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Skills available for Louisiana eighth-grade math standards

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Louisiana Student Standards (adopted in 2025): Grade 8 Louisiana Student Standards (adopted in 2025): Grade 8
Louisiana Student Standards: Grade 8 Louisiana Student Standards: Grade 8
Louisiana Student Standards: Mathematical Practices Louisiana Student Standards: Mathematical Practices

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8.NOF Numeracy & Operational Fluency

8.NOF.A Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.NOF.A.1 Understand the real number system.
  - 8.NOF.A.1a Distinguish between rational and irrational numbers.
    - Identify rational and irrational square roots (8-F.1)
    - Identify rational and irrational numbers (8-F.2)
  - 8.NOF.A.1b Understand informally that every number has a decimal expansion.
  - 8.NOF.A.1c For rational numbers, show that the decimal expansion repeats eventually.
  - 8.NOF.A.1d Convert a decimal expansion that repeats eventually into a rational number by analyzing repeating patterns.
    - Convert between repeating decimals and fractions (8-B.1)
    - Convert between decimals and fractions or mixed numbers (8-B.2)
- 8.NOF.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
- Checkpoint opportunity
  - Checkpoint: Rational and irrational numbers (8-F.6)
  - Checkpoint: Approximate irrational numbers (8-F.7)

8.AR Algebraic Reasoning

8.AR.A Work with radicals and integer exponents.
- 8.AR.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- 8.AR.A.2 Represent solutions to equations, in the form x² = p and x³ = p, using the square root and cube root symbols, and determine if the solution is rational or irrational. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
- 8.AR.A.3 Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times larger or smaller one number is compared to another.
  - Convert between standard and scientific notation (8-D.1)
  - Compare numbers written in scientific notation (8-D.3)
- 8.AR.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.
- Checkpoint opportunity
8.AR.B Understand the connections between proportional relationships, lines, and linear equations.
- 8.AR.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
- 8.AR.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
- Checkpoint opportunity
  - Checkpoint: Proportional relationships (8-X.13)
  - Checkpoint: Slope and linear equations (8-AA.15)
8.AR.C Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.AR.C.7 Solve linear equations in one variable.
  - 8.AR.C.7a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
    - Find the number of solutions (8-M.20)
    - Create equations with no solutions or infinitely many solutions (8-M.21)
  - 8.AR.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
- 8.AR.C.8 Analyze and solve pairs of simultaneous linear equations.
  - 8.AR.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  - 8.AR.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
  - 8.AR.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables.
- Checkpoint opportunity
  - Checkpoint: Solve linear equations (8-M.22)
  - Checkpoint: Systems of equations (8-GG.14)

8.GL Geometric Reasoning & Logic

8.GL.A Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.GL.A.1 Verify experimentally the properties of rotations, reflections, and translations:
  - 8.GL.A.1a Lines are taken to lines, and line segments to line segments of the same length.
  - 8.GL.A.1b Angles are taken to angles of the same measure.
  - 8.GL.A.1c Parallel lines are taken to parallel lines.
- 8.GL.A.2 Explain that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (Rotations are only about the origin, and reflections are only over the y-axis and x-axis in grade 8.)
- 8.GL.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in grade 8.)
- 8.GL.A.4 Explain that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in grade 8.)
- 8.GL.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- Checkpoint opportunity
8.GL.B Understand and apply the Pythagorean Theorem.
- 8.GL.B.6 Explain a proof of the Pythagorean Theorem and its converse using the areas of squares.
  - Converse of the Pythagorean theorem: is it a right triangle? (8-T.6)
- 8.GL.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- 8.GL.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
  - Find the distance between two points (8-O.4)
- Checkpoint opportunity
  - Checkpoint: Pythagorean theorem and its converse (8-T.7)
  - Checkpoint: Applications of the Pythagorean theorem (8-T.8)
8.GL.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- 8.GL.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
- Checkpoint opportunity
  - Checkpoint: Volume (8-W.10)

8.DA Data Analysis

8.DA.A Investigate patterns of association in bivariate data.
- 8.DA.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
- 8.DA.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
  - Identify lines of best fit (8-II.8)
  - Write equations for lines of best fit (8-II.9)
- 8.DA.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
  - Interpret lines of best fit: word problems (8-II.10)
- 8.DA.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
  - 8.DA.A.4a Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
    - Create and interpret two-way frequency tables (8-JJ.1)
  - 8.DA.A.4b Use relative frequencies calculated for rows or columns to describe the possible association between the two variables.
- Checkpoint opportunity

