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### 8.NS The Number System

- 8.NS.1 Explore the real number system and its appropriate usage in real-world situations.
- 8.NS.1.a Recognize the differences between rational and irrational numbers.
- 8.NS.1.b Understand that all real numbers have a decimal expansion.
- 8.NS.1.c Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.

- 8.NS.2 Estimate and compare the value of irrational numbers by plotting them on a number line.
- 8.NS.3 Extend prior knowledge to translate among multiple representations of rational numbers (fractions, decimal numbers, percentages). Include the conversion of repeating decimal numbers to fractions.
- Checkpoint opportunity

### 8.F Functions

- 8.F.1 Explore the concept of functions.
- 8.F.1.a Understand that a function assigns to each input exactly one output.
- 8.F.1.b Relate inputs (x- values or domain) and outputs (y- values or range) to independent and dependent variables.
- 8.F.1.c Translate among the multiple representations of a function, including mappings, tables, graphs, equations, and verbal descriptions.
- 8.F.1.d Determine if a relation is a function using multiple representations, including mappings, tables, graphs, equations, and verbal descriptions.
- 8.F.1.e Graph a function from a table of values. Understand that the graph and table both represent a set of ordered pairs of that function.

- 8.F.2 Compare multiple representations of two functions, including mappings, tables, graphs, equations, and verbal descriptions, in order to draw conclusions.
- 8.F.3 Investigate the differences between linear and nonlinear functions using multiple representations (i.e. tables, graphs, equations, and verbal descriptions).
- 8.F.3.a Define an equation in slope-intercept form (y = mx + b) as being a linear function.
- 8.F.3.b Recognize that the graph of a linear function has a constant rate of change.
- 8.F.3.c Provide examples of nonlinear functions.

- Checkpoint opportunity
- 8.F.4 Apply the concepts of linear functions to real-world and mathematical situations.
- 8.F.4.a Understand that the slope is the constant rate of change and the y- intercept is the point where x = 0.
- 8.F.4.b Determine the slope and the y-intercept of a linear function given multiple representations, including two points, tables, graphs, equations, and verbal descriptions.
- 8.F.4.c Construct a function in slope-intercept form that models a linear relationship between two quantities.
- 8.F.4.d Interpret the meaning of the slope and the y – intercept of a linear function in the context of the situation.
- 8.F.4.e Explore the relationship between linear functions and arithmetic sequences.

- 8.F.5 Apply the concepts of linear and nonlinear functions to graphs in real-world and mathematical situations.
- 8.F.5.a Analyze and describe attributes of graphs of functions (e.g., constant, increasing/decreasing, linear/nonlinear, maximum/minimum, discrete/continuous).
- 8.F.5.b Sketch the graph of a function from a verbal description.
- 8.F.5.c Write a verbal description from the graph of a function with and without scales.

- Checkpoint opportunity

### 8.EEI Expressions, Equations, and Inequalities

- 8.EEI.1 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.
- 8.EEI.2 Investigate concepts of square and cube roots.
- 8.EEI.2.a 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. - 8.EEI.2.b Evaluate square roots of perfect squares.
- 8.EEI.2.c Evaluate cube roots of perfect cubes.
- 8.EEI.2.d Recognize that square roots of non-perfect squares are irrational.

- 8.EEI.2.a Find the exact and approximate solutions to equations of the form
- 8.EEI.3 Explore the relationship between quantities in decimal and scientific notation.
- 8.EEI.3.a Express very large and very small quantities in scientific notation in the form a x 10 to the b power = p where 1 ² a < 10 and b is an integer.
- 8.EEI.3.b Translate between decimal notation and scientific notation.
- 8.EEI.3.c Estimate and compare the relative size of two quantities in scientific notation.

- 8.EEI.4 Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.
- 8.EEI.4.a Multiply and divide numbers expressed in both decimal and scientific notation.
- 8.EEI.4.b Select appropriate units of measure when representing answers in scientific notation.
- 8.EEI.4.c Translate how different technological devices display numbers in scientific notation.

- Checkpoint opportunity
- 8.EEI.5 Apply concepts of proportional relationships to real-world and mathematical situations.
- 8.EEI.5.a Graph proportional relationships.
- 8.EEI.5.b Interpret unit rate as the slope of the graph.
- 8.EEI.5.c Compare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.

- 8.EEI.6 Apply concepts of slope and y – intercept to graphs, equations, and proportional relationships.
- 8.EEI.6.a Explain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.
- 8.EEI.6.b Derive the slope-intercept form (y = mx + b) for a non-vertical line.
- 8.EEI.6.c Relate equations for proportional relationships (y = kx) with the slope-intercept form (y = mx + b) where b = 0.

