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AZ.M06-S1. Number and Operations
M06-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.
M06-S1C1-01. Convert between expressions for positive rational numbers, including fractions, decimals, percents, and ratios.
M06-S1C1-02. Use prime factorization to
M06-S1C1-02.a. Express a whole number as a product of its prime factors
M06-S1C1-02.b. Determine the greatest common factor and least common multiple of two whole numbers.
M06-S1C1-03. Demonstrate an understanding of fractions as rates, division of whole numbers, parts of a whole, parts of a set, and locations on a real number line.
M06-S1C1-04. Compare and order integers; and positive fractions, decimals, and percents.
M06-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another.
M06-S1C2-01. Apply and interpret the concepts of addition and subtraction with integers using models.
M06-S1C2-02. Multiply multi-digit decimals through thousandths.
M06-S1C2-03. Divide multi-digit whole numbers and decimals by decimal divisors with and without remainders.
M06-S1C2-04. Multiply and divide fractions.
M06-S1C2-05 Provide a mathematical argument to explain operations with two or more fractions or decimals.
M06-S1C2-06. Apply the commutative, associative, distributive, and identity properties to evaluate numerical expressions involving whole numbers.
M06-S1C2-07. Simplify numerical expressions (involving fractions, decimals, and exponents) using the order of operations with or without grouping symbols.
M06-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.
M06-S1C3-01. Use benchmarks as meaningful points of comparison for rational numbers.
M06-S1C3-02. Make estimates appropriate to a given situation and verify the reasonableness of the results.
AZ.M06-S2. Data Analysis, Probability, and Discrete Mathematics
M06-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.
M06-S2C1-01. Solve problems by selecting, constructing, and interpreting displays of data, including histograms and stem-and-leaf plots.
M06-S2C1-02. Formulate and answer questions by interpreting, analyzing, and drawing inferences from displays of data, including histograms and stem-and-leaf plots.
M06-S2C1-03. Use extreme values, mean, median, mode, and range to analyze and describe the distribution of a given data set.
M06-S2C2. Probability: Understand and apply the basic concepts of probability.
M06-S2C2-01. Use data collected from multiple trials of a single event to form a conjecture about the theoretical probability.
M06-S2C2-02. Use theoretical probability to
M06-S2C2-02.a. Predict experimental outcomes
M06-S2C2-02.b. Compare the outcome of the experiment to the prediction
M06-S2C2-02.c. Replicate the experiment and compare results.
AZ.M06-S3. Patterns, Algebra, and Functions
M06-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations.
M06-S3C3-01. Use an algebraic expression to represent a quantity in a given context.
M06-S3C3-02. Create and solve two-step equations that can be solved using inverse properties with fractions and decimals.
M06-S3C3-03. Translate both ways between a verbal description and an algebraic expression or equation.
M06-S3C3-04. Evaluate an expression involving the four basic operations by substituting given fractions and decimals for the variable.
M06-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.
M06-S3C4-01. Determine a pattern to predict missing values on a line graph or scatterplot.
AZ.M06-S4. Geometry and Measurement
M06-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.
M06-S4C1-01. Define pi (pi) as the ratio between the circumference and diameter of a circle and explain the relationship among the diameter, radius, and circumference.
M06-S4C1-02. Solve problems using properties of supplementary, complementary, and vertical angles.
M06-S4C3. Coordinate Geometry: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.
M06-S4C3-01. Graph ordered pairs in any quadrant of the coordinate plane.
M06-S4C3-02. State the missing coordinate of a given figure on the coordinate plane using geometric properties to justify the solution.
M06-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.
M06-S4C4-01. Determine the appropriate unit of measure for a given context and the appropriate tool to measure to the needed precision (including length, capacity, angles, time, and mass).
M06-S4C4-02. Solve problems involving conversion within the U.S. Customary and within the metric system.
M06-S4C4-03. Estimate the measure of objects using a scale drawing or map.
M06-S4C4-04. Solve problems involving the area of simple polygons using formulas for rectangles and triangles.
M06-S4C4-05. Solve problems involving area and perimeter of regular and irregular polygons.
AZ.M06-S5. Structure and Logic
M06-S5C1. Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems.
M06-S5C1-01. Analyze algorithms for multiplying and dividing fractions and decimals using the associative, commutative, and distributive properties.
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