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## Tennessee Math Standards - 8th Grade

MathScore aligns to the Tennessee Math Standards for 8th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.

View the Tennessee Math Standards at other levels.

## Numbers and Operations

8.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
a. recognize the place value of a given digit; (Place Value , Decimal Place Value )
b. use exponents to express a monomial written in expanded form; (Exponent Basics )
c. determine the square root of perfect squares; (Perfect Squares )
d. use a variety of models to demonstrate the relationships within the real number system (e.g., Venn diagrams, webs);
e. work flexibly with fractions, decimals, and percents to solve problems;
f. compare and order fractions, decimals, and percents; (Compare Mixed Values , Compare Mixed Values 2 , Fraction Comparison , Compare Decimals )
g. connect whole numbers, fractions, decimals, percents and integers to locations on the number line; (Positive Number Line , Number Line , Compare Integers )
h. develop meaning for percents greater than 100 and less than one; (Percent of Quantity )
i. understand and use ratios and proportions to represent quantitative relationships; (Proportions 1 , Ratios )
j. recognize and use exponential, scientific, and calculator notation to represent large numbers in real-world situations; (Scientific Notation )
k. demonstrate understanding of opposites, reciprocals, and integers;
l. identify the opposite of a rational number;
m. use concrete, pictorial, and symbolic representations of integers; (Compare Integers )
n. apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime). (Prime Factoring , Prime Factoring 2 , Greatest Common Factor , Least Common Multiple , Divisibility Rules )
8.1.2 Understand operations and how they relate to one another.
a. understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;
b. apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals; (Integer Equivalence )
c. use the distributive property to simplify computations with integers, fractions, and decimals; (Distributive Property , Distributive Property 2 )
d. apply order of operations in computing with rational numbers; (Using Parentheses , Order Of Operations )
e. understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. (Missing Factor , Missing Term , Missing Operator , Single Variable Equations , Estimating Square Roots )
8.1.3 Solve problems, compute fluently, and make reasonable estimates.
a. select and use appropriate methods and tools for computing with whole numbers, fractions, decimals, percents, and integers in problem-solving situations (e.g., mental computation, estimation, calculators, computers, paper and pencil); (Making Change , Unit Cost , Fraction Word Problems , Fraction Word Problems 2 , Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity , Integers In Word Problems )
b. develop and analyze procedures for computing with fractions, decimals, and integers; (Fraction Addition , Fraction Subtraction , Fraction Multiplication , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division , Fractions to Decimals , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence )
c. develop and use strategies to estimate the results of rational number computations in real-world situations; (Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
d. judge the reasonableness of the results of rational number estimates and computations;
e. solve one-step real-world problems involving whole numbers, fractions, decimals, and percents; (Making Change , Unit Cost , Fraction Word Problems , Fraction Word Problems 2 , Purchases At Stores , Restaurant Bills , Commissions , Simple Interest , Compound Interest )
f. raise rational numbers to whole number powers; (Exponent Basics , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases )
g. solve multi-step real-world problems involving whole numbers, fractions, decimals, and percents; (Commissions )
h. develop, analyze, and explain methods for solving problems involving proportions (e.g., scaling, finding equivalent ratios); (Unit Cost , Proportions 1 , Proportions 2 , Distance, Rate, and Time )
i. calculate rates involving cost per unit to determine the best buy

## Algebra

8.2.1 Understand patterns, relations, and functions.
a. represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible symbolic rules; (Function Tables , Function Tables 2 )
b. develop understanding for arithmetic and geometric sequences; (Patterns: Numbers , Patterns: Shapes )
c. relate and compare different forms of representation for a relationship;
d. identify functions as linear or nonlinear;
e. compare and contrast properties of functions from tables, graphs, or equations. (Nonlinear Functions )
8.2.2 Represent and analyze mathematical situations and structures using algebraic symbols.
a. formulate multi-step equations that represent relationships and real-world situations;
b. develop meaning for intercept and slope; (Determining Slope )
c. use symbolic algebra to represent situations and solve problems; (Algebraic Word Problems , Mixture Word Problems , Work Word Problems )
d. use a variety of forms to represent linear relationships; (Linear Equations , Graphs to Linear Equations , Graphs to Linear Equations 2 )
e. recognize and generate equivalent forms for simple algebraic expressions; (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Binomial Fraction Simplification , Simplifying Radical Expressions )
f. evaluate a first-degree algebraic expression given values for two or more variables; (Distance, Rate, and Time )
g. solve one- and two-step linear equations involving integers; (Single Variable Equations , Single Variable Equations 2 )
h. use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper);
i. apply given formulas to solve real-world problems; (Triangle Area 2 , Rectangular Solids 2 , Simple Interest , Compound Interest , Continuous Compound Interest , Distance, Rate, and Time , Train Problems )
j. solve one-step linear inequalities; (Single Variable Inequalities )
k. identify the graph of a linear equation; (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 )
l. identify the graphical representation of the solution to a one-variable linear inequality; (Number Line Inequalities )
m. develop understanding for particular values of patterns, relationships, and functions (e.g., x- and y- intercepts, slope, maximum and minimum values).
8.2.3 Use mathematical models to represent and understand quantitative relationships.
a. use a variety of representations to solve real-world problems (e.g., graphs, tables, equations).
8.2.4 Analyze change in various contexts.
a. compare linear relationships to non-linear relationships;
b. develop meaning for rate of change in real-world situations.

## Geometry

8.3.1 Analyze characteristics and properties of two- and three-dimensional geometric figures.
a. describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
b. understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (Identifying Angles )
c. solve problems using angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding); (Solving For Angles , Angle Measurements , Angle Measurements 2 )
d. determine the measure of an angle of a triangle given the measures of the other two angles; (Triangle Angles )
e. understand relationships among the angles and side lengths of similar geometric figures; (Proportions 2 )
f. determine congruence of line segments, angles, and polygons by direct comparison of given attributes;
g. develop understanding of the Pythagorean theorem. (Pythagorean Theorem )
8.3.2 Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
a. graph points in the coordinate system. (Ordered Pairs )
8.3.3 Apply transformations and use symmetry to analyze mathematical situations.
a. describe sizes, positions, and orientations of shapes under transformations (e.g., rotations, translations, reflections, dilations);
b. relate symmetry and congruence to reflections about a line.
8.3.4 Use visualization, spatial reasoning, and geometric modeling to solve problems.
a. use appropriate tools and methods to draw geometric objects with specified properties, (e.g., side lengths, angle measure);
b. use two-dimensional representations of three-dimensional objects to visualize;
c. use visualization and spatial reasoning to solve real-world problems;
d. recognize and apply geometric ideas and relationships such as tessellations in areas outside the mathematics classroom (e.g., art, science, everyday life)

## Measurement

8.4.1 Understand measurable attributes of objects and the units, systems, and processes of measurement.
a. understand both metric and customary systems of measurement;
b. understand relationships among units and convert from one unit to another within the same system; (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Area and Volume Conversions )
c. understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume.
8.4.2 Apply appropriate techniques, tools, and formulas to determine measurements.
a. use a variety of strategies to estimate length, perimeter, circumference, area, and volume;
b. select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision;
c. apply formulas and/or other strategies to solve problems involving perimeter, circumference of circles, and the area of triangles, parallelograms, trapezoids, and circles; (Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Circle Area , Circle Circumference , Trapezoids )
d. find area of complex and irregular shapes; (Irregular Shape Areas , Perimeter and Area of Composite Figures )
e. apply given formulas to find volume of selected prisms and cylinders; (Rectangular Solids , Triangular Prisms , Cylinders )
f. compare and contrast the volumes of a variety of geometric solids;
g. solve problems involving rate/time/distance (i.e., d = rt); (Distance, Rate, and Time , Train Problems )
h. solve problems involving scale factors using ratio and proportion; (Area And Volume Proportions )
i. solve real-world problems using the Pythagorean Theorem;
j. construct tables and graphs to represent rates of change;
k. find measures using proportional relationships and properties of similar figures; (Triangle Angles 2 , Solving For Angles , Proportions 2 )
l. determine the measure of angles by applying angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding) (Polygon Angles , Angle Measurements , Angle Measurements 2 )

## Data Analysis and Probability

8.5.1 Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.
a. formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g., random sampling, simulations);
b. select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatterplots).
8.5.2 Select and use appropriate statistical methods to analyze data.
a. find, use, and interpret measures of center and spread (e.g., mean, interquartile range); (Mean, Median, Mode , Stem And Leaf Plots )
b. develop meaning for frequency, distribution, and outliers;
c. discuss and understand the relationship between data sets and their graphical representations (e.g., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots).
8.5.3 Develop and evaluate inferences and predictions that are based on data.
a. make conjectures and predictions based on data; (Batting Averages )
b. recognize misleading presentations of data;
c. develop meaning for lines of best fit;
d. determine an appropriate sample to test a hypothesis;
e. make conjectures to formulate new questions for future studies.
8.5.4 Understand and apply basic concepts of probability.
a. develop meaning of mutually exclusive events; (Probability 2 )
b. connect the symbolic representation of a probability to an experiment;
c. use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models); (Probability 2 )
d. distinguish between theoretical and experimental probability;
e. find the probability of dependent and independent events (Object Picking Probability )