Gizmos for Alabama - Mathematics: 8th Grade (Course of Study adopted 2016)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

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: : Students will: 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.

8.NS.2: : Students will: 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 (e.g., pi²).

8.EE: : Expressions and Equations

2.1: : Work with radicals and integer exponents.

8.EE.3: : Students will: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

8.EE.4: : Students will: Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that the square root of 2 is irrational.

8.EE.5: : Students will: 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.6: : Students will: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

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

8.EE.7: : Students will: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

8.EE.8: : Students will: Use similar triangles to 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 = 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.9: : Students will: Solve linear equations in one variable.

8.EE.9.a: : Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. 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.9.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.10: : Students will: Analyze and solve pairs of simultaneous linear equations.

8.EE.10.a: : Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously.

8.EE.10.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.10.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.11: : Students will: 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.12: : Students will: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.13: : Students will: Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear.

3.2: : Use functions to model relationships between quantities.

8.F.14: : Students will: Construct a function to model a linear relationship between two quantities. 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. 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.15: : Students will: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). 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.16: : Students will: Verify experimentally the properties of rotations, reflections, and translations:

8.G.16.a: : Lines are taken to lines, and line segments are taken to line segments of the same length.

8.G.16.b: : Angles are taken to angles of the same measure.

8.G.16.c: : Parallel lines are taken to parallel lines.

8.G.17: : Students will: 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; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.18: : Students will: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.19: : Students will: 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; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.20: : Students will: 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.

4.2: : Understand and apply the Pythagorean Theorem.

8.G.21: : Students will: Explain a proof of the Pythagorean Theorem and its converse.

8.G.22: : Students will: 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.23: : Students will: 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.24: : Students will: Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.

8.SP: : Statistics and Probability

5.1: : Investigate patterns of association in bivariate data.

8.SP.25: : Students will: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.26: : Students will: 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.27: : Students will: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

8.SP.28: : Students will: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Correlation last revised: 9/16/2020

Alabama - Mathematics: 8th Grade

Course of Study | Adopted: 2016

8.NS: : The Number System

8.EE: : Expressions and Equations

8.F: : Functions

8.G: : Geometry

8.SP: : Statistics and Probability