# Academic standards list

### Algebra I — 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

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

Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.

Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.

Recognize and express the effect of changing constants and/or coefficients in problem solving.

Determine and interpret slope in multiple contexts including rate of change in real-world problems.

### 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 computational results and operations involving real numbers in multiple representations.

Understand properties of and relationships between subsets and elements of the real number system.

State Performance Indicator

Operate (add, subtract, multiply, divide, simplify, powers) with radicals and radical expressions including radicands involving rational numbers and algebraic…

Describe and/or order a given set of real numbers including both rational and irrational numbers.

### 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 in order to perform operations with, evaluate, simplify, and factor expressions and polynomials.

Understand and use relations and functions in various representations to solve contextual problems.

Construct and solve systems of linear equations and inequalities in two variables by various methods.

State Performance Indicator

Express a generalization of a pattern in various representations including algebraic and function notation.

Operate with, evaluate, and simplify rational expressions including determining
restrictions on the domain of the variables.

Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value.

Determine domain and range of a relation, determine whether a relation is a function
and/or evaluate a function at a specified rational value.

Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

### 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

Use algebraic reasoning in applications involving geometric formulas and contextual problems.

State Performance Indicator

### 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

State Performance Indicator

Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).

Identify the effect on mean, median, mode, and range when values in the data set are changed.

Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.

Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.

**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.**

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