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8Grade 8 Standards
Top Mathematicians
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Two-dimensional Shapes
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8.TDS.111.28.b.10A
Generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane.
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8.60Reflections: Graph the Image5
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8.62Dilations Graph the Image5
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8.71Rotations: Graph the Image10
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8.72Translations: Graph the Image5
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8.TDS.111.28.b.10B
Differentiate between transformations that preserve congruence and those that do not.
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8.TDS.111.28.b.10C
Explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90�, 180�, 270�, and 360� as applied to two-dimensional shapes on a coordinate plane using an algebraic representation.
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8.57Identify Reflections, Rotations and Translations5
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8.60Reflections: Graph the Image5
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8.61Reflections Find the Coordinates10
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8.62Dilations Graph the Image5
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8.63Dilations: Find the Coordinates5
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8.71Rotations: Graph the Image10
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8.72Translations: Graph the Image5
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8.73Translations Find the Coordinates10
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8.74Rotations Find the Coordinates10
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8.TDS.111.28.b.10D
Model the effect on linear and area measurements of dilated two-dimensional shapes.
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8.TDS.111.28.b.10A
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Measurement and Data
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8.MD.111.28.b.11A
Construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data.
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8.22Scatter Plots5
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8.MD.111.28.b.11B
Determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points.
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8.MD.111.28.b.11C
Simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected.
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8.MD.111.28.b.11A
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Personal Financial Literacy
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8.PFL.111.28.b.12A
Solve real-world problems comparing how interest rate and loan length affect the cost of credit.
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8.PFL.111.28.b.12B
Calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator.
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8.PFL.111.28.b.12C
Explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time.
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8.PFL.111.28.b.12D
Calculate and compare simple interest and compound interest earnings.
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8.13Compound Interest15
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8.14Simple Interest15
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8.PFL.111.28.b.12E
Identify and explain the advantages and disadvantages of different payment methods.
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8.PFL.111.28.b.12F
Analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility.
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8.PFL.111.28.b.12G
Estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college.
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8.PFL.111.28.b.12A
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Mathematical Process Standards
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8.MPS.111.28.b.1A
Apply mathematics to problems arising in everyday life, society, and the workplace.
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8.1Solve a System of Equations Using Elimination15
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8.2Algebra: Linear Function10
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8.3Solve a System of Equations Using Substitution15
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8.4Find the Constant of Variation15
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8.5Solve a System of Equations by Graphing5
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8.6Find the Constant of Variation with Tables15
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8.7Algebra: Linear Function with Intercepts10
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8.8Graph a Proportional Relationship5
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8.9Proportional Relationships15
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8.10Find the Proportional Relationship15
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8.11Unit Rates10
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8.12Solve Multi Step Equations5
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8.13Compound Interest15
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8.14Simple Interest15
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8.15Convert Between Decimals and Fractions or Mixed Numbers15
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8.16Solve One-Step Linear Equations5
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8.17Solve Two-Step Linear Equations5
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8.18Identify Linear and Nonlinear Functions5
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8.MPS.111.28.b.1B
Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
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8.1Solve a System of Equations Using Elimination15
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8.6Find the Constant of Variation with Tables15
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8.12Solve Multi Step Equations5
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8.17Solve Two-Step Linear Equations5
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8.18Identify Linear and Nonlinear Functions5
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8.19Interpret Histograms5
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8.20Interpret Stem and Leaf Plots10
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8.21Graph a Line Using Slope10
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8.22Scatter Plots5
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8.23Find the Slope of a Graph10
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8.24Solve a System of Equations Using Elimination5
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8.25Find the Number of Solutions to a System of Equations5
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8.26Solve a System of Equations Using Substitution5
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8.27Write a Rule for a Function Table10
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8.MPS.111.28.b.1C
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
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8.28Simplify Variable Expressions Using Properties10
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8.29Distributive Property5
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8.30Properties of Addition and Multiplication15
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8.31Multiplication with Exponents10
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8.32Multiplication and Division with Exponents10
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8.33Multiply and Divide Monomials10
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8.34Evaluate Variable Expressions with Squares and Square Roots10
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8.35Evaluate Negative Exponents10
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8.36Exponents with Decimal and Fractional Bases15
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8.37Exponents: Solve for the Variable10
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8.38Exponents with Negative Bases10
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8.39Division with Exponents10
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8.40Simplify Expressions Involving Exponents5
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8.41Understanding Negative Exponents5
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8.42Estimate Positive and Negative Square Roots10
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8.43Estimate Cube Roots10
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8.44Cube Roots of Perfect Cubes10
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8.45Relationship Between Squares and Square Roots10
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8.46Positive and Negative Square Roots10
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8.47Square Roots of Perfect Squares5
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8.49Solve Equations Involving Squares and Square Roots10
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8.MPS.111.28.b.1D
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
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8.18Identify Linear and Nonlinear Functions5
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8.31Multiplication with Exponents10
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8.33Multiply and Divide Monomials10
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8.41Understanding Negative Exponents5
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8.51Classify a System of Equations by Graphing10
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8.52Classify a System of Equations5
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8.53Identify Rational and Irrational Numbers5
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8.54Understanding Exponents10
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8.55Ratios and Proportions10
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8.56Ratios and Proportions10
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8.57Identify Reflections, Rotations and Translations5
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8.58Complementary, Supplementary, Vertical and Adjacent Angles5
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8.59Congruence Statements and Corresponding Parts5
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8.60Reflections: Graph the Image5
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8.61Reflections Find the Coordinates10
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8.62Dilations Graph the Image5
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8.63Dilations: Find the Coordinates5
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8.64Powers of Monomials5
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8.65Powers of Monomials10
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8.66Divide Monomials5
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8.67Combination and Permutation Notation10
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8.MPS.111.28.b.1E
Create and use representations to organize, record, and communicate mathematical ideas.
