and division to integers.
Understand and work with the properties of and operations on the system of rational numbers.
Develop an understanding of and apply proportionality.
Use ratios, rates and percents to solve single- and multi-step problems in various contexts.
Understand and work with squares, cubes, square roots and cube roots.
Introduce the concept of negative exponents.
Understand and use scientific notation.
State Performance Indicator
Simplify numerical expressions involving rational numbers.

Compare rational numbers using appropriate inequality symbols.

Use rational numbers and roots of perfect squares/cubes to solve contextual problems.

Determine the approximate location of square/cube roots on a number line.

Solve contextual problems that involve operations with integers.

Express the ratio between two quantities as a percent, and a percent as a ratio or fraction.

Use ratios and proportions to solve 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?

Recognize and generate equivalent forms for simple algebraic expressions.
Understand and compare various representations of relations and functions.
Understand the concept of function as a rule that assigns to a given input one and only one number (the output).
Use function notation where f(x) represents the output that the function f assigns to the input x.
Understand and graph proportional relationships.
Conceptualize the meanings of slope using various interpretations, representations, and contexts.
Use mathematical models involving linear equations to analyze real-world phenomena.
Use a variety of strategies to efficiently solve linear equations and inequalities.
State Performance Indicator
Evaluate algebraic expressions involving rational values for coefficients and/or variables.

Determine whether a relation (represented in various ways) is a function.

Given a table of inputs x and outputs f(x), identify the function rule and continue the pattern.

Interpret the slope of a line as a unit rate given the graph of a proportional relationship.

Represent proportional relationships with equations, tables and graphs.

Solve linear equations with rational coefficients symbolically or graphically.

Translate between verbal and symbolic representations of real-world phenomena involving linear equations.

Solve contextual problems involving two-step linear equations.

Solve linear inequalities in one variable with rational coefficients symbolically or graphically.

### 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?

Understand the application of proportionality with similar triangles.
Apply proportionality to converting among different units of measurements to solve problems involving rates such as motion at a constant speed.
Understand and use scale factor to describe the relationships between length, area, and volume.
Understand and use ratios, derived quantities, and indirect measurements.
State Performance Indicator
Solve contextual problems involving similar triangles.

Use SSS, SAS, and AA to determine if two triangles are similar.

Apply scale factor to solve problems involving area and volume.

### 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?

Collect, organize, and analyze both single- and two-variable data.
Select, create, and use appropriate graphical representations of data.
Formulate questions and design studies to collect data about a characteristic shared by two populations, or different characteristics within one population.
Use descriptive statistics to summarize and compare data.
Understand and apply basic concepts of probability.
State Performance Indicator
Interpret and employ various graphs and charts to represent data.

Select suitable graph types (such as bar graphs, histograms, line graphs, circle graphs, box-and-whisker plots, and stem-and-leaf plots) and use them to create

Calculate and interpret the mean, median, upper-quartile, lower-quartile, and interquartile range of a set of data.

Use theoretical probability to make predictions.

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.