Arkansas State Standards for Mathematics: Grade 8

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

NO.1.8.1. Rational Numbers: Read, write, compare and solve problems, with and without appropriate technology, including numbers less than 1 in scientific notation

NO.1.8.2. Rational Numbers: Convert between scientific notation and standard notation, including numbers from zero to one.

NO.1.8.3. Rational Numbers: Compare and order real numbers including irrational numbers and find their approximate location on a number line (Use technology when appropriate)

NO.1.8.4. Rational Numbers: Understand and justify classifications of numbers in the real number system

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

NO.2.8.1. Number Theory: Apply the addition, subtraction, multiplication and division properties of equality to two-step equations

NO.2.8.2. Number Theory: Understand and apply the inverse and identity properties

NO.2.8.3. Number Theory: Use inverse relationships (addition and subtraction, multiplication and division, squaring and square roots) in problem solving situations

NO.2.8.4. Number Theory: Apply rules (conventions) for order of operations to rational numbers

NO.2.8.5. Number Theory: Model and develop addition, subtraction, multiplication and division of rational numbers

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

NO.3.8.1. Computational Fluency: Compute, with and without appropriate technology, with rational numbers in multi-step problems

NO.3.8.2. 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.3.8.3. Estimation: Use estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutions

NO.3.8.4. Application of Computation: Apply factorization to find LCM and GCF of algebraic expressions

NO.3.8.5. Application of Computation: Calculate and find approximations of square roots with appropriate technology

NO.3.8.6. Application of Computation: Solve, with and without technology, real world percent problems including percent of increase or decrease

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

A.4.8.1. Patterns, Relations and Functions: Find the nth term in a pattern or a function table

A.4.8.2. Patterns, Relations and Functions: Using real world situations, describe patterns in words, tables, pictures, and symbolic representations

A.4.8.3. Patterns, Relations and Functions: Interpret and represent a two operation function as an algebraic equation

A.4.8.4. Patterns, Relations and Functions: Use tables, graphs, and equations to identify independent/dependent variables (input/output)

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

A.5.8.1. Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology

A.5.8.2. Expressions, Equations and Inequalities: Solve and graph linear equations (in the form y=mx+b)

A.5.8.3. Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials

A.5.8.4. Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using rational numbers

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

A.6.8.1. Algebraic Models and Relationships: Describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real-world problems

A.6.8.2. Algebraic Models and Relationships: Represent, with and without appropriate technology, linear relationships concretely, using tables, graphs and equations.

A.6.8.3. Algebraic Models and Relationships: Differentiate between independent/dependent variables given a linear relationship in context

A.6.8.4 Algebraic Models and Relationships: Represent, with and without appropriate technology, simple exponential and/or quadratic functions using verbal descriptions, tables, graphs and formulas and translate among these representations

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

A.7.8.1. Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)

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.8.8.1. Characteristics of Geometric Shapes: Form generalizations and validate conclusions about properties of geometric shapes

G.8.8.2. Characteristics of Geometric Shapes: Make, with and without appropriate technology, and test conjectures about characteristics and properties between two-dimensional figures and three-dimensional objects

G.8.8.3. Characteristics of Geometric Shapes: Determine appropriate application of geometric ideas and relationships, such as congruence, similarity, and the Pythagorean Theorem, with and without appropriate technology

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

G.9.8.1. Symmetry and Transformations: Determine a transformation's line of symmetry and compare the properties of the figure and its transformation

G.9.8.2. Symmetry and Transformations: Draw the results of translations and reflections about the x and y-axis and rotations of objects about the origin

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

G.10.8.1. Coordinate Geometry: Use coordinate geometry to explore the links between geometric and algebraic representations of problems (lengths of segments/distance between points, slope/perpendicular-parallel lines)

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

G.11.8.1. Spatial Visualization and Models: Using isometric dot paper interpret and draw different views of buildings

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

M.12.8.1. Attributes and Tools: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problems

M.12.8.2. Attributes and Tools: Describe and apply equivalent measures using a variety of units within the same system of measurement

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

M.13.8.1. Attributes and Tools: Draw and apply measurement skills with fluency to appropriate levels of precision

M.13.8.2. Attributes and Tools: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology

M.13.8.3. Attributes and Tools: Apply proportional reasoning to solve problems involving indirect measurements, scale drawings or rates

M.13.8.4. Attributes and Tools: Find the distance between two points on a coordinate plane using with the Pythagorean Theorem

M.13.8.5. Attributes and Tools: Estimate and compute the area of irregular two-dimensional 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.14.8.1. Collect, organize and display data: Design and conduct investigations which include adequate number of trials, unbiased sampling, accurate measurement, and record-keeping

DAP.14.8.2. Collect, organize and display data: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit)

DAP.14.8.3. Collect, organize and display data: Interpret or solve real-world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs

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

DAP.15.8.1. Data Analysis: Compare and contrast the reliability of data sets with different size populations

DAP.15.8.2. Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread

DAP.15.8.3. Data Analysis: Given at least one of the measures of central tendency create a data set

DAP.15.8.4. Data Analysis: Describe how the inclusion of outliers affects those measures

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

DAP.16.8.1. Data Analysis: Use observations about differences between sets of data to make conjectures about the populations from which the data was taken

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

DAP.17.8.1. Data Analysis: Compute, with and without appropriate technology, probabilities of compound events, using organized lists, tree diagrams and logic grid

DAP.17.8.2. Data Analysis: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predict results, and explain differences