Standards for Mathematical Practice  

The Number System 


Abbreviation 
Standard 
Know that there are numbers that are not rational, and approximate them by rational numbers.  
NC.8.NS.1  Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a nonrepeating, nonterminating decimal. 
NC.8.NS.2  Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:

Expressions and Equations 


Abbreviation 
Standard 
Work with radicals and integer exponents.  
NC.8.EE.1  Develop and apply the properties of integer exponents to generate equivalent numerical expressions. 
NC.8.EE.2  Use square root and cube root symbols to:

NC.8.EE.3  Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other. 
NC.8.EE.4  Perform multiplication and division with numbers expressed in scientific notation to solve realworld problems, including problems where both decimal and scientific notation are used. 
Analyze and solve linear equations and inequalities.  
NC.8.EE.7  Solve realworld and mathematical problems by writing and solving equations and inequalities in one variable.

Analyze and solve pairs of simultaneous linear equations.  
NC.8.EE.8  Analyze and solve a system of two linear equations in two variables in slopeintercept form.

Functions 


Abbreviation 
Standard 
Define, evaluate, and compare functions.  
NC.8.F.1  Understand that a function is a rule that assigns to each input exactly one output.

NC.8.F.2  Compare properties of two linear functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 
NC.8.F.3  Identify linear functions from tables, equations, and graphs. 
Use functions to model relationships between quantities.  
NC.8.F.4  Analyze functions that model linear relationships.

NC.8.F.5  Qualitatively analyze the functional relationship between two quantities.

Geometry 


Abbreviation 
Standard 
Understand congruence and similarity using physical models, transparencies, or geometry software.  
NC.8.G.2  Use transformations to define congruence.

NC.8.G.3  Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the axis and axis on twodimensional figures using coordinates. 
NC.8.G.4  Use transformations to define similarity.

Analyze angle relationships.  
NC.8.G.5  Use informal arguments to analyze angle relationships.

Understand and apply the Pythagorean Theorem.  
NC.8.G.6  Explain the Pythagorean Theorem and its converse. 
NC.8.G.7  Apply the Pythagorean Theorem and its converse to solve realworld and mathematical problems. 
NC.8.G.8  Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 
Solve realworld and mathematical problems involving volume of cylinders, cones, and spheres.  
NC.8.G.9  Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve realworld and mathematical problems. 
Statistics and Probability 


Abbreviation 
Standard 
Investigate patterns of association in bivariate data.  
NC.8.SP.1  Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 
NC.8.SP.2  Model the relationship between bivariate quantitative data to:

NC.8.SP.3  Use the equation of a linear model to solve problems in the context of bivariate quantitative data, interpreting the slope and  intercept. 
NC.8.SP.4  Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a twoway table.
