Grade: K
Patterns, Function, and Algebra Standard
Use Algebraic Representations
Standard Number: 4
Model a problem situation using physical materials
Use Patterns, Relations, and Functions
Standard Number: 1
Sort, classify and order objects by size, number and other properties
a Identify how objects are alike and different
b Order three events or objects according to a given attribute, such as time or size
c Recognize and explain how objects can be classified in more than one way
d Identify what attribute was used to sort groups of objects that have already been sorted
Standard Number: 2
Identify, create, extend and copy sequences of sounds (such as musical notes), shapes (such as buttons, leaves or blocks), motions (such as hops or skips), and numbers from 1 to 10
Standard Number: 3
Describe orally the pattern of a given sequence
Grade: Gr. 1
Patterns, Function, and Algebra Standard
Use Algebraic Representations
Standard Number: 4
Solve open sentences by representing an expression in more than one way using the commutative property; e.g., 4 + 5 = 5 + 4 or the number of blue balls plus red balls is the same as the number of red balls plus blue balls (R+B=B+R)
Standard Number: 5
Describe orally and model a problem situation using words, objects or number phrase or sentence
Use Patterns, Relations, and Functions
Standard Number: 1
Sort, classify and order objects by two or more attributes, such as color and shape, and explain how objects were sorted
Standard Number: 2
Extend sequences of sounds, shapes or simple number patterns, and create and record similar patterns
a Analyze and describe patterns with multiple attributes using numbers and shapes; e.g., AA, B, aa, b, AA, B, aa, b
b Continue repeating and growing patterns with materials, pictures and geometric items; e.g., XO, XOO, XOOO, XOOOO
Standard Number: 3
Describe orally the basic unit or general plan of a repeating or growing pattern
Grade: Gr. 2
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 7
Describe qualitative and quantitative changes, especially those involving addition and subtraction; e.g., a student growing taller versus a student growing two inches in one year
Use Algebraic Representations
Standard Number: 4
Use objects, pictures, numbers and other symbols to represent a problem situation
Standard Number: 5
Understand equivalence and extend the concept to situations involving symbols
Standard Number: 6
Use symbols to represent unknown quantities and identify values for symbols in an expression or equation using addition and subtraction
Use Patterns, Relations, and Functions
Standard Number: 1
Extend simple number patterns (both repeating and growing patterns), and create similar patterns using different objects, such as using physical materials or shapes to represent numerical patterns
Standard Number: 2
Use patterns to make generalizations and predictions; e.g., determine a missing element in a pattern
Standard Number: 3
Create new patterns with consistent rules or plans, and describe the rule or general plan of existing patterns
Grade: Gr. 3
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 7
Create tables to record, organize and analyze data to discover patterns and rules
Standard Number: 8
Identify and describe quantitative changes, especially those involving addition and subtraction; e.g., the height of water in a glass becoming 1 centimeter lower each week due to evaporation
Use Algebraic Representations
Standard Number: 4
Model problem situations using objects, pictures, tables, numbers, letters and other symbols
Standard Number: 5
Write, solve and explain simple mathematical statements, such as 7 + ? > 8 or ? + 8 = 10.
Standard Number: 6
Express mathematical relationships as equations and inequalities
Use Patterns, Relations, and Functions
Standard Number: 1
Extend multiplicative and growing patterns, and describe the pattern or rule in words
Standard Number: 2
Analyze and replicate arithmetic sequences with and without a calculator
Standard Number: 3
Use patterns to make predictions, identify relationships, and solve problems
Grade: Gr. 4
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 6
Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases
Use Algebraic Representations
Standard Number: 3
Construct a table of values to solve problems associated with a mathematical relationship
Standard Number: 4
Use rules and variables to describe patterns and other relationships
Standard Number: 5
Represent mathematical relationships with equations or inequalities
Use Patterns, Relations, and Functions
Standard Number: 1
Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications
Standard Number: 2
Represent and analyze patterns and functions using words, tables and graphs
Grade: Gr. 5
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 6
Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph
Use Algebraic Representations
Standard Number: 3
Use variables as unknown quantities in general rules when describing patterns and other relationships
Standard Number: 4
Create and interpret the meaning of equations and inequalities representing problem situations
Standard Number: 5
Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions
Use Patterns, Relations, and Functions
Standard Number: 1
Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs
Standard Number: 2
Use calculators or computers to develop patterns, and generalize them using tables and graphs
Grade: Gr. 6
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 7
Identify and describe situations with constant or varying rates of change, and compare them
Standard Number: 8
Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change
Use Algebraic Representations
Standard Number: 3
Recognize and generate equivalent forms of Algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(1 + w) or 21 + 2w
Standard Number: 4
Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs
Standard Number: 5
Produce and interpret graphs that represent the relationship between two variables
Standard Number: 6
Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations
Use Patterns, Relations, and Functions
Standard Number: 1
Represent and analyze patterns, rules and functions, using physical materials, tables and graphs
Standard Number: 2
Use words and symbols to describe numerical and geometric patterns, rules and functions
Grade: Gr. 7
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 10
Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another
Standard Number: 11
Use graphing calculators or computers to analyze change; e.g., distance-time relationships
Use Algebraic Representations
Standard Number: 4
Create visual representations of equation-solving processes that model the use of inverse operations
Standard Number: 5
Represent linear equations by plotting points in the coordinate plane
Standard Number: 6
Represent inequalities on a number line or a coordinate plane
Standard Number: 7
Justify that two forms of an Algebraic expression are equivalent, and recognize when an expression is simplified
Standard Number: 8
Use formulas in problem-solving situati
Standard Number: 9
Recognize a variety of uses for variables; e.g., placeholder for an unknown quantity in an equation, generalization for a pattern, formula
Use Patterns, Relations, and Functions
Standard Number: 1
Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions
Standard Number: 2
Generalize patterns by describing in words how to find the next term
Standard Number: 3
Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1,3,5,7... is linear and 1,3,4,8,16... is nonlinear
Grade: Gr. 8
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 14
Differentiate and explain types of changes in mathematical relationships, such as linear, nonlinear, continuous vs. noncontinuous, direct variation vs. indirect variaiton
Standard Number: 15
Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts
Standard Number: 16
Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern
Use Algebraic Representations
Standard Number: 4
Extend the uses of variables to include covariants where y depends on x.
