Arizona State Standards for Mathematics: Grade 6

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-S1C1-05. Express that a number's distance from zero on the number line is its absolute value.

M06-S1C1-06. Express the inverse relationships between exponents and roots for perfect squares and cubes.

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-S2C1-04. Compare two or more sets of data by identifying trends.

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.

M06-S2C2-03. Determine all possible outcomes (sample space) of a given situation using a systematic approach.

M06-S2C3. Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes.

M06-S2C3-01. Build and explore tree diagrams where items repeat.

M06-S2C3-02. Explore counting problems with Venn diagrams using three attributes.

M06-S2C4. Vertex-Edge Graphs: Understand and apply vertex-edge graphs.

M06-S2C4-01. Investigate properties of vertex-edge graphs

M06-S2C4-01.a. Hamilton paths

M06-S2C4-01.b. Hamilton circuits

M06-S2C4-01.c. Shortest route.

M06-S2C4-02. Solve problems related to Hamilton paths and circuits.

AZ.M06-S3. Patterns, Algebra, and Functions

M06-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

M06-S3C1-01. Recognize, describe, create, and analyze a numerical sequence involving fractions and decimals using all four basic operations.

M06-S3C2. Functions and Relationships: Describe and model functions and their relationships.

M06-S3C2-01. Recognize and describe a relationship between two quantities, given by a chart, table, or graph, using words and expressions.

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

M06-S4C2-01. Identify a simple translation or reflection and model its effect on a 2-dimensional figure on a coordinate plane using all four quadrants.

M06-S4C2-02. Draw a reflection of a polygon in the coordinate plane using a horizontal or vertical line of reflection.

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.

M06-S4C4-06. Describe the relationship between the volume of a figure and the area of its base.

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.

M06-S5C1-02. Create and justify an algorithm to determine the area of a given compound figure using parallelograms and triangles.

M06-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

M06-S5C2-01. Analyze a problem situation to determine the question(s) to be answered.

M06-S5C2-02. Identify relevant, missing, and extraneous information related to the solution to a problem.

M06-S5C2-03. Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem

M06-S5C2-04. Apply a previously used problem-solving strategy in a new context.

M06-S5C2-05. Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.

M06-S5C2-06. Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

M06-S5C2-07. Isolate and organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.

M06-S5C2-08. Make and test conjectures based on information collected from explorations and experiments.

M06-S5C2-09. Solve simple logic problems, including conditional statements, and justify solution methods and reasoning.