N-Gen Math™ 8 Workbook

Standard Alignment

The N-Gen Math™ 8 workbook covers required topics aligned with the Next Generation Learning Standards (NGLS). Below are some of the key areas addressed in the workbook, though this is not a comprehensive list:

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
NY-8.EE.7 Solve linear equations in one variable.
NY-8.EE.7.a Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions.
NY-8.EE.7.b Solve linear equations with rational number coefficients, including equations requiring the distributive property and combining like terms.
NY-8.G.5 Use informal arguments to establish facts about: The angle sum and exterior angle of triangles. Angles created when parallel lines are cut by a transversal. The angle-angle criterion for similarity of triangles.
NY-8.G.1 Verify properties of rotations, reflections, and translations.
NY-8.G.1.a Verify that lines map to lines, and line segments to line segments of the same length.
NY-8.G.1.b Verify that angles map to angles of the same measure.
NY-8.G.1.c Verify that parallel lines map to parallel lines.
NY-8.G.2 Recognize that two-dimensional figures are congruent if they have corresponding congruent angles and sides.
NY-8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures.
NY-8.G.4 Recognize that two-dimensional figures are similar if they maintain proportional sides and congruent angles.
NY-8.F.1 Understand that a function is a rule assigning exactly one output to each input. Recognize graphs as function representations.
NY-8.F.3 Interpret y=mx+by = mx + by=mx+b as defining a linear function and recognize examples of linear and nonlinear functions.
NY-8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value from a description, table, or graph.
NY-8.F.5 Describe qualitatively the relationship between two quantities by analyzing a graph and sketch a graph based on a description.
NY-8.G.1 Verify properties of rotations, reflections, and translations.
NY-8.G.1.a Verify that lines map to lines, and segments to segments of the same length.
NY-8.G.1.b Verify that angles map to angles of the same measure.
NY-8.G.1.c Verify that parallel lines map to parallel lines.
NY-8.G.3 Describe the effect of transformations (dilations, translations, rotations, reflections) using coordinates.
NY-8.G.4 Recognize that two-dimensional figures are similar if corresponding angles are congruent and corresponding sides are proportional.
NY-8.G.5 Use informal arguments to establish facts about angles created when parallel lines are cut by a transversal and the angle-angle criterion for triangle similarity.
NY-8.G.6 Understand a proof of the Pythagorean Theorem and its converse.
NY-8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in two and three dimensions.
NY-8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
NY-8.G.9 Solve real-world problems involving the volume of cones, cylinders, and spheres.
NY-8.SP.1 Construct and interpret scatter plots for bivariate data, investigating patterns such as clustering, outliers, and associations.
NY-8.SP.2 Recognize that a straight line can be used to model a linear relationship between two variables. Informally assess the fit of a model by judging the closeness of data points to the line.
NY-8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate data, interpreting the slope and intercept.
NY-8.SP.1 Construct and interpret scatter plots for bivariate data, investigating patterns such as clustering, outliers, and associations.
NY-8.SP.2 Recognize that a straight line can be used to model a linear relationship between two variables. Informally assess the fit of a model by judging the closeness of data points to the line.
NY-8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate data, interpreting the slope and intercept.

CCSS equivalent standards include:

CCSS.MP.1 Make sense of problems and persevere in solving them.
CCSS.MP.2 Reason abstractly and quantitatively.
CCSS.MP.3 Construct viable arguments and critique the reasoning of others.
CCSS.MP.4 Model with mathematics.
CCSS.MP.5 Use appropriate tools strategically.
CCSS.MP.6 Attend to precision.
CCSS.MP.7 Look for and make use of structure.
CCSS.8.NS.1 Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion repeats. Recognize that numbers that are not rational are called irrational.
CCSS.8.EE.1 Know and apply properties of integer exponents to generate equivalent numerical expressions.
CCSS.8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or small quantities and compare them.
CCSS.8.EE.4 Perform multiplication and division with numbers in scientific notation, including problems with standard decimal notation.
CCSS.8.EE.5 Graph proportional relationships and interpret the unit rate as the slope of the graph. Compare proportional relationships represented in different ways.
CCSS.8.EE.6 Use similar triangles to explain why the slope is the same between any two points on a non-vertical line in the coordinate plane. Derive the equations y=mxy = mxy=mx and y=mx+by = mx + by=mx+b.
CCSS.8.EE.7 Solve linear equations in one variable.
CCSS.8.EE.7.a Recognize when an equation has one solution, infinitely many solutions, or no solution.
CCSS.8.EE.7.b Solve linear equations with rational number coefficients, including equations requiring the distributive property and combining like terms.
CCSS.8.EE.8 Analyze and solve systems of two linear equations in two variables.
CCSS.8.EE.8.b Solve systems of two linear equations using graphs, tables, and algebraic methods.
CCSS.8.F.1 Understand that a function is a rule assigning exactly one output to each input. Recognize graphs as function representations.
CCSS.8.F.3 Interpret y=mx+by = mx + by=mx+b as defining a linear function and recognize examples of linear and nonlinear functions.
CCSS.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value from a description, table, or graph.
CCSS.8.F.5 Describe qualitatively the relationship between two quantities by analyzing a graph and sketch a graph based on a description.
CCSS.8.SP.1 Construct and interpret scatter plots for bivariate data, investigating patterns such as clustering, outliers, and associations.
CCSS.8.SP.2 Recognize that a straight line can be used to model a linear relationship between two variables. Informally assess the fit of a model by judging the closeness of data points to the line.
CCSS.8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate data, interpreting the slope and intercept.
CCSS.8.F.1 Understand that a function is a rule assigning exactly one output to each input. Recognize graphs as function representations.
CCSS.8.F.3 Interpret y=mx+by = mx + by=mx+b as defining a linear function and recognize examples of linear and nonlinear functions.
CCSS.8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value from a description, table, or graph.
CCSS.8.F.5 Describe qualitatively the relationship between two quantities by analyzing a graph and sketch a graph based on a description.