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Mathematics

Grade Level Benchmarks

Algebra Benchmarks

Number and Operations Standard
E	Understand irrational and complex numbers as extensions of the real-number system
E	Understand the inverse relationship between squaring and finding square roots
E	Understand undefined numerical expressions (6 divided by 0, square root of -4, etc.)
E	Find rational powers and take roots (other than square roots)
T	Use exponents and scientific notation
T	Use the order of operations to simplify numerical expressions
T	Use a variety of methods to compute, including using objects, mental computation,
	estimation, and paper and pencil
T	Use calculators appropriately to compute, check calculations, and aid in processing
	large amounts of data
T	Understand division of fractions as multiplication by the reciprocal
T	Develop, analyze, and explain methods for solving problems involving proportions
T	Judge the reasonableness of numerical computations
R	Understand and use ratios and proportions
R	Use integers to represent and compare quantities
R	Understand the meanings and effects of arithmetic operations with fractions, decimals, and integers
R	Develop and use algorithms for multiplying fractions
R	Develop and use algorithms for adding, subtracting, multiplying, and dividing integers
Algebra Standards
E	Use quadratic and exponential functions as models for real-world situations
E	Graph and analyze quadratic functions
E	Graph and analyze exponential functions
T	Factor polynomial expressions
T	Solve systems of linear equations
T	Solve linear inequalities
T	Identify dependent and independent variables in real-world situations
T	Model constant growth rate situations using linear equations
T	Identify functions as linear or non-linear from their graphs, tables, or equations
T	Investigate how a change in one variable relates to a change in a second variable
T	Identify and describe situations with constant or varying rates of change and compare them
T	Relate the rate of change in a situation (speed, etc.) to the slope of a line
T	Find the slope of a line given a graph, table, or equation
T	Give a linear equation for a relationship represented in a table or graph
T	Write and interpret equations in y= mx+b form
T	Identify x- and y- intercepts from a graph or an equation
T	Solve linear equations of form ax+b=c
T	Solve linear equations of form ax+b=cx+d
T	Solve literal linear equations (solve ab+c=d for b)
T	Simplify simple algebraic expressions (laws of exponents, binomial multiplication, like
	terms, etc.)
R	Use tables, graphs, and equations to draw conclusions about real-world situations
Geometry Standard
E	Understand the relationship between the slopes of parallel and perpendicular lines
	graphed in the coordinate plane
R	Plot points and draw two-dimensional figures in the coordinate plane
Measurement Standard
T	Choose appropriate scales for graphs (hand drawn and those generated by graphing
	calculators)
T	Convert units using scale factors
T	Solve problems using rates and other derived units (velocity, density, etc.)
T	Use unit analysis to analyze and understand real-world problems
Data Analysis and Probability Standard
E	Calculate simple probabilities (dice, marbles, cards, etc.)
E	Calculate probability of a compound event
E	Fit linear regression equations to bivariate data and determine correlation coefficients
T	Draw lines of best fit to a scatter plot
T	Use extrapolation and interpolation to make predictions based on data
T	Understand direct and inverse relationships between two quantities
R	Predict the probability of outcomes of simple experiments and test the predictions
R	Understand that the measure of likelihood of an event can be represented by a number from 0 to 1
R	Make scatter plots for bivariate data

Geometry Benchmarks

Number and Operations Standard
E	Understand irrational and complex numbers as extensions of the real-number system
T	Understand the inverse relationship between squaring and finding square roots
R	Use exponents and scientific notation
R	Use a variety of methods to compute, including using objects, mental computation,
	estimation, and paper and pencil
R	Use calculators appropriately to compute, check calculations, and aid in processing
	large amounts of data
R	Judge the reasonableness of numerical computations
Geometry Standard
E	Solve right triangles using trigonometric relationships
T	Determine and predict the sums of the interior and exterior angle measures of regular
	polygons
T	Construct two- and three- dimensional models of objects
T	Draw orthogonal views of three-dimensional objects
T	Recognize and apply slides, flips, and turns to two-dimensional objects
T	Determine which types of transformations preserve similarity
T	Transform figures using compass and straight-edge constructions
T	Understand the effect of composition of transformations
T	Prove simple theorems regarding geometric relationships in two dimensions
T	Understand relationships between angles formed by intersecting lines
T	Understand relationships between the number of faces, edges, and vertices in three-
	dimensional objects
T	Understand the relationship between the slopes of parallel and perpendicular lines
	graphed in the coordinate plane