IXL - Ohio ninth-grade math standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2003 Ohio Academic Content Standards 2003 Ohio Academic Content Standards

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9.1 Number, Number Sense and Operations

9.1.A Use scientific notation to express large numbers and numbers less than one.
- Scientific notation: Convert between standard and scientific notation (Algebra - W.1)
9.1.B Identify subsets of the real number system.
- Numbers: Classify numbers (Algebra - A.1)
9.1.C Apply properties of operations and the real number system, and justify when they hold for a set of numbers.
9 Number and Number Systems
9.1.C.1 Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.
9.1.D Connect physical, verbal and symbolic representations of integers, rational numbers and irrational numbers.
- Numbers: Number lines (Algebra - A.4)
9.1.E Compare, order and determine equivalent forms of real numbers.
9 Number and Number Systems
9.1.E.2 Compare, order and determine equivalent forms for rational and irrational numbers.
9.1.F Explain the effects of operations on the magnitude of quantities.
9 Meaning of Operations
9.1.F.3 Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities.
9.1.G Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.
9 Computation and Estimation
9.1.G.4 Demonstrate fluency in computations using real numbers.
9.1.H Find the square root of perfect squares, and approximate the square root of non-perfect squares.
9.1.I Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.
9 Computation and Estimation
9.1.I.5 Estimate the solutions for problem situations involving square and cube roots.

9.2 Measurement

9.2.A Solve increasingly complex non-routine measurement problems and check for reasonableness of results.
9.2.B Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.
- Geometry: Volume (Algebra - F.3)
- Geometry: Surface area (Algebra - F.4)
9.2.C Apply indirect measurement techniques, tools and formulas, as appropriate, to find perimeter, circumference and area of circles, triangles, quadrilaterals and composite shapes, and to find volume of prisms, cylinders, and pyramids.
9.2.D Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.
9 Measurement Units
9.2.D.1 Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.
9 Use Measurement Techniques and Tools
9.2.D.2 Use unit analysis to check computations involving measurement.
- Ratios and proportions: Unit rates (Algebra - C.3)
- Ratios and proportions: Unit prices (Algebra - C.4)
9.2.D.3 Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.
- Geometry: Perimeter, area, and volume: changes in scale (Algebra - F.11)
9.2.D.4 Use scale drawings and right triangle trigonometry to solve problems that include unknown distances and angle measures.
9.2.D.5 Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.
9.2.E Estimate and compute various attributes, including length, angle measure, area, surface area and volume, to a specified level of precision.
9.2.F Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions.

9.3 Geometry and Spatial Sense

9.3.A Formally define geometric figures.
9.3.B Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.
9.3.C Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.
9.3.D Use coordinate geometry to represent and examine the properties of geometric figures.
- Geometry: Dilations and scale factors (Algebra - F.7)
9.3.E Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
9.3.F Represent and model transformations in a coordinate plane and describe the results.
9.3.G Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.
9 Visualization and Geometric Models
9.3.G.3 Analyze two-dimensional figures in a coordinate plane; e.g., use slope and distance formulas to show that a quadrilateral is a parallelogram.
9.3.H Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
9.3.I Use right triangle trigonometric relationships to determine lengths and angle measures.
9 Characteristics and Properties
9.3.I.1 Define the basic trigonometric ratios in right triangles: sine, cosine and tangent.
9.3.I.2 Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures.

