Download 2016.17, Algebra II, Quarter 2

2016.17, Algebra II, Quarter 2
The following practice standards will be used throughout the quarter:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Ongoing Standards
Note to Teachers: The following ongoing standards will be practiced all year long and embedded into your instruction instead of being taught
in isolation.
WCE.AII.1 Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and
symbolic) of non-linear and transcendental functions to solve problems, to model mathematical ideas, and to communicate solution strategies.
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the
assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
F.BF.1 Write a function that describes a relationship between two quantities.
WCE.AII.2 Graph a variety of functions identifying the domain, range, x-intercept(s), y-intercept, increasing intervals, decreasing intervals, the
maximums, and minimums of a function by looking at its graph.
WCE.AII.3 Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations
which the functions represent.
WCE.AII.4 Multiply polynomials.
**Unless otherwise noted, all resources are from HMH Algebra 2, 2015 Edition.
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Standards
Student Friendly “I Can” Statements
Unit 3 ( con’t) Polynomial Functions, Expressions, and Equations
A.APR.4 Prove polynomial identities and use them to describe
I can multiply polynomials and use the patterns observed in identities
numerical relationships. For example, the polynomial identity
such as the difference of squares to multiply polynomials.
(x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean
triples.
A.SSE.2 Use the structure of an expression to identify ways to rewrite
it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).
I can recognize the patterns in the sum and differences of cubes.
I can factor sum and difference of cubic expressions.
A.APR.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.
WCE.AII.7 Divide a polynomial by a lower degree polynomial.
I can divide polynomials using long division and synthetic division.
A.APR.2 Know and apply the Remainder Theorem: For a polynomial
p(x) and a number a, the remainder on division by x – a is p(a), so p(a)
=0 if and only if (x – a) is a factor of p(x).
I can explain and apply the Remainder Theorem to check answers when
dividing polynomials.
I understand that a is a root of a polynomial function if and only if x-a is
a factor of the function.
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A.APR.3 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.
I can find the zeros of a polynomial when the polynomial is factored.
Unit 4- Rational Functions, Expressions, and Equations
WCE.AII.8 Add subtract, multiply, and divide simple rational
I can add, subtract, multiply, and divide simple rational expressions.
expressions.
A.REI.2 Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
I can simplify rational expressions by adding, subtracting, multiplying or
dividing.
I can define extraneous solution.
I can solve a rational equation in one variable.
I can determine which numbers cannot be solutions of rational
equation and explain why they cannot be solutions.
Unit 5- Radical Functions, Expressions, and Equations
F.BF.4 Find inverse functions.
I can find the inverses of simple quadratic and cubic 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) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
F.IF.7 Graph functions expressed symbolically and show key features
of the graph, by hand in simple cases and using technology for more
complicated cases.
I can name the vertex, max or min, and the x and y intercepts of a
quadratic and a polynomial function.
I can graph a quadratic and a polynomial function by hand and using
technology.
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N.RN.1 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
I can evaluate and simplify an expression with a rational exponent.
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terms of rational exponents. For example, we define 53 to be the
1
1
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cube root of 5 because we want (53 )3 = 5(3)3 to hold, so (53 )3 must
equal 5.
N.RN.2 Rewrite expressions involving radicals and rational exponents
using the properties of exponents.
I can move flexibly between radical notation and rational exponents.
A.REI.2 Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
I can solve an equation containing radicals or rational exponents.
I can determine which numbers cannot be solutions of a radical
equation and explain why they cannot be solutions.
Honors Addendum
Note for Teachers of Honors: Do not teach this Honors Addendum at
the end of the quarter.
Embed the Honors Addendum within the regular Scope & Sequence.
A.APR.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.
I can graph rational functions.
I can identify asymptotes and holes of rational functions.
I can solve rational inequalities.
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