Arizona State Standards for Mathematics: Grade 5

AZ.M05-S1. Number and Operations

M05-S1C1. Number Sense: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

M05-S1C1-01. Determine equivalence by converting between benchmark fractions, decimals, and percents.

M05-S1C1-02. Differentiate between prime and composite numbers; differentiate between factors and multiples for whole numbers.

M05-S1C1-03. Locate integers on a number line.

M05-S1C1-04. Compare and order positive fractions, decimals, and percents.

M05-S1C1-05. Use ratios and unit rates to model, describe and extend problems in context.

M05-S1C1-06. Express or interpret positive and negative numbers in context.

M05-S1C2. Numerical Operations: Understand and apply numerical operations and their relationship to one another.

M05-S1C2-01. Add and subtract decimals through thousandths and fractions expressing solutions in simplest form.

M05-S1C2-02. Multiply multi-digit whole numbers.

M05-S1C2-03. Divide multi-digit whole numbers by whole number divisors with and without remainders.

M05-S1C2-04. Apply the associative, commutative, and distributive properties to solve numerical problems.

M05-S1C2-05. Simplify numerical expressions (including fractions and decimals) using the order of operations with or without grouping symbols.

M05-S1C3. Estimation: Use estimation strategies reasonably and fluently while integrating content from each of the other strands.

M05-S1C3-01. Make estimates appropriate to a given situation or computation with whole numbers, fractions, and decimals.

AZ.M05-S2. Data Analysis, Probability, and Discrete Mathematics

M05-S2C1. Data Analysis (Statistics): Understand and apply data collection, organization, and representation to analyze and sort data.

M05-S2C1-01. Collect, record, organize, and display data using multi-bar graphs or double line graphs.

M05-S2C1-02. Formulate and answer questions by interpreting and analyzing displays of data, including multi-bar graphs or double line graphs.

M05-S2C1-03. Use mean, median, mode, and range to analyze and describe the distribution of a given data set.

M05-S2C2. Probability: Understand and apply the basic concepts of probability.

M05-S2C2-01. Describe the theoretical probability of events and represent the probability as a fraction, decimal, or percent.

M05-S2C2-02. Explore probability when performing experiments by

M05-S2C2-02.a. Predicting the outcome

M05-S2C2-02.b. Recording the data

M05-S2C2-02.c. Comparing outcomes of the experiment to predictions

M05-S2C2-02.d. Comparing the results of multiple repetitions of the experiment.

M05-S2C3. Systematic Listing and Counting: Understand and demonstrate the systematic listing and counting of possible outcomes.

M05-S2C3-01. Analyze relationships among representations and make connections to the multiplication principle of counting.

M05-S2C3-02. Solve a variety of counting problems and explain the multiplication principle of counting.

M05-S2C4. Vertex-Edge Graphs: Understand and apply vertex-edge graphs.

M05-S2C4-01. Investigate properties of vertex-edge graphs

M05-S2C4-01.a. Euler paths

M05-S2C4-01.b. Euler circuits

M05-S2C4-01.c. Degree of a vertex.

M05-S2C4-02. Solve problems related to Euler paths and circuits.

AZ.M05-S3. Patterns, Algebra, and Functions

M05-S3C1. Patterns: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

M05-S3C1-01. Recognize, describe, create, and analyze a numerical sequence involving fractions and decimals using addition and subtraction.

M05-S3C3. Algebraic Representations: Represent and analyze mathematical situations and structures using algebraic representations.

M05-S3C3-01. Create and solve two-step equations that can be solved using inverse operations with whole numbers.

M05-S3C4. Analysis of Change: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

M05-S3C4-01. Describe patterns of change including constant rate and increasing or decreasing rate.

AZ.M05-S4. Geometry and Measurement

M05-S4C1. Geometric Properties: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

M05-S4C1-01. Draw and label 2-dimensional figures given specific attributes including angle measure and side length.

M05-S4C1-02. Solve problems by understanding and applying the property that the sum of the interior angles of a triangle is 180°.

M05-S4C1-03. Classify quadrilaterals by their properties.

M05-S4C1-04. Compare attributes of 2-dimensional figures with 3-dimensional figures by drawing and constructing nets and models.

M05-S4C4. Measurement: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

M05-S4C4-01. Solve problems using elapsed time.

M05-S4C4-02. State an appropriate measure and degree of accuracy in a given context.

M05-S4C4-03. Measure angles between 0 and 360 degrees.

M05-S4C4-04. Solve problems involving the area of 2-dimensional figures by using the properties of parallelograms and triangles.

M05-S4C4-05. Solve problems involving area and perimeter of regular and irregular polygons using reallotment of square units.

AZ.M05-S5. Structure and Logic

M05-S5C1. Algorithms and Algorithmic Thinking: Use reasoning to solve mathematical problems.

M05-S5C1-01. Analyze common algorithms for adding and subtracting fractions and decimals using the associative, commutative, and distributive properties.

M05-S5C1-02. Develop an algorithm or formula to calculate areas and perimeters of simple polygons.

M05-S5C2. Logic, Reasoning, Problem Solving, and Proof: Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications.

M05-S5C2-01. Analyze a problem situation to determine the question(s) to be answered.

M05-S5C2-02. Identify relevant, missing, and extraneous information related to the solution to a problem.

M05-S5C2-03. Select and use one or more strategies to efficiently solve the problem and justify the selection.

M05-S5C2-04. Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem.

M05-S5C2-05. Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols.

M05-S5C2-06. Summarize mathematical information, explain reasoning, and draw conclusions.

M05-S5C2-07. Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question.

M05-S5C2-08. Make and test conjectures based on data or information collected from explorations and experiments.

M05-S5C2-09. Identify simple valid arguments using if...then statements based on graphic organizers.

M05-S5C2-10. Construct if... then statements to generalize rules for computation, geometric properties and algebraic functions.