Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions
Standard: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Arithmetic with Polynomials and Rational Functions
Standard: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Creating Equations
Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Creating Equations
Standard: Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: Solve quadratic equations in one variable.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Reasoning with Equations and Inequalities
Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Interpret expressions that represent a quantity in terms of its context.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 - y^2)(x^2 + y^2).
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Algebra: Seeing Structure in Expressions
Standard: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Building Functions
Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Number and Quantity: The Real Number System
Standard: Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Use properties of rational and irrational numbers
Standard: Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret the structure of expressions.
Standard: Interpret expressions that represent a quantity in terms of its context.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret the structure of expressions.
Standard: Use the structure of an expression to identify ways to rewrite it. For example, see x^4 – y^4 as (x^2)^2 – (y^2)^2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^2)(x^2 + y^2).
Degree of Alignment:
Not Rated
(0 users)
Cluster: Write expressions in equivalent forms to solve problems
Standard: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Perform arithmetic operations on polynomials
Standard: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Understand the relationship between zeros and factors of polynomial
Standard: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Create equations that describe numbers or relationship
Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Create equations that describe numbers or relationship
Standard: Create equations that describe numbers or relationship. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Solve equations and inequalities in one variable
Standard: Solve quadratic equations in one variable.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Represent and solve equations and inequalities graphically
Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret functions that arise in applications in terms of the context
Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Analyze functions using different representations
Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Analyze functions using different representations
Standard: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Analyze functions using different representations
Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Build new functions from existing functions
Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Degree of Alignment:
Not Rated
(0 users)
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