- Checkpoint opportunity
- 8.EEI.7 Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.
- 8.EEI.7.a 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.
- 8.EEI.7.b Recognize the three types of solutions to linear equations: one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b).
- 8.EEI.7.c Generate linear equations with the three types of solutions.
- 8.EEI.7.d Justify why linear equations have a specific type of solution.

- 8.EEI.8 Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.
- 8.EEI.8.a Graph systems of linear equations and estimate their point of intersection.
- 8.EEI.8.b 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.
- 8.EEI.8.c Solve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.
- 8.EEI.8.d Understand that systems of linear equations can have one solution, no solution, or infinitely many solutions.

- Checkpoint opportunity

### 8.GM Geometry and Measurement

- 8.GM.1 Investigate the properties of rigid transformations (rotations, reflections, translations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, technology).
- 8.GM.1.a Verify that lines are mapped to lines, including parallel lines.
- 8.GM.1.b Verify that corresponding angles are congruent.
- 8.GM.1.c Verify that corresponding line segments are congruent.

- 8.GM.2 Apply the properties of rigid transformations (rotations, reflections, translations).
- 8.GM.2.a Rotate geometric figures 90, 180, and 270 degrees, both clockwise and counterclockwise, about the origin.
- 8.GM.2.b Reflect geometric figures with respect to the x – axis and/or y – axis.
- 8.GM.2.c Translate geometric figures vertically and/or horizontally.
- 8.GM.2.d 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.
- 8.GM.2.e Given two congruent figures, describe the series of rigid transformations that justifies this congruence.

- 8.GM.3 Investigate the properties of transformations (rotations, reflections, translations, dilations) using a variety of tools (e.g., grid paper, reflective devices, graphing paper, dynamic software).
- 8.GM.3.a Use coordinate geometry to describe the effect of transformations on two-dimensional figures.
- 8.GM.3.b Relate scale drawings to dilations of geometric figures.

- 8.GM.4 Apply the properties of transformations (rotations, reflections, translations, dilations).
- 8.GM.4.a Dilate geometric figures using scale factors that are positive rational numbers.
- 8.GM.4.b Recognize that two-dimensional figures are only similar if a series of transformations can be performed to map the pre-image to the image.
- 8.GM.4.c Given two similar figures, describe the series of transformations that justifies this similarity.
- 8.GM.4.d Use proportional reasoning to find the missing side lengths of two similar figures.

- 8.GM.5 Extend and apply previous knowledge of angles to properties of triangles, similar figures, and parallel lines cut by a transversal.
- 8.GM.5.a Discover that the sum of the three angles in a triangle is 180 degrees.
- 8.GM.5.b Discover and use the relationship between interior and exterior angles of a triangle.
- 8.GM.5.c Identify congruent and supplementary pairs of angles when two parallel lines are cut by a transversal.
- 8.GM.5.d Recognize that two similar figures have congruent corresponding angles.

- Checkpoint opportunity
- 8.GM.6 Use models to demonstrate a proof of the Pythagorean Theorem and its converse.
- 8.GM.7 Apply the Pythagorean Theorem to model and solve real-world and mathematical problems in two and three dimensions involving right triangles.
- 8.GM.8 Find the distance between any two points in the coordinate plane using the Pythagorean Theorem.
- Checkpoint opportunity
- 8.GM.9 Solve real-world and mathematical problems involving volumes of cones, cylinders, and spheres and the surface area of cylinders.

### 8.DSP Data Analysis, Statistics, and Probability

- 8.DSP.1 Investigate bivariate data.
- 8.DSP.1.a Collect bivariate data.
- 8.DSP.1.b Graph the bivariate data on a scatter plot.
- 8.DSP.1.c Describe patterns observed on a scatter plot, including clustering, outliers, and association (positive, negative, no correlation, linear, nonlinear).

- 8.DSP.2 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.
- 8.DSP.3 Apply concepts of an approximate line of best fit in real-world situations.
- 8.DSP.3.a Find an approximate equation for the line of best fit using two appropriate data points.
- 8.DSP.3.b Interpret the slope and intercept.
- 8.DSP.3.c Solve problems using the equation.

- 8.DSP.4 Investigate bivariate categorical data in two-way tables.
- 8.DSP.4.a Organize bivariate categorical data in a two-way table.
- 8.DSP.4.b Interpret data in two-way tables using relative frequencies.
- 8.DSP.4.c Explore patterns of possible association between the two categorical variables.

- 8.DSP.5 Organize data in matrices with rational numbers and apply to real-world and mathematical situations.
- 8.DSP.5.a Understand that a matrix is a way to organize data.
- 8.DSP.5.b Recognize that a m x n matrix has m rows and n columns.
- 8.DSP.5.c Add and subtract matrices of the same size.
- 8.DSP.5.d Multiply a matrix by a scalar.

- Checkpoint opportunity