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## CO.8.1.Number Sense, Properties, and Operations

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 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 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 Applying Percents
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)
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 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 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)
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)
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)
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

## CO.8.2.Patterns, Functions, and Algebraic Structures

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 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 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 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)
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)
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)

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)

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

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 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 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 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 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

## CO.8.3.Data Analysis, Statistics, and Probability

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)
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)
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)
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)

## CO.8.4.Shape, Dimension, and Geometric Relationships

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 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)
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 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)