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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-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-S1C2-03. 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.
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-S2C1-04. 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-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-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.
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-S3C2-02. 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-S3C2-05. 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-S3C3-05. 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-S4C1-03. 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-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
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-S5C2-05. Apply a previously used problem-solving strategy in a new context.
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-S5C2-12. Make, validate, and justify conclusions and generalizations about linear relationships.
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