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8.5Solve a System of Equations by Graphing5
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8.6Find the Constant of Variation with Tables15
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8.8Graph a Proportional Relationship5
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8.18Identify Linear and Nonlinear Functions5
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8.19Interpret Histograms5
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8.20Interpret Stem and Leaf Plots10
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8.21Graph a Line Using Slope10
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8.22Scatter Plots5
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8.23Find the Slope of a Graph10
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8.27Write a Rule for a Function Table10
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8.40Simplify Expressions Involving Exponents5
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8.51Classify a System of Equations by Graphing10
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8.60Reflections: Graph the Image5
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8.61Reflections Find the Coordinates10
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8.62Dilations Graph the Image5
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8.68Find the Constant of Variation Graphs5
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8.69Find Points on a Function Graph5
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8.70Constant Rate of Change5
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8.71Rotations: Graph the Image10
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8.72Translations: Graph the Image5
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8.73Translations Find the Coordinates10
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8.74Rotations Find the Coordinates10
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8.75Create Histograms5
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8.76Create Frequency Charts5
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8.78Solutions to a System of Equations by Graphing10
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8.79Graph a Line from a Function Table10
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8.80Graph a Line from an Equation10
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8.81Graph a Line from an Equation Using Algebra10
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8.82Complete a Function Table10
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8.MPS.111.28.b.1F
Analyze mathematical relationships to connect and communicate mathematical ideas.
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8.6Find the Constant of Variation with Tables15
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8.15Convert Between Decimals and Fractions or Mixed Numbers15
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8.18Identify Linear and Nonlinear Functions5
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8.28Simplify Variable Expressions Using Properties10
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8.34Evaluate Variable Expressions with Squares and Square Roots10
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8.40Simplify Expressions Involving Exponents5
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8.41Understanding Negative Exponents5
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8.42Estimate Positive and Negative Square Roots10
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8.43Estimate Cube Roots10
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8.45Relationship Between Squares and Square Roots10
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8.46Positive and Negative Square Roots10
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8.47Square Roots of Perfect Squares5
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8.49Solve Equations Involving Squares and Square Roots10
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8.54Understanding Exponents10
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8.65Powers of Monomials10
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8.83Solving Proportions10
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8.84Power Rule5
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8.85Evaluate Exponents10
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8.MPS.111.28.b.1G
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
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8.28Simplify Variable Expressions Using Properties10
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8.29Distributive Property5
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8.30Properties of Addition and Multiplication15
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8.86Divisibility Rules20
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8.MPS.111.28.b.1A
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Number and Operations
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8.NO.111.28.b.2A
Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers.
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8.87Identify Angles by Type5
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8.NO.111.28.b.2B
Approximate the value of an irrational number, including p and square roots of numbers less than 225, and locate that rational number approximation on a number line.
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8.42Estimate Positive and Negative Square Roots10
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8.88Parts of a Circle5
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8.89Circles5
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8.90Quarter Circles5
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8.NO.111.28.b.2C
Convert between standard decimal notation and scientific notation.
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8.NO.111.28.b.2D
Order a set of real numbers arising from mathematical and real-world contexts.
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8.NO.111.28.b.2A
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Proportionality
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8.RP.111.28.b.3A
Generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation.
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8.62Dilations Graph the Image5
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8.63Dilations: Find the Coordinates5
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8.97Similar and Congruent Figures5
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8.98Similar Figures Side Lengths and Angle Measures5
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8.99Similar Solids5
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8.RP.111.28.b.3B
Compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane.
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8.RP.111.28.b.3C
Use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
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8.62Dilations Graph the Image5
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8.63Dilations: Find the Coordinates5
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8.102Scale Drawings and Scale Factors15
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8.RP.111.28.b.4A
Use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line.
