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# Colorado Standards Eighth Grade Mathematics resources

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Number Sense, Properties, and Operations

8.1.1. In the real number system, rational and irrational numbers are in one to one correspondence to points on the number line. Students can:

8.1.1.a. Define irrational numbers.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

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

8.1.1.b. Demonstrate informally that every number has a decimal expansion. (CCSS: 8.NS.1)

8.1.1.b.i. For rational numbers show that the decimal expansion repeats eventually. (CCSS: 8.NS.1)

Flip Charts Math Grade 8

Flip Charts The Real Numbers

8.1.1.b.ii. Convert a decimal expansion which repeats eventually into a rational number. (CCSS: 8.NS.1)

Flip Charts All About Percents

Flip Charts Applying Percents

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Numbers and percents

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

8.1.1.d. Apply the properties of integer exponents to generate equivalent numerical expressions. (CCSS: 8.EE.1)

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

8.1.1.e. 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. (CCSS: 8.EE.2)

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

8.1.1.f. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. (CCSS: 8.EE.2)

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

8.1.1.g. 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. (CCSS: 8.EE.3)

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

8.1.1.h. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. (CCSS: 8.EE.4)

8.1.1.h.i. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (CCSS: 8.EE.4)

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

8.1.1.h.ii. Interpret scientific notation that has been generated by technology. (CCSS: 8.EE.4)

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

Patterns, Functions, and Algebraic Structures

8.2.1. Linear functions model situations with a constant rate of change and can be represented numerically, algebraically, and graphically. Students can:

8.2.1.a. Describe the connections between proportional relationships, lines, and linear equations. (CCSS: 8.EE)

Flip Charts Math: Grade 7

Flip Charts Nonlinear Functions & Set Theory

Flip Charts Slope

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

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

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

8.2.1.b. Graph proportional relationships, interpreting the unit rate as the slope of the graph. (CCSS: 8.EE.5)

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

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

8.2.1.d. 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. (CCSS: 8.EE.6)

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

8.2.1.e. 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. (CCSS: 8.EE.6)

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

8.2.2. Properties of algebra and equality are used to solve linear equations and systems of equations. Students can:

8.2.2.a. Solve linear equations in one variable. (CCSS: 8.EE.7)

8.2.2.a.i. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. (CCSS: 8.EE.7a)

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

8.2.2.a.ii. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. (CCSS: 8.EE.7b)

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

8.2.2.b. Analyze and solve pairs of simultaneous linear equations. (CCSS: 8.EE.8)

8.2.2.b.i. Explain 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. (CCSS: 8.EE.8a)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

8.2.2.b.ii. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. (CCSS: 8.EE.8b)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

8.2.2.b.iii. Solve real-world and mathematical problems leading to two linear equations in two variables. (CCSS: 8.EE.8c)

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

8.2.3. Graphs, tables and equations can be used to distinguish between linear and nonlinear functions. Students can:

8.2.3.a. Define, evaluate, and compare functions. (CCSS: 8.F)

8.2.3.a.i. Define a function as a rule that assigns to each input exactly one output. (CCSS: 8.F.1)

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

8.2.3.a.ii. Show that the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (CCSS: 8.F.1)

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

8.2.3.a.iv. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. (CCSS: 8.F.3)

Flip Charts Math: Grade 7

Flip Charts Nonlinear Functions & Set Theory

Flip Charts Slope

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

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

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

8.2.3.b. Use functions to model relationships between quantities. (CCSS: 8.F)

8.2.3.b.ii. 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. (CCSS: 8.F.4)

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

8.2.3.b.iii. 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. (CCSS: 8.F.4)

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

8.2.3.b.iv. Describe qualitatively the functional relationship between two quantities by analyzing a graph. (CCSS: 8.F.5)

Quiz, Flash Cards, Worksheet, Game & Study Guide Nonlinear Functions and Set Theory

8.2.3.b.v. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (CCSS: 8.F.5)

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

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

Data Analysis, Statistics, and Probability

8.3.1. Visual displays and summary statistics of two-variable data condense the information in data sets into usable knowledge. Students can:

8.3.1.a. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. (CCSS: 8.SP.1)

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

8.3.1.b. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. (CCSS: 8.SP.1)

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

8.3.1.c. 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. (CCSS: 8.SP.2)

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

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

8.3.1.e. Explain patterns of association seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. (CCSS: 8.SP.4)

8.3.1.e.i. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. (CCSS: 8.SP.4)

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Shape, Dimension, and Geometric Relationships

8.4.1. Transformations of objects can be used to define the concepts of congruence and similarity. Students can:

8.4.1.a. Verify experimentally the properties of rotations, reflections, and translations. (CCSS: 8.G.1)

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

8.4.1.c. Demonstrate 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. (CCSS: 8.G.2)

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

8.4.1.e. Demonstrate 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. (CCSS: 8.G.4)

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 Ratios, proportions and percents

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

8.4.1.g. 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. (CCSS: 8.G.5)

Flip Charts Math Grade 8

Flip Charts Plane Geometry

8.4.2. Direct and indirect measurement can be used to describe and make comparisons. Students can:

8.4.2.b. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (CCSS: 8.G.7)

Flip Charts Math: Grade 7

Flip Charts The Pythagorean Theorem

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

8.4.2.d. State the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. (CCSS: 8.G.9)

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