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Arizona Math Standards - 9th Grade
MathScore aligns to the Arizona Math Standards for 9th 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.
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View the Arizona Math Standards at other levels.
Number Sense and Operations
C1 Number Sense1. Classify real numbers as members of one or more subsets: natural, whole, integers, rational, or irrational numbers.
2. Identify properties of the real number system: commutative, associative, distributive, identity, inverse, and closure. (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Distributive Property , Distributive Property 2 )
3. Distinguish between finite and infinite sets of numbers.
C2 Numerical Operations
1. Select the grade-level appropriate operation to solve word problems.
2. Solve word problems using grade-level appropriate operations and numbers. (Age Problems , Distance, Rate, and Time , Train Problems , Mixture Word Problems , Work Word Problems , Integer Word Problems )
3. Simplify numerical expressions including signed numbers and absolute values. (Absolute Value 2 , Absolute Value Equations )
4. Apply subscripts to represent ordinal position.
5. Use grade level-appropriate mathematical terminology.
6. Compute using scientific notation. (Scientific Notation 2 )
7. Simplify numerical expressions using the order of operations. (Order Of Operations )
C3 Estimation
1. Solve grade-level appropriate problems using estimation.
2. Determine if a solution to a problem is reasonable.
3. Determine rational approximations of irrational numbers.
Data Analysis, Probability, and Discrete Mathematics
C1 Data Analysis (Statistics)1. Formulate questions to collect data in contextual situations.
2. Organize collected data into an appropriate graphical representation.
3. Display data as lists, tables, matrices, and plots.
4. Construct equivalent displays of the same data.
5. Identify graphic misrepresentations and distortions of sets of data.
6. Identify which of the measures of central tendency is most appropriate in a given situation.
7. Make reasonable predictions based upon linear patterns in data sets or scatter plots.
8. Make reasonable predictions for a set of data, based on patterns.
9. Draw inferences from charts, tables, graphs, plots, or data sets.
10. Apply the concepts of mean, median, mode, range, and quartiles to summarize data sets. (Stem And Leaf Plots )
11. Evaluate the reasonableness of conclusions drawn from data analysis.
12. Recognize and explain the impact of interpreting data (making inferences or drawing conclusions) from a biased sample.
13. Draw a line of best fit for a scatter plot.
14. Determine whether displayed data has positive, negative, or no correlation.
15. Identify a normal distribution.
16. Identify differences between sampling and census.
17. Identify differences between biased and unbiased samples.
C2 Probability
1. Find the probability that a specific event will occur, with or without replacement. (Object Picking Probability )
2. Determine simple probabilities related to geometric figures. (Probability , Probability 2 , Object Picking Probability )
3. Predict the outcome of a grade-level appropriate probability experiment.
4. Record the data from performing a grade-level appropriate probability experiment.
5. Compare the outcome of an experiment to predictions made prior to performing the experiment.
6. Distinguish between independent and dependent events. (Object Picking Probability )
7. Compare the results of two repetitions of the same grade-level appropriate probability experiment.
C3 Discrete Mathematics - Systematic Listing and Counting
1. Determine the number of possible outcomes for a contextual event using a chart, a tree diagram, or the counting principle.
2. Determine when to use combinations versus permutations in counting objects.
3. Use combinations or permutations to solve contextual problems.
C4 Vertex-Edge Graphs
Patterns, Algebra, and Functions
C1 Patterns1. Communicate a grade-level appropriate iterative or recursive pattern, using symbols or numbers.
2. Find the nth term of an iterative or recursive pattern.
3. Evaluate problems using basic recursion formulas.
C2 Functions and Relationships
1. Determine if a relationship is a function, given a graph, table, or set of ordered pairs.
2. Describe a contextual situation that is depicted by a given graph.
3. Identify a graph that models a given real-world situation.
4. Sketch a graph that models a given contextual situation.
5. Determine domain and range for a function. (Domain and Range )
6. Determine the solution to a contextual maximum/minimum problem, given the graphical representation.
7. Express the relationship between two variables using tables/matrices, equations, or graphs. (Function Tables , Function Tables 2 )
8. Interpret the relationship between data suggested by tables/matrices, equations, or graphs.
9. Determine from two linear equations whether the lines are parallel, perpendicular, coincident, or intersecting but not perpendicular. (Applied Linear Equations 2 )
C3 Algebraic Representations
1. Evaluate algebraic expressions, including absolute value and square roots. (Absolute Value 2 , Foil Method , Roots Of Exponential Expressions )
2. Simplify algebraic expressions. (Simplifying Algebraic Expressions , Simplifying Algebraic Expressions 2 , Trinomial Factoring , Binomial Fraction Simplification , Polynomial Fraction Simplification )
3. Multiply and divide monomial expressions with integral exponents. (Binomial Fraction Simplification , Negative Exponents Of Fractional Bases , Multiplying and Dividing Exponent Expressions , Exponent Rules For Fractions )
4. Translate a written expression or sentence into a mathematical expression or sentence. (Phrases to Algebraic Expressions , Algebraic Sentences 2 , Algebraic Sentences )
5. Translate a sentence written in context into an algebraic equation involving multiple operations. (Age Problems , Train Problems )