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8.21Graph a Line Using Slope10
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8.23Find the Slope of a Graph10
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8.80Graph a Line from an Equation10
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8.103Find Slope from Two Points15
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8.104Find Slope from an Equation10
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8.RP.111.28.b.4B
Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.
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8.4Find the Constant of Variation15
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8.6Find the Constant of Variation with Tables15
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8.8Graph a Proportional Relationship5
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8.9Proportional Relationships15
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8.10Find the Proportional Relationship15
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8.11Unit Rates10
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8.55Ratios and Proportions10
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8.56Ratios and Proportions10
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8.68Find the Constant of Variation Graphs5
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8.70Constant Rate of Change5
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8.83Solving Proportions10
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8.105Solving Proportions10
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8.RP.111.28.b.4C
Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
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8.6Find the Constant of Variation with Tables15
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8.21Graph a Line Using Slope10
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8.23Find the Slope of a Graph10
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8.68Find the Constant of Variation Graphs5
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8.70Constant Rate of Change5
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8.79Graph a Line from a Function Table10
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8.RP.111.28.b.5A
Represent linear proportional situations with tables, graphs, and equations in the form of y = kx.
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8.2Algebra: Linear Function10
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8.6Find the Constant of Variation with Tables15
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8.23Find the Slope of a Graph10
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8.68Find the Constant of Variation Graphs5
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8.RP.111.28.b.5B
Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ? 0.
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8.2Algebra: Linear Function10
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8.7Algebra: Linear Function with Intercepts10
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8.16Solve One-Step Linear Equations5
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8.17Solve Two-Step Linear Equations5
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8.18Identify Linear and Nonlinear Functions5
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8.21Graph a Line Using Slope10
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8.79Graph a Line from a Function Table10
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8.80Graph a Line from an Equation10
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8.81Graph a Line from an Equation Using Algebra10
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8.RP.111.28.b.5C
Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation.
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8.22Scatter Plots5
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8.RP.111.28.b.5D
Use a trend line that approximates the linear relationship between bivariate sets of data to make predictions.
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8.RP.111.28.b.5E
Solve problems involving direct variation.
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8.9Proportional Relationships15
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8.10Find the Proportional Relationship15
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8.23Find the Slope of a Graph10
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8.68Find the Constant of Variation Graphs5
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8.70Constant Rate of Change5
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8.83Solving Proportions10
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8.106Rate of Change10
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8.RP.111.28.b.5F
Distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ? 0.
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8.RP.111.28.b.5G
Identify functions using sets of ordered pairs, tables, mappings, and graphs.
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8.RP.111.28.b.5H
Identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems.
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8.RP.111.28.b.5I
Write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.
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8.23Find the Slope of a Graph10
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8.103Find Slope from Two Points15
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8.104Find Slope from an Equation10
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8.RP.111.28.b.3A
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Expressions, Equations, and Relationships
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8.EE.111.28.b.6A
Describe the volume formula V = Bh of a cylinder in terms of its base area and its height.
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8.108Volume of Prisms and Cylinders5
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8.EE.111.28.b.6B
Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.
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8.EE.111.28.b.6C
Use models and diagrams to explain the Pythagorean theorem.
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8.EE.111.28.b.7A
Solve problems involving the volume of cylinders, cones, and spheres.
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8.100Volume and Surface Area of Spheres5
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8.108Volume of Prisms and Cylinders5
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8.109Volume of Pyramids and Cones5
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8.EE.111.28.b.7B
Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
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8.100Volume and Surface Area of Spheres5
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8.110Surface Area5
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8.EE.111.28.b.7C
Use the Pythagorean Theorem and its converse to solve problems.
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8.101Pythagorean Theorem: Find the Perimeter5
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8.111Pythagorean Theorem: Find the Hypotenuse5
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8.112Pythagorean Theorem: Find the Leg5
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8.113Pythagorean Theorem5
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8.114Converse of the Pythagorean Theorem5
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8.EE.111.28.b.7D
Determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
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8.115Find the Distance Between Two Points10
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8.EE.111.28.b.8A
Write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
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8.EE.111.28.b.8B
Write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.
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8.EE.111.28.b.8C
Model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants.
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8.12Solve Multi Step Equations5
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8.16Solve One-Step Linear Equations5
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8.17Solve Two-Step Linear Equations5
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8.28Simplify Variable Expressions Using Properties10
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8.34Evaluate Variable Expressions with Squares and Square Roots10
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8.37Exponents: Solve for the Variable10
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8.49Solve Equations Involving Squares and Square Roots10
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8.116Solve Equations Involving Like Terms10
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8.EE.111.28.b.8D
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
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8.EE.111.28.b.9
The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.
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8.EE.111.28.b.6A