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: 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: 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: Algebra: Seeing Structure in Expressions
Standard: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Building Functions
Standard: Write a function that describes a relationship between two quantities.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Building Functions
Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
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: Building Functions
Standard: Find inverse functions.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Interpreting Functions
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 䊫 1 (n is greater than or equal to 1).
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: Functions: Linear, Quadratic, and Exponential Models
Standard: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Functions: Linear, Quadratic, and Exponential Models
Standard: Interpret the parameters in a linear or exponential function in terms of a context.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Number and Quantity: Quantities
Standard: Define appropriate quantities for the purpose of descriptive modeling.*
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Number and Quantity: The Real Number System
Standard: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
Degree of Alignment:
Not Rated
(0 users)
Learning Domain: Number and Quantity: The Real Number System
Standard: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Extend the properties of exponents to rational exponents
Standard: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to hold, so [5^(1/3)]^3 must equal 5.
Degree of Alignment:
Not Rated
(0 users)
Standard: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Reason quantitatively and use units to solve problems
Standard: Define appropriate quantities for the purpose of descriptive modeling.*
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: Write expressions in equivalent forms to solve problems
Standard: Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.*
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: 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: Understand the concept of a function and use function notation.
Standard: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 (n is greater than or equal to 1).
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 a function that models a relationship between two quantities
Standard: Write a function that describes a relationship between two quantities.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Build a function that models a relationship between two quantities
Standard: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
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)
Cluster: Build new functions from existing functions
Standard: Find inverse functions.
Degree of Alignment:
Not Rated
(0 users)
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Standard: Construct and compare linear, quadratic, and exponential models and solve problems. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Construct and compare linear, quadratic, and exponential models and solve problems
Standard: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.*
Degree of Alignment:
Not Rated
(0 users)
Cluster: Interpret expressions for functions in terms of the situation they model
Standard: Interpret the parameters in a linear or exponential function in terms of a context.*
Degree of Alignment:
Not Rated
(0 users)
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