Common Core State Standards - Mathematics: 8th Grade

  • Common Core State Standards     Adopted: 2011

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below to go to the Gizmo Details page.

8.NS: The Number System

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 (e.g., Square root of 2). For example, by truncating the decimal expansion of square root of 2, show that it is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

Circle: Circumference and Area
Ordering and Approximating Square Roots

8.EE: Expressions & Equations

8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 squared × 3 to the -5 = 3 to the?3 = 1/(3 to the 3) = 1/27.

Exponents and Power Rules

8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Direct Variation
Estimating Population Size

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

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.

Modeling and Solving Two-Step Equations
Solving Equations with Decimals
Solving Two-Step Equations

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.

Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems

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. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Solving Linear Systems by Graphing
Systems of Linear Equations - Activity A

8.EE.8.c: Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Modeling Linear Systems - Activity A

8.F: Functions

8.F.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

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Using Tables, Rules and Graphs

8.F.3: 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. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

Linear Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

8.F.4: 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.

Distance-Time Graphs
Modeling Linear Systems - Activity A
Simple and Compound Interest

8.F.5: 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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions

8.G: Geometry

8.G.1: Verify experimentally the properties of rotations, reflections, and translations:

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

Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Translations

8.G.1.b: Angles are taken to angles of the same measure.

Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Translations

8.G.1.c: Parallel lines are taken to parallel lines.

Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Translations

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

Dilations
Reflections
Translations

8.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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Investigating Angle Theorems - Activity A
Polygon Angle Sum - Activity B
Similar Polygons
Triangle Angle Sum - Activity A

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

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

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.

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

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

Distance Formula - Activity A

8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Balancing Blocks (Volume)
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

8.SP: Statistics & Probability

8.SP.1: 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.

Scatter Plots - Activity A
Solving Using Trend Lines

8.SP.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.

Correlation
Solving Using Trend Lines

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. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

Determining a Spring Constant

Content correlation last revised: 12/10/2010