Standard Number: 5
Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial
Standard Number: 6
Describe 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 and y-intercept in real-world problems
Standard Number: 7
Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems
Standard Number: 8
Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems
Standard Number: 9
Solve linear equations and inequalities graphically, symbolically and using technology
Standard Number: 10
Solve 2 by 2 systems of linear equations graphically and by simple substitution
Standard Number: 11
Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution
Standard Number: 12
Solve simple quadratic equations graphically; e.g., y = x2 – 16
Standard Number: 13
Compute and interpret slope, midpoint and distance given a set of ordered pairs.
Use Patterns, Relations, and Functions
Standard Number: 1
Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form
Standard Number: 2
Generalize patterns and sequences by describing how to find the nth term
Standard Number: 3
Identify functions as linear or nonlinear based on information given in a table, graph or equation
Grade: Gr. 9
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 13
Model and solve problems involving direct and inverse variation using proportional reasoning
Standard Number: 14
Describe the relationship between slope and the graph of a direct variation and inverse variation
Standard Number: 15
Describe how a change in the value of a constant in a linear or quadratic equation affects the related graphs
Use Algebraic Representations
Standard Number: 6
Write and use equivalent forms of equations and inequalities in problem situations; e.g., changing a linear equation to the slope-intercept form.
Standard Number: 7
Use formulas to solve problems involving exponential growth and decay
Standard Number: 8
Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point
Standard Number: 9
Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology
Standard Number: 10
Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology
Standard Number: 11
Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only
Standard Number: 12
Simplify rational expressions by eliminating common factors and applying properties of integer exponents
Use Patterns, Relations, and Functions
Standard Number: 1
Define function with ordered pairs in which each domain element is assigned exactly one range element
Standard Number: 2
Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations
Standard Number: 3
Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.
Standard Number: 4
Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words
Standard Number: 5
Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum
Grade: Gr. 10
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 12
Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis
Use Algebraic Representations
Standard Number: 3
Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height
Standard Number: 4
Use algebraic representations and functions to describe and generalize geometric properties and relationships
Standard Number: 5
Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions
Standard Number: 6
Solve equations and inequalities having rational expressions as coefficients and solutions
Standard Number: 7
Solve systems of linear inequalities
Standard Number: 8
Graph the quadratic relationship that defines circles
Standard Number: 9
Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals
Standard Number: 10
Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions
Standard Number: 11
Solve real-world problems that can be modeled, using systems of linear equations and inequalities
Use Patterns, Relations, and Functions
Standard Number: 1
Define function formally and with f(x) notation
Standard Number: 2
Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range
Grade: Gr. 11
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 11
Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation
Use Algebraic Representations
Standard Number: 6
Represent the inverse of a function symbolically and graphically as a reflection about y = x.
Standard Number: 7
Model and solve problems with matrices and vectors
Standard Number: 8
Solve equations involving radical expressions and complex roots
Standard Number: 9
Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution).
Standard Number: 10
Describe the characteristics of the graphs of conic sections
Use Patterns, Relations, and Functions
Standard Number: 1
Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest
Standard Number: 2
Translate a recursive function into a closed form expression or formula for the nth term to solve a problem situation involving an iterative process; e.g., find the value of an annuity after 7 years
Standard Number: 3
Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior
Standard Number: 4
Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology
Standard Number: 5
Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x
Grade: Gr. 12
Patterns, Function, and Algebra Standard
Analyze Change
Standard Number: 10
Use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point.
Use Algebraic Representations
Standard Number: 5
Set up and solve systems of equations using matrices and graphs, with and without technology
Standard Number: 6
Make arguments about mathematical properties using mathematical induction
Standard Number: 7
Make mathematical arguments using the concepts of limit
Standard Number: 8
Compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; e.g., make successive estimates using progressively smaller rectangles
Standard Number: 9
Translate freely between polar and Cartesian coordinate systems
Use Patterns, Relations, and Functions
Standard Number: 1
Analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases
Standard Number: 2
Translate between the numeric and symbolic form of a sequence or series
Standard Number: 3
Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior
Standard Number: 4
Represent the inverse of a transcendental function symbolically
|
|