9.4 Patterns, Functions and Algebra

9.4.A Generalize and explain patterns and sequences in order to find the next term and the nth term.
9 Use Patterns, Relations and Functions
9.4.A.2 Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.
- Number sequences: Identify arithmetic and geometric sequences (Algebra - P.1)
- Number sequences: Arithmetic sequences (Algebra - P.2)
- Number sequences: Geometric sequences (Algebra - P.3)
- Number sequences: Evaluate variable expressions for number sequences (Algebra - P.4)
- Number sequences: Write variable expressions for arithmetic sequences (Algebra - P.5)
- Number sequences: Write variable expressions for geometric sequences (Algebra - P.6)
- Number sequences: Number sequences: mixed review (Algebra - P.7)
9.4.B Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.
9 Use Patterns, Relations and Functions
9.4.B.1 Define function with ordered pairs in which each domain element is assigned exactly one range element.
- Relations and functions: Identify functions (Algebra - Q.4)
- Relations and functions: Identify functions: vertical line test (Algebra - Q.5)
9.4.B.3 Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
- Solve equations: Solve linear equations: word problems (Algebra - J.8)
- Relations and functions: Write a function rule: word problems (Algebra - Q.10)
- Direct and inverse variation: Write direct variation equations (Algebra - R.4)
- Direct and inverse variation: Write and solve direct variation equations (Algebra - R.5)
- Direct and inverse variation: Write inverse variation equations (Algebra - R.7)
- Direct and inverse variation: Write and solve inverse variation equations (Algebra - R.8)
- Linear functions: Linear function word problems (Algebra - S.8)
- Linear inequalities: Linear inequalities: word problems (Algebra - T.4)
9.4.C Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.
9 Use Patterns, Relations and Functions
9.4.C.2 Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.
- Relations and functions: Relations: convert between tables, graphs, mappings, and lists of points (Algebra - Q.1)
- Relations and functions: Complete a function table (Algebra - Q.6)
- Relations and functions: Evaluate function rules I (Algebra - Q.7)
- Relations and functions: Evaluate function rules II (Algebra - Q.8)
- Relations and functions: Graph a function (Algebra - Q.9)
- Relations and functions: Write a function rule: word problems (Algebra - Q.10)
- Relations and functions: Find points on a function graph (Algebra - Q.11)
- Relations and functions: Write a rule for a function table (Algebra - Q.12)
- Direct and inverse variation: Find the constant of variation (Algebra - R.2)
- Direct and inverse variation: Graph a proportional relationship (Algebra - R.3)
- Direct and inverse variation: Write direct variation equations (Algebra - R.4)
- Direct and inverse variation: Write and solve direct variation equations (Algebra - R.5)
- Direct and inverse variation: Write inverse variation equations (Algebra - R.7)
- Direct and inverse variation: Write and solve inverse variation equations (Algebra - R.8)
- Linear functions: Slope-intercept form: graph an equation (Algebra - S.5)
- Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
- Linear functions: Write equations in standard form (Algebra - S.9)
- Linear functions: Standard form: graph an equation (Algebra - S.11)
- Linear functions: Graph a horizontal or vertical line (Algebra - S.13)
- Linear functions: Point-slope form: graph an equation (Algebra - S.14)
- Linear functions: Point-slope form: write an equation from a graph (Algebra - S.15)
- Linear functions: Point-slope form: write an equation (Algebra - S.16)
- Linear functions: Write an equation for a parallel or perpendicular line (Algebra - S.18)
9.4.D Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.
9 Use Algebraic Representations
9.4.D.7 Use formulas to solve problems involving exponential growth and decay.
- Exponential functions: Exponential growth and decay: word problems (Algebra - X.3)
9.4.D.11 Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only).
- Monomials: Multiply monomials (Algebra - Y.2)
- Monomials: Divide monomials (Algebra - Y.3)
- Monomials: Multiply and divide monomials (Algebra - Y.4)
- Polynomials: Add and subtract polynomials using algebra tiles (Algebra - Z.3)
- Polynomials: Add and subtract polynomials (Algebra - Z.4)
- Polynomials: Add polynomials to find perimeter (Algebra - Z.5)
- Polynomials: Multiply a polynomial by a monomial (Algebra - Z.6)
- Polynomials: Multiply two polynomials using algebra tiles (Algebra - Z.7)
- Polynomials: Multiply two binomials (Algebra - Z.8)
- Polynomials: Multiply two binomials: special cases (Algebra - Z.9)
- Polynomials: Multiply polynomials (Algebra - Z.10)
9.4.D.12 Simplify rational expressions by eliminating common factors and applying properties of integer exponents.
- Rational functions and expressions: Simplify rational expressions (Algebra - GG.3)
- Rational functions and expressions: Multiply and divide rational expressions (Algebra - GG.4)
- Rational functions and expressions: Divide polynomials (Algebra - GG.5)
