Academic standards list

Algebra I — Mathematics


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
Interpret patterns found in sequences, tables, and other forms of quantitative information using variables or function notation.
Write an equation symbolically to express a contextual problem.
Apply properties to evaluate expressions, simplify expressions, and justify solutions to problems.
Translate between representations of functions that depict real-world situations.
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

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 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
Multiply, divide, and square numbers expressed in scientific notation.
Describe and/or order a given set of real numbers including both rational and irrational numbers.


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 algebraic thinking to analyze and generalize patterns.
Understand and apply properties in order to perform operations with, evaluate, simplify, and factor expressions and polynomials.
Understand and apply operations with rational expressions and equations.
Solve problems involving linear equations and linear inequalities.
Manipulate formulas and solve literal equations.
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.
Solve and understand solutions of quadratic equations with real roots.
Understand and use exponential functions to solve contextual problems.
State Performance Indicator
Express a generalization of a pattern in various representations including algebraic and function notation.
Operate with polynomials and simplify results.
Factor polynomials.
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.
Interpret various relations in multiple representations.
Determine domain and range of a relation, determine whether a relation is a function and/or evaluate a function at a specified rational value.
Determine the equation of a line and/or graph a linear equation.
Solve systems of linear equation/inequalities in two variables.
Find the solution of a quadratic equation and/or zeros of a quadratic function.
Analyze nonlinear graphs including quadratic and exponential functions that model a contextual situation.

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
Use algebraic reasoning in applications involving geometric formulas and contextual problems.
Apply appropriate units of measure and convert measures in problem solving situations.
State Performance Indicator
Develop and apply strategies to estimate the area of any shape on a plane grid.
Solve contextual problems using the Pythagorean Theorem.
Solve problems involving the distance between points or midpoint of a segment.
Convert rates and measurements.

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 and interpret quantitative information.
Use statistical thinking to draw conclusions and make predictions.
Understand basic counting procedures and concepts of probability.
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.
Generate the equation of a line that fits linear data and use it to make a prediction.
Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.
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