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### 8.NS The Number System

- 8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Explore the real number system and its appropriate usage in real-world situations.
- 8.NS.A.1A Make comparisons between rational and irrational numbers.
- 8.NS.A.1B Understand that all real numbers have a decimal expansion.
- 8.NS.A.1C Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.
- 8.NS.A.1D Convert repeating decimals to fractions.

- 8.NS.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.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Explore the real number system and its appropriate usage in real-world situations.

### 8.EE Expressions and Equations

- 8.EE.B Work with radicals and integer exponents.
- 8.EE.B.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 generate equivalent numerical expressions limited to integer exponents.
- 8.EE.B.2 Investigate concepts of square and cube roots.
- 8.EE.B.2A Use radical notation, if applicable, to represent the exact solutions to equations of the form
*x*² =*p*and*x*³ =*q*where*p*is a positive rational number and*q*is any rational number. - 8.EE.B.2B Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
- 8.EE.B.2C Recognize that square roots of non-perfect squares and the cube roots of non-perfect cubes are irrational.

- 8.EE.B.2A Use radical notation, if applicable, to represent the exact solutions to equations of the form
- 8.EE.B.3 Explore the relationship between quantities in decimal and scientific notation.
- 8.EE.B.3A Express very large and very small quantities,
*p*, in scientific notation in the form*a*× 10^{b}=*p*where 1 ≤*a*<10 and b is an integer. - 8.EE.B.3B Translate between decimal notation and scientific notation.
- 8.EE.B.3C Estimate and compare the relative size of two quantities in scientific notation.

- 8.EE.B.3A Express very large and very small quantities,
- 8.EE.B.4 Apply the concepts of decimal and scientific notation to real-world and mathematical problems.
- 8.EE.B.4A Select appropriate units of measure when representing answers in scientific notation.
- 8.EE.B.4B Interpret scientific notation that has been generated by a variety of technologies.

- Checkpoint opportunity

- 8.EE.C Understand the connections between proportional relationships, lines, and linear equations.
- 8.EE.C.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
- 8.EE.C.6 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*=*m**x*for a line through the origin and the equation*y*=*m**x*+ b for a line intercepting the vertical axis at (0, b). - Checkpoint opportunity

- 8.EE.D Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.EE.D.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.EE.D.7A Solve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variable terms on both sides.
- 8.EE.D.7B Recognize the three types of solutions to linear equations: one solution, infinitely many solutions, or no solutions.
- 8.EE.D.7C Generate linear equations with the three types of solutions.
- 8.EE.D.7D Justify why linear equations have a specific type of solution.

- 8.EE.D.8 Analyze and solve pairs of simultaneous linear equations.
- 8.EE.D.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.EE.D.8B Solve systems of two linear equations in two variables with integer solutions by graphing the equations.
- 8.EE.D.8C Solve simple real-world and mathematical problems leading to two linear equations in two variables given
*y*=*m**x*+ b form with integer solutions.

- Checkpoint opportunity

- 8.EE.D.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.F Functions

- 8.F.E Define, evaluate, and compare functions.
- 8.F.E.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.
- 8.F.E.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- 8.F.E.3 Interpret the equation
*y*=*m**x*+ b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. - Checkpoint opportunity

- 8.F.F Use functions to model relationships between quantities.
- 8.F.F.4 Apply the concepts of linear functions to real-world and mathematical situations.
- 8.F.F.4A Understand that the slope is the constant rate of change and the
*y*-intercept is the point where*x*= 0. - 8.F.F.4B 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.F.4C Construct a function in slope-intercept form that models a linear relationship between two quantities.
- 8.F.F.4D Interpret the meaning of the slope and the
*y*-intercept of a linear function in the context of the situation.

- 8.F.F.4A Understand that the slope is the constant rate of change and the
- 8.F.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph where the function is increasing, decreasing, constant, linear, or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
- Checkpoint opportunity

- 8.F.F.4 Apply the concepts of linear functions to real-world and mathematical situations.

### 8.G Geometry

- 8.G.G Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.G.1 Verify experimentally the properties of rotations, reflections, and translations.
- 8.G.G.1A Lines are taken to lines, and line segments to line segments of the same length.
- 8.G.G.1B Angles are taken to angles of the same measure.
- 8.G.G.1C Parallel lines are taken to parallel lines.

- 8.G.G.2 Recognize through visual comparison 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.
- 8.G.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
- 8.G.G.4 Recognize through visual comparison 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.
- 8.G.G.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.G.G.1 Verify experimentally the properties of rotations, reflections, and translations.
- 8.G.H Understand and apply the Pythagorean Theorem.
- 8.G.H.6 Use models or diagrams to explain the Pythagorean Theorem and its converse.
- 8.G.H.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems.
- 8.G.H.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
- Checkpoint opportunity

- 8.G.I Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
- 8.G.I.9 Given the formulas, solve real-world and mathematical problems involving volume and surface area of cylinders.
- Checkpoint opportunity

### 8.SP Statistics and Probability

- 8.SP.J Investigate patterns of association in bivariate data.
- 8.SP.J.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe the association by form (linear/nonlinear), direction (positive/negative), strength (correlation), and unusual features.
- 8.SP.J.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.SP.J.3 Use an equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
- 8.SP.J.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.SP.J.4A Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
- 8.SP.J.4B Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

- Checkpoint opportunity