8th

The Number System

Functions

Expressions, Equations, and Inequalities

Geometry and Measurement

Data Analysis, Statistics, and Probability

Explore the real number system and its appropriate usage in real-world situations. 

Estimate and compare the value of irrational numbers by plotting them on a number line. 

Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.

Explore the concept of functions.

Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.

Investigate the differences between linear and nonlinear functions using multiple representations (i.e., tables, graphs, equations, and verbal descriptions).

Apply the concepts of linear functions to real-world and mathematical situations. 

Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.

Understand and apply the laws of exponents (i.e., product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.

Investigate concepts of square and cube roots. 

Explore the relationship between quantities in decimal and scientific notation. 

Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems. 

Apply concepts of proportional relationships to real-world and mathematical situations. 

Apply concepts of slope and 𝑦-intercept to graphs, equations, and proportional relationships.

Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations. 

Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.

Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).

Apply the properties of rigid transformations (rotations, reflections, translations). 

Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).

Apply the properties of transformations (rotations, reflections, translations, dilations). 

Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.

Use models to demonstrate a proof of the Pythagorean Theorem and its converse. 

Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles. 

Find the distance between any two points in the coordinate plane using the Pythagorean Theorem. 

Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders. 

Investigate bivariate data. 

Draw an approximate line of best fit on a scatter plot that appears to have a linear association and informally assess the fit of the line to the data points. 

Apply concepts of an approximate line of best fit in real-world situations.

Investigate bivariate categorical data in two-way tables. 

Organize data in matrices with rational numbers and apply to real-world and mathematical situations.

Recognize the differences between rational and irrational numbers.

Understand that all real numbers have a decimal expansion.

Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.

Understand that a function assigns to each input exactly one output.

 Relate inputs (𝑥-values or domain) and outputs (𝑦-values or range) to independent and dependent variables. 

Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.

Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions. 

Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

Define an equation in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) as being a linear function.

Recognize that the graph of a linear function has a constant rate of change.

Provide examples of nonlinear functions.

Understand that the slope is the constant rate of change and the 𝑦-intercept is the point where 𝑥 = 0.

Determine the slope and the 𝑦-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.

Construct a function in slope-intercept form that models a linear relationship between two quantities.

Interpret the meaning of the slope and the 𝑦-intercept of a linear function in the context of the situation.

Explore the relationship between linear functions and arithmetic sequences.

Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).

Sketch the graph of a function from a verbal description.

Write a verbal description from the graph of a function with and without scales.

Find the exact and approximate solutions to equations of the form 𝑥 2 = 𝑝 and 𝑥 3 = 𝑝 where 𝑝 is a positive rational number.

 Evaluate square roots of perfect squares.

Evaluate cube roots of perfect cubes.

Recognize that square roots of non-perfect squares are irrational.

Express very large and very small quantities in scientific notation in the form 𝑎 × 10𝑏 = 𝑝 where 1 ≤ 𝑎 < 10 and 𝑏 is an integer.

Translate between decimal notation and scientific notation. 

Estimate and compare the relative size of two quantities in scientific notation.

Multiply and divide numbers expressed in both decimal and scientific notation.

Select appropriate units of measure when representing answers in scientific notation.

Translate how different technological devices display numbers in scientific notation.

Graph proportional relationships.

Interpret unit rate as the slope of the graph.

Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.

Explain why the slope, 𝑚, is the same between any two distinct points on a nonvertical line using similar triangles.

Derive the slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) for a non-vertical line.

Relate equations for proportional relationships (𝑦 = 𝑘𝑥) with the slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏) where 𝑏 = 0.

Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.

Recognize the three types of solutions to linear equations: one solution (𝑥 = 𝑎), infinitely many solutions (𝑎 = 𝑎), or no solutions (𝑎 = 𝑏).

Generate linear equations with the three types of solutions.

Justify why linear equations have a specific type of solution.

Graph systems of linear equations and estimate their point of intersection.

Understand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.

Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection. 

Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

Verify that lines are mapped to lines, including parallel lines.

Verify that corresponding angles are congruent.

Verify that corresponding line segments are congruent

Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.

. Reflect geometric figures with respect to the 𝑥-axis and/or 𝑦-axis.

Translate geometric figures vertically and/or horizontally.

Recognize that two-dimensional figures are only congruent if a series of rigid transformations can be performed to map the pre-image to the image.

Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

Use coordinate geometry to describe the effect of transformations on two-dimensional figures.

Relate scale drawings to dilations of geometric figures.

Dilate geometric figures using scale factors that are positive rational numbers.

Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image. 

Given two similar figures, describe the series of transformations that justifies this similarity.

Use proportional reasoning to find the missing side lengths of two similar figures.

Discover that the sum of the three angles in a triangle is 180 degrees.

Discover and use the relationship between interior and exterior angles of a triangle.

Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.

Recognize that two similar figures have congruent corresponding angles

Collect bivariate data

Graph the bivariate data on a scatter plot.

Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).

Find an approximate equation for the line of best fit using two appropriate data points.

Interpret the slope and intercept.

Solve problems using the equation.

Organize bivariate categorical data in a two-way table

Interpret data in two-way tables using relative frequencies.

Explore patterns of possible association between the two categorical variables.

Understand that a matrix is a way to organize data. 

Recognize that a 𝑚 × 𝑛 matrix has 𝑚 rows and 𝑛 columns.

Add and subtract matrices of the same size.

Multiply a matrix by a scalar.