6. Write a linear equation for a table of values.
7. Write a linear algebraic sentence that represents a data set that models a contextual situation. (Algebraic Sentences )
8. Solve linear (first degree) equations in one variable (may include absolute value). (Single Variable Equations 3 )
9. Solve linear inequalities in one variable. (Single Variable Inequalities , Absolute Value Equations )
10. Write an equation of the line given: two points on the line, the slope and a point on the line, or the graph of the line. (Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Applied Linear Equations 1 )
11. Solve an algebraic proportion. (Proportions 2 )
12. Solve systems of linear equations in two variables (integral coefficients and rational solutions). (System of Equations Substitution , System of Equations Addition )
13. Add, subtract, and perform scalar multiplication with matrices.
14. Calculate powers and roots of real numbers, both rational and irrational, using technology when appropriate.
15. Simplify square roots and cube roots with monomial radicands (including those with variables) that are perfect squares or perfect cubes. (Simplifying Algebraic Expressions 2 , Simplifying Algebraic Expressions )
16. Solve square root radical equations involving only one radical. (Simplifying Radical Expressions , Adding and Subtracting Radical Expressions , Multiplying and Dividing Radical Expressions )
17. Solve quadratic equations. (Quadratic Zero Equations , Quadratic Formula , Quadratic X-Intercepts , Integer Word Problems )
18. Identify the sine, cosine, and tangent ratios of the acute angles of a right triangle.
C4 Analysis of Change
1. Determine slope, x-, and y-intercepts of a linear equation.
2. Solve formulas for specified variables. (Two Variable Equations )
Geometry and Measurement
C1 Geometric Properties1. Identify the attributes of special triangles (isosceles, equilateral, right). (Triangle Types )
2. Identify the hierarchy of quadrilaterals. (Quadrilateral Types )
3. Make a net to represent a 3-dimensional object.
4. Make a 3-dimensional model from a net.
5. Draw 2-dimensional and 3-dimensional figures with appropriate labels.
6. Solve problems related to complementary, supplementary, or congruent angle concepts. (Triangle Angles 2 , Angle Measurements )
7. Solve problems by applying the relationship between circles, angles, and intercepted arcs.
8. Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants.
9. Solve problems using the triangle inequality property.
10. Solve problems using special case right triangles.
11. Determine when triangles are congruent by applying SSS, ASA, AAS, or SAS.
12. Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.
13. Construct a triangle congruent to a given triangle.
14. Solve contextual situations using angle and side length relationships.
C2 Transformation of Shapes
1. Sketch the planar figure that is the result of two or more transformations.
2. Identify the properties of the planar figure that is the result of two or more transformations.
3. Determine the new coordinates of a point when a single transformation is performed on a planar geometric figure.
4. Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.
5. Classify transformations based on whether they produce congruent or similar figures.
6. Determine the effects of a single transformation on linear or area measurements of a planar geometric figure. (Area And Volume Proportions )
C3 Coordinate Geometry
1. Graph a quadratic equation with lead coefficient equal to one.
2. Graph a linear equation in two variables.
3. Graph a linear inequality in two variables.
4. Determine the solution to a system of equations in two variables from a given graph.
5. Determine the midpoint between two points in a coordinate system.
6. Determine changes in the graph of a linear function when constants and coefficients in its equation are varied.
7. Determine the distance between two points in the coordinate system.
C4 Measurement - Units of Measure - Geometric Objects
1. Calculate the area of geometric shapes composed of two or more geometric figures. (Irregular Shape Areas , Perimeter and Area of Composite Figures )
2. Calculate the volumes of 3-dimensional geometric figures. (Rectangular Solids , Triangular Prisms , Cylinders )
3. Calculate the surface areas of 3-dimensional geometric figures. (Rectangular Solids , Cylinders )
4. Compare perimeter, area, or volume of figures when dimensions are changed. (Compare Rectangle Area and Perimeter , Area And Volume Proportions )
5. Find the length of a circular arc.
6. Find the area of a sector of a circle.
7. Solve for missing measures in a pyramid (i.e., slant height, height).
8. Find the sum of the interior and exterior angles of a polygon. (Polygon Angles )
9. Solve scale factor problems using ratios and proportions. (Solving For Angles , Proportions 2 )
10. Solve applied problems using similar triangles.
Structure and Logic
C1 Algorithms and Algorithmic Thinking1. Determine whether a given procedure for simplifying an expression is valid.
2. Determine whether a given procedure for solving an equation is valid.
3. Determine whether a given procedure for solving a linear inequality is valid.
4. Select an algorithm that explains a particular mathematical process.
5. Determine the purpose of a simple mathematical algorithm.
6. Determine whether given simple mathematical algorithms are equivalent.
C2 Logic, Reasoning, Arguments, and Mathematical Proof
1. Draw a simple valid conclusion from a given if...then statement and a minor premise.
2. List related if...then statements in logical order.
3. Write an appropriate conjecture given a certain set of circumstances.
4. Analyze assertions related to a contextual situation by using principles of logic.
5. Identify a valid conjecture using inductive reasoning.
6. Distinguish valid arguments from invalid arguments.
7. Create inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
8. Critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
9. Identify a counterexample for a given conjecture.
10. Construct a counterexample to show that a given conjecture is false.
11. State the inverse, converse, or contrapositive of a given statement.
12. Determine if the inverse, converse, or contrapositive of a given statement is true or false.
13. Construct a simple formal or informal deductive proof.
14. Verify characteristics of a given geometric figure using coordinate formulas such as distance, mid-point, and slope to confirm parallelism, perpendicularity, and congruency.
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