# Arkansas State Standards for Mathematics: Grade 5

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AR.NO.1. Number and Operations: Number Sense: Students shall understand numbers, ways of representing numbers, relationships among numbers and number systems

NO.1.5.1. Rational Numbers: Use models and visual representations to develop the concepts of the following: Fractions: parts of unit wholes; parts of a collection; locations on number lines; locations on ruler (benchmark fractions); divisions of whole numbers. Ratios: part-to-part (2 boys to 3 girls); part-to-whole (2 boys to 5 people). Percents: part-to-100

NO.1.5.2. Rational Numbers: Develop understanding of decimal place value using models

NO.1.5.3. Rational Numbers: Identify decimal and percent equivalents for benchmark fractions

NO.1.5.4. Rational Numbers: Round and compare decimals to a given place value (whole number, tenths, hundredths)

NO.1.5.5. Rational Numbers: Use models of benchmark fractions and their equivalent forms to analyze the size of fractions; to determine that simplification does not change the value of the fraction; to convert between mixed numbers and improper fractions

NO.1.5.6. Rational Numbers: Use models to differentiate between perfect squares up to 100 and other numbers

AR.NO.2. Number and Operations: Properties of Number Operations: Students shall understand meanings of operations and how they relate to one another

NO.2.5.1. Number Theory: Use divisibility rules to determine if a number is a factor of another number (2, 3, 5, 10)

NO.2.5.2. Number Theory: Identify commutative and associative properties

NO.2.5.3. Number Theory: Identify the distributive property by using physical models to solve computation and real world problems

NO.2.5.4. Number Theory: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses

NO.2.5.5. Number Theory: Model addition, subtraction, and multiplication of fractions with like and unlike denominators and decimals

AR.NO.3. Number and Operations: Numerical Operations and Estimation: Students shall compute fluently and make reasonable estimates

NO.3.5.1. Computational Fluency: Develop and use a variety of algorithms with computational fluency to perform whole number operations using addition and subtraction (up to 5 digit numbers), multiplication (up to 3-digit x 2 digit), division (up to 2-digit divisor) interpreting remainders, including real world problems

NO.3.5.2. Computational Fluency: Develop and use algorithms to add and subtract numbers containing decimals (up to thousandths place), to multiply decimals, (hundredths x tenths), to divide decimals by whole number divisors, and to add and subtract fractions with like denominators

NO.3.5.3. Computational Fluency: Solve, with and without appropriate technology, two-step problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)

NO.3.5.4. Estimation: Develop and use strategies to estimate the results of whole number computations and to judge the reasonableness of such results

NO.3.5.5. Application of Computation: Use factors of numbers: to introduce exponents; to find common factors of two numbers; to simplify fractions to the lowest terms

AR.A.4. Algebra: Patterns, Relations and Functions: Students shall recognize, describe, and develop patterns, relations and functions

A.4.5.1. Patterns, Relations and Functions: Solve problems by finding the next term or missing term in a pattern or function table using real world situations

A.4.5.2. Patterns, Relations and Functions: Interpret and write a rule for a one-operation function table

AR.A.5. Algebra: Algebraic Representations: Students shall represent and analyze mathematical situations and structures using algebraic symbols

A.5.5.1. Expressions, Equations and Inequalities: Model and solve simple equations by informal methods using manipulatives and appropriate technology

A.5.5.2. Expressions, Equations and Inequalities: Write expressions containing one variable (a letter representing an unknown quantity) using rules for addition and subtraction

A.5.5.3. Expressions, Equations and Inequalities: Select, write and evaluate algebraic expressions with one variable by substitution

AR.A.6. Algebra: Algebraic Models: Students shall develop and apply mathematical models to represent and understand quantitative relationships

A.6.5.1. Algebraic Models and Relationships: Draw conclusions and make predictions, with and without appropriate technology, from models, tables and line graphs

AR.A.7. Algebra: Analysis of Change: Students shall analyze change in various contexts

A.7.5.1. Analyze Change: Model and describe quantities that change using real world situations

AR.G.8. Geometry: Geometric Properties: Students shall analyze characteristics and properties of 2 and 3 dimensional geometric shapes and develop mathematical arguments about geometric relationships

