Arizona State Standards for Mathematics: Grade 8

AZ.M08-S1. Number and Operations

M08-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

M08-S1C1-01. Compare and order real numbers including very large and small integers, and decimals and fractions close to zero.

M08-S1C1-02. Classify real numbers as rational or irrational.

M08-S1C1-03. Model the relationship between the subsets of the real number system.

M08-S1C1-04. Model and solve problems involving absolute value.

M08-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another.

M08-S1C2-01. Solve problems with factors, multiples, divisibility or remainders, prime numbers, and composite numbers.

M08-S1C2-02. Describe the effect of multiplying and dividing a rational number by

M08-S1C2-02.a. A number less than zero

M08-S1C2-02.b. A number between zero and one

M08-S1C2-02.c. One

M08-S1C2-02.d. A number greater than one.

M08-S1C2-03. Solve problems involving percent increase, percent decrease, and simple interest rates.

M08-S1C2-04. Convert standard notation to scientific notation and vice versa (include positive and negative exponents).

M08-S1C2-05. Simplify numerical expressions using the order of operations that include grouping symbols, square roots, cube roots, absolute values, and positive exponents.

M08-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

M08-S1C3-01. Make estimates appropriate to a given situation.

M08-S1C3-02. Estimate the location of rational and common irrational numbers on a number line.

AZ.M08-S2. Data Analysis, Probability, and Discrete Mathematics

M08-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

M08-S2C1-01. Solve problems by selecting, constructing, interpreting, and calculating with displays of data, including box and whisker plots and scatterplots.

M08-S2C1-02. Make inferences by comparing the same summary statistic for two or more data sets.

M08-S2C1-03. Describe how summary statistics relate to the shape of the distribution.

M08-S2C1-04. Determine whether information is represented effectively and appropriately given a graph or a set of data by identifying sources of bias and compare and contrast the effectiveness of different representations of data.

M08-S2C1-05. Evaluate the design of an experiment.

M08-S2C2. Probability: Understand and apply the basic concepts of probability.

M08-S2C2-01. Determine theoretical and experimental conditional probabilities in compound probability experiments.

M08-S2C2-02. Interpret probabilities within a given context and compare the outcome of an experiment to predictions made prior to performing the experiment.

M08-S2C2-03. Use all possible outcomes (sample space) to determine the probability of dependent and independent events.

M08-S2C3. Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes.

M08-S2C3-01. Represent, analyze, and solve counting problems with or without ordering and repetitions.

M08-S2C3-02. Solve counting problems and represent counting principles algebraically including factorial notation.

M08-S2C4. Vertex-Edge Graphs: Understand and apply vertex-edge graphs.

M08-S2C4-01. Use directed graphs to solve problems.

AZ.M08-S3. Patterns, Algebra, and Functions

M08-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

M08-S3C1-01. Recognize, describe, create, and analyze numerical and geometric sequences using tables, graphs, words, or symbols; make conjectures about these sequences.

M08-S3C2. Functions and Relationships: Describe and model functions and their relationships.

M08-S3C2-01. Sketch and interpret a graph that models a given context; describe a context that is modeled by a given graph.

M08-S3C2-02. Determine if a relationship represented by a graph or table is a function.

M08-S3C2-03. Write the rule for a simple function using algebraic notation.

M08-S3C2-04. Identify functions as linear or nonlinear and contrast distinguishing properties of functions using equations, graphs, or tables.

M08-S3C2-05. Demonstrate that proportional relationships are linear using equations, graphs, or tables.

M08-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations.

M08-S3C3-01. Write or identify algebraic expressions, equations, or inequalities that represent a situation.

M08-S3C3-02. Evaluate an expression containing variables by substituting rational numbers for the variables.

M08-S3C3-03. Analyze situations, simplify, and solve problems involving linear equations and inequalities using the properties of the real number system.

M08-S3C3-04. Translate between different representations of linear equations using symbols, graphs, tables, or written descriptions.

M08-S3C3-05. Graph an inequality on a number line.

M08-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

M08-S3C4-01. Interpret the relationship between a linear equation and its graph, identifying and computing slope and intercepts.

M08-S3C4-02. Solve problems involving simple rates.

AZ.M08-S4. Geometry and Measurement

M08-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

M08-S4C1-01. Identify the attributes of circles: radius, diameter, chords, tangents, secants, inscribed angles, central angles, intercepted arcs, circumference, and area.

M08-S4C1-02. Predict results of combining, subdividing, and changing shapes of plane figures and solids.

M08-S4C1-03. Use proportional reasoning to determine congruence and similarity of triangles.

M08-S4C1-04. Use the Pythagorean Theorem to solve problems.

M08-S4C2. Transformation of Shapes: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

M08-S4C2-01. Model the result of rotations in multiples of 45 degrees of a 2-dimensional figure about the origin.

M08-S4C2-02. Describe the transformations that create a given tessellation.

M08-S4C2-03. Identify lines of symmetry in plane figures or classify types of symmetries of 2-dimensional figures.

M08-S4C3. Coordinate Geometry: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

M08-S4C3-01. Make and test a conjecture about how to find the midpoint between any two points in the coordinate plane.

M08-S4C3-02. Use the Pythagorean Theorem to find the distance between two points in the coordinate plane.

M08-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

M08-S4C4-01. Solve problems involving conversions within the same measurement system.

M08-S4C4-02. Solve geometric problems using ratios and proportions.

M08-S4C4-03. Calculate the surface area and volume of rectangular prisms, right triangular prisms, and cylinders.

AZ.M08-S5. Structure and Logic

M08-S5C1. Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems.

M08-S5C1-01. Create an algorithm to solve problems involving indirect measurements, using proportional reasoning, dimensional analysis, and the concepts of density and rate.

M08-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

M08-S5C2-01. Analyze a problem situation to determine the question(s) to be answered.

M08-S5C2-02. Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.

M08-S5C2-03. Identify relevant, missing, and extraneous information related to the solution to a problem.

M08-S5C2-04. Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.

M08-S5C2-05. Apply a previously used problem-solving strategy in a new context.

M08-S5C2-06. Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

M08-S5C2-07. Isolate and organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.

M08-S5C2-08. Describe when to use proportional reasoning to solve a problem.

M08-S5C2-09. Make and test conjectures based on information collected from explorations and experiments.

M08-S5C2-10. Solve logic problems involving multiple variables, conditional statements, conjectures, and negation using words, charts, and pictures.

M08-S5C2-11. Identify simple valid arguments using if... then statements.

M08-S5C2-12. Make, validate, and justify conclusions and generalizations about linear relationships.

M08-S5C2-13. Verify the Pythagorean Theorem using a valid argument.