8.PF Proportionality & Functions

8.PF.A Define, evaluate, and compare functions.
- 8.PF.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in this grade level.)
- 8.PF.A.2 Compare properties of two functions where each fraction is represented in a different way (algebraically, graphically, numerically, or through verbal descriptions).
  - Compare linear functions: graphs and equations (8-CC.9)
  - Compare linear functions: tables, graphs, and equations (8-CC.10)
- 8.PF.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; categorize functions as linear or nonlinear when given equations, graphs, or tables.
- Checkpoint opportunity
8.PF.B Use functions to model relationships between quantities.
- 8.PF.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.
- 8.PF.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
  - Identify graphs: word problems (8-EE.3)
- Checkpoint opportunity
  - Checkpoint: Construct and interpret linear functions (8-CC.13)
  - Checkpoint: Sketch and describe graphs (8-EE.4)

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8.NOF Numeracy & Operational Fluency

8.NOF.A Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NOF.A.1 Understand the real number system.

8.NOF.A.1a Distinguish between rational and irrational numbers.

8.NOF.A.1b Understand informally that every number has a decimal expansion.

8.NOF.A.1c For rational numbers, show that the decimal expansion repeats eventually.

8.NOF.A.1d Convert a decimal expansion that repeats eventually into a rational number by analyzing repeating patterns.

8.NOF.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

Checkpoint opportunity

8.AR Algebraic Reasoning

8.AR.A Work with radicals and integer exponents.

8.AR.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

8.AR.A.2 Represent solutions to equations, in the form x2 = p and x3 = p, using the square root and cube root symbols, and determine if the solution is rational or irrational. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

8.AR.A.3 Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times larger or smaller one number is compared to another.

Checkpoint opportunity

8.AR.B Understand the connections between proportional relationships, lines, and linear equations.

8.AR.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.AR.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Checkpoint opportunity

8.AR.C Analyze and solve linear equations and pairs of simultaneous linear equations.

8.AR.C.7 Solve linear equations in one variable.

8.AR.C.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.AR.C.8 Analyze and solve pairs of simultaneous linear equations.

8.AR.C.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

8.AR.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

8.AR.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables.

Checkpoint opportunity

8.GL Geometric Reasoning & Logic

8.GL.A Understand congruence and similarity using physical models, transparencies, or geometry software.

8.GL.A.1 Verify experimentally the properties of rotations, reflections, and translations:

8.GL.A.1a Lines are taken to lines, and line segments to line segments of the same length.

8.GL.A.1b Angles are taken to angles of the same measure.

8.GL.A.1c Parallel lines are taken to parallel lines.

8.GL.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. (Rotations are only about the origin, dilations only use the origin as the center of dilation, and reflections are only over the y-axis and x-axis in grade 8.)

8.GL.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Checkpoint opportunity

8.GL.B Understand and apply the Pythagorean Theorem.

8.GL.B.6 Explain a proof of the Pythagorean Theorem and its converse using the areas of squares.

8.GL.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.GL.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Checkpoint opportunity

8.GL.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.GL.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Checkpoint opportunity

8.DA Data Analysis

8.DA.A Investigate patterns of association in bivariate data.

8.DA.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.DA.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.DA.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8.DA.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

8.DA.A.4a Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

8.DA.A.4b Use relative frequencies calculated for rows or columns to describe the possible association between the two variables.

Checkpoint opportunity

8.PF Proportionality & Functions

8.PF.A Define, evaluate, and compare functions.

8.PF.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in this grade level.)

8.PF.A.2 Compare properties of two functions where each fraction is represented in a different way (algebraically, graphically, numerically, or through verbal descriptions).

8.PF.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; categorize functions as linear or nonlinear when given equations, graphs, or tables.

Checkpoint opportunity

8.PF.B Use functions to model relationships between quantities.

8.PF.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Checkpoint opportunity

8.AR.A.2 Represent solutions to equations, in the form x² = p and x³ = p, using the square root and cube root symbols, and determine if the solution is rational or irrational. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.