Targets & Standards
In Algebra 2, students analyze and apply operations using multiple representations of functions to compare, interpret data, and make inferences. Functions include (but not limited to) linear, exponential, quadratic, absolute value, inverse, piecewise, cubic, polynomial, trigonometric, logarithms, etc. They use statistics in real world contexts to develop solutions.
Essential Standards
Target D: Interpret the structure of expressions. (DOK 1,2)
Target L: Interpret functions that arise in applications in terms of the context. (DOK 1, 2)
Target H: Understand solving equations as a process of reasoning and explain the
reasoning. (DOK 1, 2)
Claim 3: Build New Functions & Rational Expression Operations (DOK 2, 3, 4)
A-SSE.A.2 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).
A-CED.A.1 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. Modeling Standard
There are no substandards for this standard.
A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Modeling Standard
There are no substandards for this standard.
F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Modeling Standard
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
A−REI.D.11 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. Modeling Standard
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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.
F-IF.B.4 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. Modeling Standard
Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
A-APR.C.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
There are no substandards for this standard.
Embed with A-APR.C.7, A-APR.C.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
There are no substandards for this standard.
A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
There are no substandards for this standard.
Target D: Interpret the structure of expressions. (DOK 1,2)
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Target L: Interpret functions that arise in applications in terms of the context. (DOK 1, 2)
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Target H: Understand solving equations as a process of reasoning and explain the
reasoning. (DOK 1, 2)
Achievement Level Descriptors & Evidence
Achievement Level Descriptors
Evidence
Supporting Standards
A-SSE.1 Interpret expressions that represent a quantity in terms of its context. Modeling Standard
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the product of and a factor not depending on .
A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. Modeling Standard
There are no substandards for this standard.
A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Modeling Standard
There are no substandards for this standard.
F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
There are no substandards for this standard.
F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
There are no substandards for this standard.
F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Modeling Standard
There are no substandards for this standard.
F-IF.6 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. Modeling Standard
There are no substandards for this standard.
F-BF.A.1 Write a function that describes a relationship between two quantities.
b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
F-BF.B.4 Find inverse functions.
a. Solve an equation of the form f(x)=c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x)=2x^3 or f(x)= (x+1)/(x-1) for x not equal to 1.