Arizona State Standards for Mathematics: Grade 7

AZ.M07-S1. Number and Operations

M07-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

M07-S1C1-01. Recognize and convert between expressions for positive and negative rational numbers, including fractions, decimals, percents, and ratios.

M07-S1C1-02. Find or use factors, multiples, or prime factorization within a set of numbers.

M07-S1C1-03. Compare and order rational numbers using various models and representations.

M07-S1C1-04. Model and solve simple problems involving absolute value.

M07-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another.

M07-S1C2-01. Add, subtract, multiply, and divide integers.

M07-S1C2-02. Solve problems with rational numbers and appropriate operations using exact answers or estimates.

M07-S1C2-03. Solve problems involving percentages, ratio and proportion, including tax, discount, tips, and part/whole relationships.

M07-S1C2-04. Represent and interpret numbers using scientific notation (positive exponents only).

M07-S1C2-05. Simplify numerical expressions using the order of operations and appropriate mathematical properties.

M07-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

M07-S1C3-01. Estimate and apply benchmarks for rational numbers and common irrational numbers.

M07-S1C3-02. Make estimates appropriate to a given situation.

M07-S1C3-03. Estimate square roots of numbers less than 1000 by locating them between two consecutive whole numbers.

M07-S1C3-04. Estimate the measure of an object in one system of units given the measure of that object in another system and the approximate conversion factor.

AZ.M07-S2. Data Analysis, Probability, and Discrete Mathematics

M07-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

M07-S2C1-01. Solve problems by selecting, constructing, and interpreting displays of data including multi-line graphs and scatterplots.

M07-S2C1-02. Interpret trends in a data set, estimate values for missing data, and predict values for points beyond the range of the data set.

M07-S2C1-03. Identify outliers and determine their effect on mean, median, mode, and range.

M07-S2C1-04. Distinguish between a simple random and non-random sample.

M07-S2C2. Probability: Understand and apply the basic concepts of probability.

M07-S2C2-01. Determine conditional probabilities (experimental) in compound probability experiments.

M07-S2C2-02. Experiment with two different events to determine whether the two event are dependent or independent of each other.

M07-S2C2-03. Compare the results of multiple repetitions of the same probability experiment to the theoretical probability

M07-S2C2-04. Compare probabilities to determine fairness in experimental situations.

M07-S2C3 Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes.

M07-S2C3-01. Analyze relationships among the tree diagrams where items repeat and do not repeat; make numerical connections to the multiplication principle of counting.

M07-S2C3-02. Solve counting problems using Venn diagrams and represent the answer algebraically.

M07-S2C4. Vertex-Edge Graphs: Understand and apply vertex-edge graphs.

M07-S2C4-01. Use vertex-edge graphs and algorithmic thinking to represent and find solutions to practical problems related to Euler/Hamilton paths and circuits.

AZ.M07-S3. Patterns, Algebra, and Functions

M07-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

M07-S3C1-01. Recognize, describe, create, and analyze numerical and geometric sequences using tables or graphs; make conjectures about these sequences.

M07-S3C2. Functions and Relationships: Describe and model functions and their relationships.

M07-S3C2-01. Use a table of values to graph an equation or proportional relationship; describe the graph's characteristics.

M07-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations.

M07-S3C3-01. Write a single variable algebraic expression or one-step equation given a contextual situation.

M07-S3C3-02. Evaluate an expression containing one or two variables by substituting numbers for the variables

M07-S3C3-03. Solve multi-step equations using inverse properties with rational numbers.

M07-S3C3-04. Translate between graphs and tables that represent a linear equation.

M07-S3C3-05. Create and solve two-step equations that can be solved using inverse operations with rational numbers.

M07-S3C3-06. Create and solve one-step inequalities with whole numbers.

M07-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

M07-S3C4-01. Use graphs and tables to model and analyze change.

AZ.M07-S4. Geometry and Measurement

M07-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

M07-S4C1-01. Recognize the relationship between central angles and intercepted arcs; identify arcs and chords of a circle.

M07-S4C1-02. Analyze and determine relationships between angles created by parallel lines cut by a transversal.

M07-S4C1-03. Draw and classify 3-dimensional figures with appropriate labels showing specified attributes of parallelism, congruence, perpendicularity, and symmetry.

M07-S4C1-04. Describe the relationship between the number of sides in a regular polygon and the sum of its interior angles.

M07-S4C1-05. Identify corresponding parts of congruent figures.

M07-S4C2. Transformation of Shapes: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

M07-S4C2-01. Model the result of a double transformation (translations or reflections) of a 2-dimensional figure on a coordinate plane using all four quadrants.

M07-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

M07-S4C4-01. Solve problems involving the circumference and area of a circle by calculating and estimating.

M07-S4C4-02. Find the length of a circular arc; find the area of a sector of a circle.

M07-S4C4-03. Calculate the area and perimeter of composite 2-dimensional figures.

M07-S4C4-04. Determine actual lengths based on scale drawings or maps.

M07-S4C4-05. Create a net to calculate the surface area of a given solid.

M07-S4C4-06. Identify the appropriate unit of measure to compute the volume of an object and justify reasoning.

M07-S4C4-07. Measure to the appropriate degree of accuracy and justify reasoning.

AZ.M07-S5. Structure and Logic

M07-S5C1. Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems.

M07-S5C1-01. Create an algorithm to determine the area of a given composite figure.

M07-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

M07-S5C2-01. Analyze a problem situation to determine the question(s) to be answered.

M07-S5C2-02. Analyze and compare mathematical strategies for efficient problem solving; select and use one or more strategies to solve a problem.

M07-S5C2-03. Identify relevant, missing, and extraneous information related to the solution to a problem.

M07-S5C2-04. Represent a problem situation using multiple representations, describe the process used to solve the problem, and verify the reasonableness of the solution.

M07-S5C2-05. Apply a previously used problem-solving strategy in a new context.

M07-S5C2-06. Communicate the answer(s) to the question(s) in a problem using appropriate representations, including symbols and informal and formal mathematical language.

M07-S5C2-07. Isolate and organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.

M07-S5C2-08. Make and test conjectures based on information collected from explorations and experiments.

M07-S5C2-09. Solve logic problems using multiple variables and multiple conditional statements using words, pictures, and charts.

M07-S5C2-10. Demonstrate and explain that the process of solving equations is a deductive proof.

M07-S5C2-11. Use manipulatives and other modeling techniques to defend pi (pi) as a ratio of circumference to diameter.