Number and Quantity 
 compare two fractions
 use whole number exponents to express examples of repeated multiplication
 identify and use factors of whole numbers
 identify and use multiples of whole numbers
 describe the meaning of i, the unit imaginary number
 perform basic operations with complex numbers

Algebra and Functions 
 apply number properties to model realworld and mathematical problems that involve reasoning with proportions
 select and use appropriate units when solving realworld and mathematical problems that involve one or more units of measure
 solve literal equations (e.g., P = 2l + 2w) for any variable
 identify, interpret, and generate symbolic representations that model the contexts of realworld and mathematical problems
 represent and interpret relationships defined by equations and formulas; translate between representations as ordered pairs, graphs, and equations; and investigate symmetry and transformations (e.g., reflections, translations)
 identify characteristics of figures from a general equation

Algebra 
 graph and interpret simple inequalities on the number line
 model realworld and mathematical problems using linear equations and inequalities
 attend to the difference between values from an algebraic model and actual outcomes
 factor and perform the basic operations on seconddegree polynomials
 identify basic characteristics of a quadratic equation (e.g., seconddegree polynomial)
 use the inverse relationships for the four basic operations, exponentiation, and root extractions to determine unknown quantities
 model realworld and mathematical problems, using scientific notation
 describe the result of division by zero
 describe why square roots of negative numbers do not yield real number values
 evaluate algebraic expressions and solve multistep firstdegree equations

Functions 
 describe simple numerical patterns by writing explicit and recursive formulas
 recognize that values may be different than predictions made using a model
 describe the difference between an equation and a function
 describe examples where a function is undefined (e.g., division by zero, square roots of negative numbers)

Geometry 
 recognize when to apply geometric properties and relationships of parallel lines to find unknown angle measures
 recognize when to apply geometric properties and relationships of triangles to find unknown angle measures and side lengths
 apply the definition of symmetry (e.g., line, rotational) to describe plane and solid figures
 use appropriate units and degrees of precision to measure and describe realworld objects
 apply a variety of strategies to determine the circumference or perimeter and the area for circles, triangles, rectangles, and composite geometric figures
 identify the basic trigonometric ratios
 describe the relative locations of two points in the coordinate plane in terms of horizontal (e.g., run) and vertical (e.g., rise) distances
 identify and describe midpoints and bisectors
 investigate symmetry and transformations of points (e.g., reflections, translations, rotations)

Statistics and Probability 
 use several computations with data to solve realworld and mathematical problems
 use data presented in different displays (e.g., table, chart, histogram) to solve realworld and mathematical problems
 calculate simple probabilities to solve realworld and mathematical problems
 read and interpret information presented in a Venn diagram
 consider the impact of outliers and deviations when describing data trends
 choose the best measures of central tendency and variability to describe a data set based on the shape of its distribution