- Rational functions and expressions: Add and subtract rational expressions (Algebra - GG.6)
9.4.E Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.
9 Use Patterns, Relations and Functions
9.4.E.4 Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.
9.4.E.5 Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.
- Linear functions: Slope-intercept form: find slope and y-intercept (Algebra - S.4)
- Linear functions: Standard form: find x- and y-intercepts (Algebra - S.10)
- Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
- Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)
- Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from tables (Algebra - CC.2)
- Functions: linear, quadratic, exponential: Write linear, quadratic, and exponential functions (Algebra - CC.3)
- Absolute value functions: Domain and range of absolute value functions (Algebra - DD.2)
- Radical functions and equations: Domain and range of radical functions (Algebra - FF.2)
- Rational functions and expressions: Rational functions: asymptotes and excluded values (Algebra - GG.1)
9.4.F Solve and graph linear equations and inequalities.
9 Use Algebraic Representations
9.4.F.6 Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.
- Linear functions: Write equations in standard form (Algebra - S.9)
9.4.F.8 Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.
- Linear functions: Find slope from two points (Algebra - S.3)
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
- Linear functions: Point-slope form: write an equation from a graph (Algebra - S.15)
- Linear functions: Point-slope form: write an equation (Algebra - S.16)
- Linear functions: Slopes of parallel and perpendicular lines (Algebra - S.17)
9.4.G Solve quadratic equations with real roots by graphing, formula and factoring.
9 Use Algebraic Representations
9.4.G.10 Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
- Quadratic equations: Solve a quadratic equation using square roots (Algebra - BB.2)
- Quadratic equations: Solve an equation using the zero product property (Algebra - BB.3)
- Quadratic equations: Solve a quadratic equation by factoring (Algebra - BB.4)
- Quadratic equations: Complete the square (Algebra - BB.5)
- Quadratic equations: Solve a quadratic equation by completing the square (Algebra - BB.6)
- Quadratic equations: Solve a quadratic equation using the quadratic formula (Algebra - BB.7)
- Quadratic equations: Using the discriminant (Algebra - BB.8)
9.4.H Solve systems of linear equations involving two variables graphically and symbolically.
9 Use Algebraic Representations
9.4.H.9 Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.
- Systems of linear equations: Is (x, y) a solution to the system of equations? (Algebra - U.1)
- Systems of linear equations: Solve a system of equations by graphing (Algebra - U.2)
- Systems of linear equations: Find the number of solutions to a system of equations by graphing (Algebra - U.4)
- Systems of linear equations: Find the number of solutions to a system of equations (Algebra - U.5)
- Systems of linear equations: Classify a system of equations by graphing (Algebra - U.6)
- Systems of linear equations: Classify a system of equations (Algebra - U.7)
- Systems of linear equations: Solve a system of equations using substitution (Algebra - U.8)
- Systems of linear equations: Solve a system of equations using substitution: word problems (Algebra - U.9)
- Systems of linear equations: Solve a system of equations using elimination (Algebra - U.10)
- Systems of linear equations: Solve a system of equations using elimination: word problems (Algebra - U.11)
- Systems of linear equations: Solve a system of equations using augmented matrices (Algebra - U.12)
- Systems of linear equations: Solve a system of equations using augmented matrices: word problems (Algebra - U.13)
- Systems of linear equations: Solve a system of equations using any method (Algebra - U.14)
- Systems of linear equations: Solve a system of equations using any method: word problems (Algebra - U.15)
9.4.I Model and solve problem situations involving direct and inverse variation.
9 Analyze Change
9.4.I.13 Model and solve problems involving direct and inverse variation using proportional reasoning.
- Direct and inverse variation: Identify proportional relationships (Algebra - R.1)
- Direct and inverse variation: Find the constant of variation (Algebra - R.2)
- Direct and inverse variation: Graph a proportional relationship (Algebra - R.3)
- Direct and inverse variation: Write direct variation equations (Algebra - R.4)
- Direct and inverse variation: Write and solve direct variation equations (Algebra - R.5)
- Direct and inverse variation: Write inverse variation equations (Algebra - R.7)
- Direct and inverse variation: Write and solve inverse variation equations (Algebra - R.8)
9.4.I.14 Describe the relationship between slope and the graph of a direct variation and inverse variation.
- Direct and inverse variation: Identify direct variation and inverse variation (Algebra - R.6)
9.4.J Describe and interpret rates of change from graphical and numerical data.
9 Analyze Change
9.4.J.15 Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs.

