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- 8th Grade
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.
Circumference and Area of Circles
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.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
8.EE.3: Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.
Unit Conversions 2 - Scientific Notation and Significant Digits
8.EE.4: 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.
Unit Conversions 2 - Scientific Notation and Significant Digits
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 and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
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 on the Number Line
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 (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
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 (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
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.
Cat and Mouse (Modeling with Linear Systems) - Activity B
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
Points, Lines, and Equations
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
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B
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.
Cat and Mouse (Modeling with Linear Systems) - Activity B
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
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
Rotations, Reflections, and Translations
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 B
Similar Figures - Activity A
Triangle Angle Sum - Activity B
8.G.6: Explain a proof of the Pythagorean Theorem and its converse.
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
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.
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Distance Formula - Activity A
Pythagorean Theorem - Activity B
8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity B
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.
Correlation
Solving Using Trend Lines
Trends in Scatter Plots
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.
Content correlation last revised: 12/10/2010