G.8.5.1. Characteristics of Geometric Shapes: Identify and model regular and irregular polygons including decagon

G.8.5.2. Characteristics of Geometric Shapes: Identify and draw congruent, adjacent, obtuse, acute, right and straight angles (Label parts of an angle: vertex, rays, interior and exterior)

G.8.5.3. Characteristics of Geometric Shapes: Model and identify circle, radius, diameter, center, circumference and chord

G.8.5.4. Characteristics of Geometric Shapes: Model and identify the properties of congruent figures

AR.G.9. Geometry: Transformation of Shapes: Students shall apply transformations and the use of symmetry to analyze mathematical situations

G.9.5.1. Symmetry and Transformations: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged

AR.G.10. Geometry: Coordinate Geometry: Students shall specify locations and describe spatial relationships using coordinate geometry and other representational systems

G.10.5.1. Coordinate Geometry: Use geometric vocabulary (horizontal/x-axis, vertical/ y-axis, ordered pairs) to describe the location and plot points in Quadrant 1

AR.G.11. Geometry: Visualization and Geometric Models: Students shall use visualization, spatial reasoning and geometric modeling

G.11.5.1. Spatial Visualization and Models: Using grid paper, draw and identify two-dimensional patterns (nets) for cubes

AR.M.12. Measurement: Physical Attributes: Students shall use attributes and tools of measurement to describe and compare mathematical and real-world objects

M.12.5.1. Attributes and Tools: Identify and select appropriate units and tools to measure

M.12.5.2. Attributes and Tools: Make conversions within the customary measurement system in real world problems

M.12.5.3. Attributes and Tools: Establish through experience benchmark prefixes of milli-, centi-, and kilo-

M.12.5.4. Attributes and Tools: Understand when to use linear units to describe perimeter, square units to describe area or surface area, and cubic units to describe volume, in real world situations

M.12.5.5. Attributes and Tools: Model the differences between covering the faces (surface area/nets) and filling the interior (volume of cubes)

AR.M.13. Measurement: Systems of Measurement: Students shall identify and use units, systems and processes of measurement

M.13.5.1. Attributes and Tools: Solve real world problems involving one elapsed time, counting forward (calendar and clock)

M.13.5.2. Attributes and Tools: Determine which unit of measure or measurement tool matches the context for a problem situation

M.13.5.3. Attributes and Tools: Draw and measure distance to the nearest cm and 1/4 inch accurately

M.13.5.4. Attributes and Tools: Develop and use strategies to solve real world problems involving perimeter and area of rectangles

M.13.5.5. Attributes and Tools: Count the distance between two points on a horizontal or vertical line and compare the lengths of the paths on a grid

M.13.5.6. Attributes and Tools: Use benchmark angles to estimate the measure of angles

AR.M.14. Data Analysis and Probability: Data Representation: Students shall formulate questions that can be addressed with data and collect, organize and display

DAP.14.5.1. Collect, organize and display data: Develop appropriate questions for surveys

DAP.14.5.2. Collect, organize and display data: Collect numerical and categorical data using surveys, observations and experiments that would result in bar graphs, line graphs, line plots and stem-and-leaf plots

DAP.14.5.3. Collect, organize and display data: Construct and interpret frequency tables, charts, line plots, stem-and-leaf plots and bar graphs

AR.M.15. Data Analysis and Probability: Data Analysis: Students shall select and use appropriate statistical methods to analyze data

DAP.15.5.1. Data Analysis: Interpret graphs such as line graphs, double bar graphs, and circle graphs

DAP.15.5.2. Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data

AR.M.16. Data Analysis and Probability: Inferences and Predictions: Students shall develop and evaluate inferences and predictions that are based on data

DAP.16.5.1. Data Analysis: Make predictions and justify conclusions based on data

AR.M.17. Data Analysis and Probability: Probability: Students shall understand and apply basic concepts of probability

DAP.17.5.1. Data Analysis: Identify and predict the probability of events within a simple experiment

DAP.17.5.2. Data Analysis: List and explain all possible outcomes in a given situation

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