# Arkansas State Standards for Mathematics: Grade 7

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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.1.7.1. Rational Numbers: Relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100

NO.1.7.2. Rational Numbers: Demonstrate, with and without appropriate technology, an understanding of place value using powers of 10 and write numbers greater than one in scientific notation

NO.1.7.3. Rational Numbers: Convert between scientific notation and standard notation using numbers greater than one.

NO.1.7.4. Rational Numbers: Find decimal and percent equivalents for mixed numbers and explain why they represent the same value

NO.1.7.5. Rational Numbers: Compare and represent integers, fractions, decimals and mixed numbers and find their approximate location on a number line

NO.1.7.6. Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational 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.2.7.1. Number Theory: Apply the distributive property of multiplication over addition or subtraction to simplify computations with integers, fractions and decimals

NO.2.7.2. Number Theory: Apply the addition, subtraction, multiplication and division properties of equality to one-step equations with integers, fractions, and decimals

NO.2.7.3. Number Theory: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponents

NO.2.7.4. Number Theory: Model and develop addition, subtraction, multiplication and division of integers

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

NO.3.7.1. Computational Fluency: Compute, with and without appropriate technology, with integers and positive rational numbers using real-world situations to solve problems

NO.3.7.2. Computational Fluency: Solve with and without appropriate technology, multi-step problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil)

NO.3.7.3. Estimation: Determine when an estimate is sufficient and use estimation to decide whether answers are reasonable in problems including fractions and decimals

NO.3.7.4. Application of Computation: Apply factorization, LCM, and GCF to solve problems using more than two numbers and explain the solution

NO.3.7.5. Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology

NO.3.7.6. Application of Computation: Solve, with and without technology, real world percent problems

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

A.4.7.1. Patterns, Relations and Functions: Create and complete a function table (input/output) using a given rule with two operations

A.4.7.2. Patterns, Relations and Functions: Identify and extend patterns in real world situations

A.4.7.3. Patterns, Relations and Functions: Interpret and write a rule for a two-operation function table

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

A.5.7.1. Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology

A.5.7.2. Expressions, Equations and Inequalities: Solve simple linear equations using integers and graph on a coordinate plane

A.5.7.3. Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms

A.5.7.4. Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using positive rational numbers

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

A.6.7.1. Algebraic Models and Relationships: Use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate plane

A.6.7.2. Algebraic Models And Relationships: Represent, with and without appropriate technology, linear equations by plotting and graphing points in the coordinate plane using all four quadrants given data in a table from a real world situation,

A.6.7.3. Algebraic Models and Relationships: Create and complete a function table (input/output) using a given rule with two operations in real world situations

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

A.7.7.1. Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change

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.8.7.1. Characteristics of Geometric Shapes: Identify, draw, classify and compare geometric figures using models and real world examples

G.8.7.2. Characteristics of Geometric Shapes: Investigate geometric properties and their relationships in one-, two-, and three-dimensional models, including convex and concave polygons

G.8.7.3. Characteristics of Geometric Shapes: Recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and linear pair)

G.8.7.4. Characteristics of Geometric Shapes: Use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilaterals

G.8.7.5. Characteristics of Geometric Shapes: Model and develop the concept that pi is the ratio of the circumference to the diameter of any circle

G.8.7.6. Characteristics of Geometric Shapes: Develop the properties of similar figures (ratio of sides and congruent angles)

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

G.9.7.1. Symmetry and Transformations: Examine the congruence, similarity, and line or rotational symmetry of objects using transformations

G.9.7.2. Symmetry and Transformations: Perform translations and reflections of two-dimensional figures using a variety of methods (paper folding, tracing, graph paper)

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

G.10.7.1. Coordinate Geometry: Plot points in the coordinate plane

G.10.7.2. Coordinate Geometry: Plot points that form the vertices of a geometric figure and draw, identify and classify the figure.

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

G.11.7.1. Spatial Visualization and Models: Build three-dimensional solids from two-dimensional patterns (nets)

G.11.7.2. Spatial Visualization and Models: Construct a building out of cubes from a set of views (front, top, side)

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

M.12.7.1. Attributes and Tools: Understand, select and use the appropriate units and tools (metric and customary) to measure length, weight, mass and volume to the required degree of accuracy for real world problems

M.12.7.2. Attributes and Tools: Understand relationships among units within the same system

M.12.7.3. Attributes and Tools: Find different areas for a given perimeter and find a different perimeter for a given area

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

M.13.7.1. Attributes and Tools: Solve real world problems involving two or more elapsed times, counting forward and backward (calendar and clock)

M.13.7.2. Attributes and Tools: Draw and measure distance to the nearest mm and 1/16 inch accurately

M.13.7.3. Attributes and Tools: Develop and use strategies to solve problems involving area of a trapezoid and circumference and area of a circle

M.13.7.4. Attributes and Tools: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials

M.13.7.5. Attributes and Tools: Apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measures

M.13.7.6. Attributes and Tools: Find the distance between two points on a number line and locate the midpoint

M.13.7.7. Attributes and Tools: Estimate and compute the area of more complex or irregular two-dimensional shapes by dividing them into more basic shapes

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.14.7.1. Collect, organize and display data: Identify different ways of selecting samples and compose appropriate questions

DAP.14.7.2. Collect, organize and display data: Explain which types of display are appropriate for various data sets (line graph for change over time, circle graph for part-to-whole comparison, scatter plot for trends)

DAP.14.7.3. Collect, organize and display data: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology

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

DAP.15.7.1. Data Analysis: Analyze data displays, including ways that they can be misleading

DAP.15.7.2. Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)

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

DAP.16.7.1. Data Analysis: Make, with and without appropriate technology, conjectures of possible relationships in a scatter plot and approximate the line of best fit (trend line)

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

DAP.17.7.1. Data Analysis: Understand that probability can take any value between 0 and 1 (events that are not going to occur have probability 0, events certain to occur have probability 1)

DAP.17.7.2. Data Analysis: Design, with and without appropriate technology, an experiment to test a theoretical probability and explain how the results may vary