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AZ.MHS-S1.Number and Operations
MHS-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. MHS-S1C1-02. Sort sets of numbers as finite or infinite, and justify the sort.
MHS-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another. MHS-S1C2-02. Summarize the properties of and connections between real number operations; justify manipulations of expressions using the properties of real number operations.
MHS-S1C2-03. Calculate powers and roots of rational and irrational numbers. Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
MHS-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands. MHS-S1C3-01. Determine rational approximations of irrational numbers.
AZ.MHS-S2.Data Analysis, Probability, and Discrete Mathematics
Data Analysis, Probability, and Discrete Mathematics
MHS-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data. MHS-S2C1-03. Display data, including paired data, as lists, tables, matrices, and plots with or without technology; make predictions and observations about patterns or departures from patterns.
MHS-S2C1-08. Design simple experiments or investigations and collect data to answer questions.
MHS-S2C3. Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes. MHS-S2C3-01. Apply the addition and multiplication principles of counting, representing these principles algebraically using factorial notation.
MHS-S2C3-02. Apply appropriate means of computing the number of possible arrangements of items using permutations where order matters, and combinations where order does not matter.
AZ.MHS-S3.Patterns, Algebra, and Functions
Patterns, Algebra, and Functions
MHS-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. MHS-S3C1-01. Recognize, describe, and analyze sequences using tables, graphs, words, or symbols; use sequences in modeling. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MHS-S3C1-02. Determine a specific term of a sequence. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MHS-S3C1-03. Create sequences using explicit and recursive formulas involving both subscripts and function notation. Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MHS-S3C2. Functions and Relationships: Describe and model functions and their relationships. MHS-S3C2-02. Determine if a relationship represented by an equation, graph, table, description, or set of ordered pairs is a function. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MHS-S3C2-04. Use equations, graphs, tables, descriptions, or sets of ordered pairs to express a relationship between two variables.
MHS-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations. MHS-S3C3-02. Solve formulas for specified variables.
MHS-S3C3-05. Solve linear equations and equations involving absolute value, with one variable.
MHS-S3C3-06. Solve linear inequalities in one variable.
MHS-S3C3-07. Solve systems of two linear equations in two variables.
MHS-S3C3-08. Simplify and evaluate polynomials, rational expressions, expressions containing absolute value, and radicals.
MHS-S3C3-10. Add, subtract, and multiply polynomial and rational expressions.
MHS-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity. MHS-S3C4-01. Determine the slope and intercepts of the graph of a linear function, interpreting slope as a constant rate of change.
MHS-S3C4-03. Solve interest problems.
AZ.MHS-S4.Geometry and Measurement
MHS-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. MHS-S4C1-04. Apply properties, theorems, and constructions about parallel lines, perpendicular lines, and angles to prove theorems.
MHS-S4C1-06. Solve problems using angle and side length relationships and attributes of polygons.
MHS-S4C2. Transformation of Shapes: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. MHS-S4C2-04. Determine the effects of a single transformation on linear or area measurements of a 2-dimensional figure.
MHS-S4C3. Coordinate Geometry: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. MHS-S4C3-04. Verify characteristics of a given geometric figure using coordinate formulas for distance, midpoint, and slope to confirm parallelism, perpendicularity, and congruence.
MHS-S4C3-05. Graph a linear equation or linear inequality in two variables.
MHS-S4C3-07. Determine the solution to a system of linear equations in two variables from the graphs of the equations.
MHS-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. MHS-S4C4-04. Solve problems involving similar figures using ratios and proportions
MHS-S4C4-05. Calculate the surface area and volume of 3-dimensional figures and solve for missing measures.
AZ.MHS-S5.Structure and Logic
MHS-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. MHS-S5C2-01. Analyze a problem situation, determine the question(s) to be answered, organize given information, determine how to represent the problem, and identify implicit and explicit assumptions that have been made.
MHS-S5C2-02. Solve problems by formulating one or more strategies, applying the strategies, verifying the solution(s), and communicating the reasoning used to obtain the solution(s).
MHS-S5C2-03. Evaluate a solution for reasonableness and interpret the meaning of the solution in the context of the original problem.
MHS-S5C2-04. Generalize a solution strategy for a single problem to a class of related problems; explain the role of generalizations in inductive and deductive reasoning.
MHS-S5C2-06. Synthesize mathematical information from multiple sources to draw a conclusion, make inferences based on mathematical information, evaluate the conclusions of others, analyze a mathematical argument, and recognize flaws or gaps in reasoning.
MHS-S5C2-08. Use inductive reasoning to make conjectures, use deductive reasoning to analyze and prove a valid conjecture, and develop a counterexample to refute an invalid conjecture.
MHS-S5C2-12. Construct a simple formal deductive proof.
MHS-S5C2-13. Identify and explain the roles played by definitions, postulates, propositions and theorems in the logical structure of mathematics, including Euclidean geometry.