9.5 Data Analysis and Probability

9.5.A Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
9 Data Collection
9.5.A.1 Classify data as univariate (single variable) or bivariate (two variables) and as quantitative (measurement) or qualitative (categorical) data.
9.5.A.2 Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.
- Charts and graphs: Interpret a scatter plot (Algebra - N.6)
- Charts and graphs: Scatter plots: line of best fit (Algebra - N.7)
9 Statistical Methods
9.5.A.3 Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.
- Charts and graphs: Interpret box-and-whisker plots (Algebra - N.5)
9.5.B Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
- Charts and graphs: Choose the best type of graph (Eighth grade - N.16)
9.5.C Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.
- Statistics: Mean, median, mode, and range (Algebra - JJ.1)
9.5.D Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
- Statistics: Mean, median, mode, and range (Algebra - JJ.1)
- Statistics: Quartiles (Algebra - JJ.2)
9.5.E Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.
9 Statistical Methods
9.5.E.4 Describe and compare various types of studies (survey, observation, experiment), and identify possible misuses of statistical data.
- Statistics: Identifying biased samples (Algebra - JJ.3)
9.5.F Construct convincing arguments based on analysis of data and interpretation of graphs.
9 Statistical Methods
9.5.F.6 Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation.
- Charts and graphs: Interpret a scatter plot (Algebra - N.6)
9.5.G Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
9 Statistical Methods
9.5.G.5 Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population.
- Statistics: Identifying biased samples (Algebra - JJ.3)
9.5.H Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
9 Probability
9.5.H.7 Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations.
- Probability: Compound events: find the number of outcomes (Algebra - II.3)
- Probability: Permutations (Algebra - II.6)
- Probability: Combinations (Algebra - II.7)
- Probability: Permutation and combination notation (Algebra - II.8)
9.5.I Design an experiment to test a theoretical probability, and record and explain results.
9 Probability
9.5.I.8 Describe, create and analyze a sample space and use it to calculate probability.
- Probability: Permutations (Algebra - II.6)
- Probability: Combinations (Algebra - II.7)
- Probability: Permutation and combination notation (Algebra - II.8)
9.5.J Compute probabilities of compound events, independent events, and simple dependent events.
9 Probability
9.5.J.9 Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about probabilities associated with those events.
- Probability: Identify independent and dependent events (Algebra - II.4)
- Probability: Probability of independent and dependent events (Algebra - II.5)
9.5.K Make predictions based on theoretical probabilities and experimental results.
9 Probability
9.5.K.10 Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.
- Probability: Theoretical probability (Algebra - II.1)
- Probability: Experimental probability (Algebra - II.2)
- Probability: Identify independent and dependent events (Algebra - II.4)
- Probability: Probability of independent and dependent events (Algebra - II.5)

9.6 Mathematical Processes

9.6.A Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.
9.6.B Apply mathematical knowledge and skills routinely in other content areas and practical situations.
9.6.C Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.
9.6.D Apply reasoning processes and skills to construct logical verifications or counter-examples to test conjectures and to justify and defend algorithms and solutions.
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
- Logic: Counterexamples (Algebra - HH.2)
9.6.E Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas.
9.6.F Use precise mathematical language and notations to represent problem situations and mathematical ideas.
9.6.G Write clearly and coherently about mathematical thinking and ideas.
9.6.H Locate and interpret mathematical information accurately, and communicate ideas, processes and solutions in a complete and easily understood manner.