### 8.NS: The Number System

#### 1.1: Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1.i: Know that numbers that are not rational are called irrational.

8.NS.1.ii: Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually.

8.NS.1.iii: Convert a decimal expansion which repeats eventually into a rational number.

8.NS.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 (such as pi²).

### 8.EE: Expressions and Equations

#### 2.1: Work with radicals and integer exponents.

8.EE.1: Develop, know and apply the properties of integer exponents to generate equivalent numeric and algebraic expressions.

8.EE.2.i: Use square root and cube root symbols to represent solutions to equations of the form ??² = ?? and ??³ = ??, where ?? is a positive rational number.

8.EE.2.ii: Evaluate square roots of small perfect squares and cube roots of small perfect cubes.

8.EE.3: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

8.EE.4.i: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

8.EE.4.ii: Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (such as use millimeters per year for seafloor spreading).

8.EE.4.iii: Interpret scientific notation that has been generated by technology.

#### 2.2: Understand the connections between proportional relationships, lines, and linear equations.

8.EE.5.i: Graph proportional relationships, interpreting the unit rate as the slope of the graph.

8.EE.5.ii: Compare two different proportional relationships represented in different ways.

8.EE.6.i: Use similar triangles to explain why the slope ?? is the same between any two distinct points on a non-vertical line in the coordinate plane.

8.EE.6.ii: 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.

#### 2.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7: Solve linear equations in one variable.

8.EE.7.a.i: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.

8.EE.7.a.ii: 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).

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

8.EE.8: Analyze and solve pairs of simultaneous linear equations.

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

8.EE.8.c: Solve real world and mathematical problems leading to two linear equations in two variables.

### 8.F: Functions

#### 3.1: Define, evaluate, and compare functions.

8.F.1.i: Understand that a function is a rule that assigns to each input exactly one output.

8.F.1.ii: Understand that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, and/or by verbal descriptions).

8.F.3.i: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.

8.F.3.ii: Give examples of functions that are not linear.

#### 3.2: Use functions to model relationships between quantities.

8.F.4.i: Construct a function to model a linear relationship between two quantities.

8.F.4.ii: 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.

8.F.4.iii: 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.F.5.i: Describe qualitatively the functional relationship between two quantities by analyzing a graph (may include where the function is increasing or decreasing, linear or nonlinear, etc.).

8.F.5.ii: Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

### 8.G: Geometry

#### 4.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.1: Understand the properties of rotations, reflections, and translations by experimentation:

8.G.1.a: Lines are transformed onto lines, and line segments onto line segments of the same length.

8.G.1.b: Angles are transformed onto angles of the same measure.

8.G.1.c: Parallel lines are transformed onto parallel lines.

8.G.2.i: Understand 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.

8.G.2.ii: Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

8.G.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

8.G.4.i: Understand 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.

8.G.4.ii: Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

8.G.5: Use informal arguments to establish facts about:

8.G.5.a: the angle sum and exterior angles of triangles.

8.G.5.b: the angles created when parallel lines are cut by a transversal.

8.G.5.c: the angle-angle criterion for similarity of triangles.

#### 4.2: Understand and apply the Pythagorean Theorem.

8.G.6: Explain a proof of the Pythagorean Theorem and its converse.

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

#### 4.3: Solve real world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9.i: Know the formulas for the volume of cones, cylinders and spheres.

8.G.9.ii: Use the formulas to solve real world and mathematical problems.

### 8.SP: Statistics and Probability

#### 5.1: Investigate patterns of association in bivariate data.

8.SP.1.i: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities.

8.SP.1.ii: Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.2.i: Know that straight lines are widely used to model relationships between two quantitative variables.

8.SP.2.ii: 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.SP.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept(s).

8.SP.4.i: 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.SP.4.ii: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

8.SP.4.iii: Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Correlation last revised: 9/22/2020

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