Arizona State Standards for Mathematics: Grade 4

AZ.M04-S1. Number and Operations

M04-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

M04-S1C1-01. Express whole numbers, fractions, decimals, and percents using and connecting multiple representations.

M04-S1C1-02. Compose and decompose whole numbers using factors and multiples.

M04-S1C1-03. Express fractions as fair sharing, parts of a whole, parts of a set, and locations on a real number line.

M04-S1C1-04. Compare and order decimals to hundredths.

M04-S1C1-05. Use simple ratios to describe problems in context.

M04-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another.

M04-S1C2-01. Add and subtract decimals through hundredths including money to $1000.00 and fractions with like denominators.

M04-S1C2-02. Use multiple strategies to multiply whole numbers

M04-S1C2-02.a. Two-digit by two-digit

M04-S1C2-02.b. Multi-digit by one-digit.

M04-S1C2-03. Demonstrate fluency of multiplication and division facts through 12.

M04-S1C2-04. Use multiple strategies to divide whole numbers.

M04-S1C2-05. Apply associative and distributive properties to solve multiplication and division problems

M04-S1C2-06. Apply order of operations with whole numbers.

M04-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

M04-S1C3-01. Use benchmarks as meaningful points of comparison for whole numbers, decimals, and fractions.

M04-S1C3-02. Make estimates appropriate to a given situation or computation with whole numbers and fractions.

AZ.M04-S2. Data Analysis, Probability, and Discrete Mathematics

M04-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

M04-S2C1-01. Collect, record, organize, and display data using double bar graphs, single line graphs, or circle graphs.

M04-S2C1-02. Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs

M04-S2C1-03. Use median, mode, and range to describe the distribution of a given data set.

M04-S2C1-04. Compare two sets of related data.

M04-S2C2. Probability: Understand and apply the basic concepts of probability.

M04-S2C2-01. Describe elements of theoretical probability by listing or drawing all possible outcomes of a given event and predicting the outcome using word and number benchmarks.

M04-S2C3. Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes.

M04-S2C3-01. Construct tree diagrams to solve problems in context by

M04-S2C3-01.a. Representing all possibilities for a variety of counting problems

M04-S2C3-01.b. Explaining how its properties relate to the problem

M04-S2C3-01.c. Representing the same counting problem in multiple ways

M04-S2C3-01.d. Drawing conclusions.

M04-S2C3-02. Justify that all possibilities have been enumerated without duplication.

M04-SC4. Vertex-Edge Graphs: Understand and apply vertex-edge graphs.

M04-SC4-01. Demonstrate the connection between map coloring and vertex coloring.

M04-SC4-02. Construct vertex-edge graphs to represent concrete situations and identify paths and circuits.

M04-SC4-03. Solve conflict problems by constructing and coloring vertex-edge graphs.

AZ.M04-S3. Patterns, Algebra, and Functions

M04-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

M04-S3C1-01. Recognize, describe, create, extend, and find missing terms in a numerical sequence involving whole numbers using all four basic operations.

M04-S3C1-02. Explain the rule for a given numerical sequence, verify that the rule works, and use the rule to make predictions.

M04-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations.

M04-S3C3-01. Use a symbol to represent an unknown quantity in a simple algebraic expression involving all operations.

M04-S3C3-02. Create and solve one-step equations that can be solved using addition, subtraction, multiplication, and division of whole numbers.

M04-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

M04-S3C4-01. Identify the change in a quantity over time and make simple predictions.

AZ.M04-S4. Geometry and Measurement

M04-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

M04-S4C1-01. Draw and describe the relationships between points, lines, line segments, rays, and angles including parallelism and perpendicularity.

M04-S4C1-02. Justify which objects in a collection match a given geometric description.

M04-S4C1-03. Describe and classify triangles by angles and sides.

M04-S4C1-04. Recognize which attributes (such as shape or area) change and which do not change when 2-dimensional figures are cut up or rearranged.

M04-S4C1-05. Recognize and draw congruent figures, and match them in a given collection.

M04-S4C1-06. Draw right, acute, obtuse, and straight angles and identify these angles in other geometric figures.

M04-S4C1-07. Recognize the relationship between a 3-dimensional figure and its corresponding net(s).

M04-S4C3. Coordinate Geometry: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

M04-S4C3-01. Name, locate, and graph points in the first quadrant of the coordinate plane using ordered pairs.

M04-S4C3-02. Plot line segments in the first quadrant of the coordinate plane using a set of ordered pairs in a table.

M04-S4C3-03. Construct geometric figures with vertices at points on the coordinate plane.

M04-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

M04-S4C4-01. Compute elapsed time to the minute.

M04-S4C4-02. Apply measurement skills to measure length, mass, and capacity using metric units.

M04-S4C4-03. Solve problems involving conversions within the same measurement system.

M04-S4C4-04. Solve problems involving perimeter of 2-dimensional figures and area of rectangles.

M04-S4C4-05. Describe the change in perimeter or area when one attribute (length or width) of a rectangle changes.

AZ.M04-S5. Structure and Logic

M04-S5C1. Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems.

M04-S5C1-01. Analyze common algorithms for computing (adding, subtracting, multiplying, and dividing) with whole numbers using the associative, commutative, and distributive properties.

M04-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

M04-S5C2-01. Analyze a problem situation to determine the question(s) to be answered.

M04-S5C2-02. Identify relevant, missing, and extraneous information related to the solution to a problem.

M04-S5C2-03. Select and use one or more strategies to efficiently solve the problem and justify the selection.

M04-S5C2-04. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.

M04-S5C2-05. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.

M04-S5C2-06. Summarize mathematical information, explain reasoning, and draw conclusions.

M04-S5C2-07. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.

M04-S5C2-08. Make and test conjectures based on data (or information) collected from explorations and experiments.