Academic standards list

Mathematics - Grade 8 — 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?
Grade Level Expectation
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
Solve problems involving rate/time/distance (i.e., d = rt).
Interpret a qualitative graph representing a contextual situation.
Calculates rates involving cost per unit to determine the best buy.

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?
Grade Level Expectation
Extend understanding of the real number system to include irrational numbers.
Solve problems involving exponents and scientific notation using technology appropriately.
Solve real-world problems using rational and irrational numbers.
Understand and use the laws of exponents.
State Performance Indicator
Order and compare rational and irrational numbers and locate on the number line.
Identify numbers and square roots as rational or irrational.
Use scientific notation to compute products and quotients.
Solve real-world problems requiring scientific notation.


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?
Grade Level Expectation
Recognize and generate equivalent forms for algebraic expressions.
Represent, analyze, and solve problems involving linear equations and inequalities in one and two variables.
Solve systems of linear equations in two variables.
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
Use slope to analyze situations and solve problems.
Compare and contrast linear and nonlinear functions.
State Performance Indicator
Find solutions to systems of two linear equations in two variables.
Solve the linear equation f(x) = g(x).
Solve and graph linear inequalities in two variables.
Translate between various representations of a linear function.
Determine the slope of a line from an equation, two given points, a table or a graph.
Analyze the graph of a linear function to find solutions and intercepts.
Identify, compare and contrast functions as linear or nonlinear.

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?
Grade Level Expectation
Derive the Pythagorean theorem and understand its applications.
Understand the relationships among the angles formed by parallel lines cut by transversals.
Understand the necessary levels of accuracy and precision in measurement.
Understand both metric and customary units of measurement.
Use visualization to describe or identify intersections, cross-sections, and various views of geometric figures.
State Performance Indicator
Use the Pythagorean Theorem to solve contextual problems.
Apply the Pythagorean theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra.
Find measures of the angles formed by parallel lines cut by a transversal.
Convert between and within the U.S. Customary System and the metric system.
Identify the intersection of two or more geometric figures in the plane.

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?
Grade Level Expectation
Explore probabilities for compound, independent and/or dependent events.
Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
Evaluate the use of statistics in media reports.
State Performance Indicator
Calculate probabilities of events for simple experiments with equally probable outcomes.
Use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models).
Generalize the relationship between two sets of data using scatterplots and lines of best fit.
Recognize misrepresentations of published data in the media.
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