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# Pennsylvania Common Core Standards Eighth Grade Mathematics resources

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Expressions and Equations

Analyze and solve linear equations and pairs of simultaneous linear equations.

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

8.EE.7(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).

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Multistep Equations

Flip Charts Multistep Equations

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

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.

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Multistep Equations

Flip Charts Multistep Equations

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

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.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

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.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Understand the connections between proportional relationships, lines, and linear equations.

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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

8.EE.6. 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.

Flip Charts Math: Grade 7

Flip Charts Slope

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Work with radicals and integer exponents.

8.EE.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^-5 = 3^-3 = 1/3^3 = 1/27.

Flip Charts Exponents, Factors & Multiples

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

8.EE.2. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that square root of 2 is irrational.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

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 10^8 and the population of the world as 7 times 10^9, and determine that the world population is more than 20 times larger.

Flip Charts Exponents, Factors & Multiples

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

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.

Flip Charts Exponents, Factors & Multiples

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

Functions

Use functions to model relationships between quantities.

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.

Flip Charts Math: Grade 7

Flip Charts Slope

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Define, evaluate, and compare 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.

Flip Charts Math: Grade 7

Flip Charts Slope

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

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 = s^2 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Geometry

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

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

Flip Charts Finding Volume

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

Understand and apply the Pythagorean Theorem.

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.

Flip Charts Math: Grade 7

Flip Charts The Pythagorean Theorem

Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

Understand congruence and similarity using physical models, transparencies, or geometry software.

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.

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

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

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

8.G.1(c) Parallel lines are taken to parallel lines.

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

8.G.2. 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.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles

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.

Flip Charts Math Grade 8

Flip Charts Plane Geometry

The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.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.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers

Statistics and Probability

Investigate patterns of association in bivariate data.

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.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

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.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Mathematical Practices

MP.1. Make sense of problems and persevere in solving them.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

MP.2. Reason abstractly and quantitatively.

Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes