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Tennessee Math Standards - Algebra
MathScore aligns to the Tennessee Math Standards for Algebra. 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.
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Numbers and Operations
3102.1.1 Develop meaning for mathematical vocabulary.3102.1.2 Use the terminology of mathematics correctly. (Algebraic Terms )
3102.1.3 Understand and use mathematical symbols, notation, and common mathematical abbreviations correctly.
3102.1.4 Write a rule with variables that expresses a pattern. (Function Tables , Function Tables 2 )
3102.1.5 Use formulas, equations, and inequalities to solve real-world problems including time/rate/distance, percent increase/decrease, ratio/proportion, and mixture problems. (Percentage Change , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
3102.1.6 Use a variety of strategies to estimate and compute solutions, including real-world problems.
3102.1.7 Identify missing or irrelevant information in problems.
3102.1.8 Recognize and perform multiple steps in problem solving when necessary. (Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Two Variable Equations )
3102.1.9 Identify and use properties of the real numbers (including commutative, associative, distributive, inverse, identity element, closure, reflexive, symmetric, transitive, operation properties of equality).
3102.1.10 Use algebraic properties to develop a valid mathematical argument.
3102.1.11 Use manipulatives to model algebraic concepts. (Requires outside materials )
3102.1.12 Create and work flexibly among representations of relations (including verbal, equations, tables, mappings, graphs).
3102.1.13 Change from one representation of a relation to another representation, for example, change from a verbal description to a graph. (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Applied Linear Equations 1 , Applied Linear Equations 2 , Nonlinear Functions )
3102.1.14 Apply graphical transformations that occur when changes are made to coefficients and constants in functions.
3102.1.15 Apply arithmetic concepts in algebraic contexts.
3102.1.16 Understand and express the meaning of the slope and y-intercept of linear functions in real-world contexts.
3102.1.17 Connect the study of algebra to the historical development of algebra.
3102.1.18 Translate syntax of technology to appropriate mathematical notation.
3102.1.19 Recognize and practice appropriate use of technology in representations and in problem solving.
3102.1.20 Estimate solutions to evaluate the reasonableness of results and to check technological computation.
Algebra
3102.2.1 Recognize and use like terms to simplify expressions. (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Binomial Fraction Simplification , Polynomial Fraction Simplification )3102.2.2 Apply the order of operations to simplify and evaluate algebraic expressions. (Variable Substitution , Variable Substitution 2 , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
3102.2.3 Operate with and simplify radicals (index 2, 3, n) and radical expressions including rational numbers and variables in the radicand. (Roots Of Exponential Expressions , Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
3102.2.4 Operate efficiently with both rational and irrational numbers.
3102.2.5 Perform operations with numbers in scientific notation (multiply, divide, powers). (Scientific Notation 2 )
3102.2.6 Use appropriate technologies to apply scientific notation to real-world problems.
3102.2.7 Identify the subsets in the real number system and understand their relationships.
3102.2.8 Use multiple strategies to approximate the value of an irrational number including irrational square roots and including location on the real number line. (Estimating Square Roots )
Geometry
3102.3.1 Recognize and extend arithmetic and geometric sequences. (Patterns: Numbers )3102.3.2 Explore patterns including Pascal's Triangle and the Fibonacci sequence.
3102.3.3 Justify correct results of algebraic procedures using extension of properties of real numbers to algebraic expressions.
3102.3.4 Simplify expressions using exponent rules including negative exponents and zero exponents. (Simplifying Algebraic Expressions 2 , Exponents Of Fractional Bases , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
3102.3.5 Add, subtract, and multiply polynomials including squaring a binomial. (Simplifying Algebraic Expressions , Foil Method )
3102.3.6 Find the quotient of a polynomial and a monomial.
3102.3.7 Use various models (including area models) to represent products of polynomials. (Requires outside materials )
3102.3.8 Find the GCF of the terms in a polynomial. (Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification )
3102.3.9 Find two binomial factors of a quadratic expression. (Trinomial Factoring )
3102.3.10 Add, subtract, multiply, and divide rational expressions and simplify results.
3102.3.11 Solve multi-step linear equations with one variable. (Single Variable Equations 2 , Single Variable Equations 3 )
3102.3.12 Recognize and articulate when an equation has no solution, a single solution, or all real numbers as solutions.
3102.3.13 Solve multi-step linear inequalities with one variable and graph the solution on a number line. (Single Variable Inequalities , Number Line Inequalities )
3102.3.14 Solve absolute value equations and inequalities (including compound inequalities) with one variable and graph their solutions on a number line. (Absolute Value 1 , Absolute Value 2 , Absolute Value Equations )
3102.3.15 Determine domain and range of a relation and articulate restrictions imposed either by the operations or by the real life situation that the function represents. (Domain and Range )
3102.3.16 Determine if a relation is a function from its graph or from a set of ordered pairs.
3102.3.17 Recognize "families" of functions. (Nonlinear Functions )
3102.3.18 Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions. Use technology where appropriate.
3102.3.19 Explore the characteristics of graphs of various nonlinear relations and functions including inverse variation, quadratic, and square root function. Use technology where appropriate. (Nonlinear Functions )
3102.3.20 Understand that a linear equation has a constant rate of change called slope and represent slope in various forms. (Determining Slope )
3102.3.21 Determine the equation of a line using given information including a point and slope, two points, a point and a line parallel or perpendicular, graph, intercepts. (Graphs to Linear Equations , Graphs to Linear Equations 2 , Applied Linear Equations 1 , Applied Linear Equations 2 )
3102.3.22 Express the equation of a line in standard form, slope-intercept, and point-slope form. (Graphs to Linear Equations 2 )
3102.3.23 Determine the graph of a linear equation including those that depict contextual situations.
3102.3.24 Interpret the changes in the slope-intercept form and graph of a linear equation by looking at different values of the parameters, m and b.
3102.3.25 Find function values using f(x) notation or graphs.
3102.3.26 Graph linear inequalities on the coordinate plane and identify regions of the graph containing ordered pairs in the solution.
3102.3.27 Determine the number of solutions for a system of linear equations (0, 1, or infinitely many solutions).
3102.3.28 Solve systems of linear equations graphically, algebraically, and with technology. (System of Equations Substitution , System of Equations Addition )
3102.3.29 Solve contextual problems involving systems of linear equations or inequalities and interpret solutions in context. (Age Problems )
3102.3.30 Solve quadratic equations using multiple methods: factoring, graphing, quadratic formula, or square root principle. (Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts )
3102.3.31 Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.
3102.3.32 Recognize the connection among factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions. (Quadratic X-Intercepts , Quadratic Zero Equations , Quadratic Formula )
3102.3.33 Recognize data that can be modeled by an exponential function.
3102.3.34 Graph exponential functions in the form y = a(bx) where b ≠ 0.
3102.3.35 Apply growth/decay and simple/compound interest formulas to solve contextual problems. (Simple Interest , Compound Interest , Continuous Compound Interest )
Measurement
3102.4.1 Using algebraic expressions solve for measures in geometric figures as well as for perimeter, area, and volume. (Quadrilateral Angles , Triangle Area , Triangle Area 2 , Parallelogram Area , Perimeter , Rectangular Solids , Rectangular Solids 2 , Cylinders , Triangle Angles 2 , Irregular Shape Areas , Solving For Angles , Polygon Angles , Angle Measurements , Trapezoids , Angle Measurements 2 )3102.4.2 Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations. (Pythagorean Theorem )
3102.4.3 Understand horizontal/vertical distance in a coordinate system as absolute value of the difference between coordinates; develop the distance formula for a coordinate plane using the Pythagorean Theorem. (Line Segments )
3102.4.4 Develop the midpoint formula for segments on a number line or in the coordinate plane.
3102.4.5 Use dimensional analysis to convert rates and measurements both within a system and between systems and check the appropriateness of the solution. (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion , Area and Volume Conversions )
Data Analysis and Probability
3102.5.1 Identify patterns or trends in data.3102.5.2 Develop a meaning for and identify outliers in a data set and verify.
3102.5.3 When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range.
3102.5.4 Explore quartiles, deciles, and percentiles of a distribution.
3102.5.5 Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables). (Stem And Leaf Plots , Bar Graphs , Line Graphs )
3102.5.6 Draw qualitative graphs of functions and describe a general trend or shape.
3102.5.7 Compare two data sets using graphs and descriptive statistics.
3102.5.8 Examine real-world graphical relationship (including scatter-plots) to determine type of relationship (linear or nonlinear) and any association (positive, negative or none) between the variables of the data set.
3102.5.9 Determine an equation for a line that fits real-world linear data; interpret the meaning of the slope and y-intercept in context of the data.
3102.5.10 Using technology with a set of contextual linear data to examine the line of best fit; determine and interpret the correlation coefficient.
3102.5.11 Use an equation that fits data to make a prediction.
3102.5.12 Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.
3102.5.13 Determine the complement of an event and the probability of that complement. (Probability , Probability 2 )
3102.5.14 Determine if two events are independent or dependent. (Object Picking Probability )
3102.5.15 Explore joint and conditional probability. (Object Picking Probability )
3102.5.16 Identify situations for which the Law of Large Numbers applies.
3102.5.17 Perform simulations to estimate probabilities.
3102.5.18 Make informed decisions about practical situations using probability concepts.
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