Download Algebra-2-Pacing

Algebra II Quarter 2 Curriculum Map
2013-2014
CCSS for Mathematical Practice:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
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
Unit
Quadratics
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Unit 3: Quadratics
Quarter 2
Suggested Instructional Days: 13
Timeline Standards
Learning Expectation
Vocabulary
Resources
1 day
(S) A.CED.1 Create equations and inequalities in one
Students will identify and graph
Parabola
Algebra 2
variable and use them to solve problems. Include
quadratic functions.
Quadratic function
Common
equations arising from linear and quadratic functions,
Vertex form
Core
and simple rational and exponential functions.
Axis of Symmetry
Sec 4.1
(S) F.IF.7 Graph functions expressed symbolically
Vertex
and show key features of the graph, by hand in simple
Minimum value
cases and using technology for more complicated
Maximum value
cases.
(M) F.IF.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. Key
features include: intercepts; intervals where the
function is increasing, decreasing, positive, or
negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
(A) A.REI.6 Solve systems of linear equations exactly
and approximately (e.g., with graphs), focusing on
pairs of linear equations in two variables.
(A) F.BF.3 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.
HS FAL: Forming Quadratics http://map.mathshell.org/materials/lessons.php?taskid=224&subpage=concept
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•
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Review Standards
(M)ajor Content,
(S)upporting Content
(A)dditional Content
(+) Honors/4th Math
Algebra II Quarter 2 p. 1
Algebra II Quarter 2 Curriculum Map
2013-2014
2 days
1 day
(S) F.IF.8 a Write a function defined by an expression
in different but equivalent forms to reveal and explain
different properties of the function. Use the process of
factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry
of the graph, and interpret these in terms of a context.
(S) 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.
(M) F.IF.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. Key
features include: intercepts; intervals where the
function is increasing, decreasing, positive, or
negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
(S) F.IF.9 Compare properties of two functions each
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
descriptions).
(M) F.BF.1 Write a function that describes a
relationship between two quantities. Combine
standard function types using arithmetic
operations.
(M) 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.
A.CED.2 Create equations in two or more variables to
represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
(S) G.GPE.2 Derive the equation of a parabola given a
focus and directrix.
Students will graph quadratic functions
written in standard form.
Students will write the equation of a
parabola and graph parabolas.
(M) F.IF.4 For a function that models a
relationship between two quantities, interpret key
features of graphs and tables in terms of the
Students will model data with quadratic
functions.
standard form
focus of a parabola
directrix
focal length
Algebra 2
Common
Core
Sec 4.2
Sec 10.2
Algebra 2
Common
Core
Algebra II Quarter 2 p. 2
Algebra II Quarter 2 Curriculum Map
2013-2014
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.
(M) F.IF.5 Relate the domain of a function to its
graph and, where applicable, to the quantitative
relationship it describes.
HS Task A07: Functions http://map.mathshell.org/materials/tasks.php?taskid=255&subpage=apprentice
HS Task A16: Sorting Functions http://map.mathshell.org/materials/tasks.php?taskid=264&subpage=apprentice
HS Task E13: Sidewalk Stones http://map.mathshell.org/materials/tasks.php?taskid=285&subpage=expert
Rocket Activity – See Department Chair for files
2 days
(M) A.SSE.2 Use the structure of an expression to
Students will find common and binomial
identify ways to rewrite it. For example, see x4 – y4
factors of quadratic expressions.
as (x2)2 – (y2)2, thus recognizing it as a difference of
Students will factor special quadratic
squares that can be factored as (x2 – y2)(x2 + y2).
expressions.
A.SSE.1a Interpret expressions that represent a
quantity in terms of its context. Interpret parts of an
expression, such as terms, factors, and coefficients.
Sec 4.3
Factoring
Greatest common
factor of an
expression
Perfect square
trinomial
Difference of two
squares
Algebra 2
Common
Core
Sec 4.4
1 day
(S) A.CED1 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.
A.SSE.1a Interpret expressions that represent a
quantity in terms of its context. Interpret parts of an
expression, such as terms, factors, and coefficients.
Students will solve quadratic equations
by factoring and graphing.
Zero of a function
Zero-product
property
Algebra 2
Common
Core
Sec 4.5
1 day
(S) A.REI.4 a, b Solve quadratic equations in one
variable. Use the method of completing the square to
transform any quadratic equation in x into an equation
of the form (x – p)2 = q that has the same solutions.
Derive the quadratic formula from this form. Solve
quadratic equations by inspection (e.g., for x2 = 49),
taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the
initial form of the equation. Recognize when the
quadratic formula gives complex solutions and write
Students will solve quadratic equations
using the Quadratic Formula.
Students will determine the number of
solutions by using the discriminant.
Quadratic formula
Discriminant
Algebra 2
Common
Core
Sec 4.7
Algebra II Quarter 2 p. 3
Algebra II Quarter 2 Curriculum Map
2013-2014
them as a ± bi for real numbers a and b.
HS Task N04: Creating Equations http://map.mathshell.org/materials/tasks.php?taskid=292&subpage=novice
HS FAL: Solving Quadratic Equations: Cutting Corners http://map.mathshell.org/materials/lessons.php?taskid=432&subpage=problem
Aussie Fir Treehttp://schools.nyc.gov/NR/rdonlyres/48D7F470-FDD4-477F-B108-E02F7D969E93/0/NYCDOEHSAlgebraAussieFirTree_Final.pdf
Parabola Project http://www.fallriverschools.org/Brogan-Price/CP%20Algebra%202%20Parabola%20Project%20-%20Student%20Handout.pdf
2 days
(A) N.CN.1 Know there is a complex number i such
Students will identify, graph and perform Imaginary unit
Algebra 2
that i2 = -1, and every complex number has the form a
operations with complex numbers.
Imaginary number
Common
+ bi with a and b real.
Students will find complex number
Complex number
Core
(A) N.CN.2 Use the relation i2 = -1 and the
solutions of quadratic equations.
Pure imaginary
Sec 4.8
commutative, associative, and distributive properties
number
to add, subtract, and multiply complex numbers.
Complex number
(A) N.CN.7 Solve quadratic equations with real
plane
coefficients that have complex solutions.
Absolute value of a
(+)N.CN.8 Extend polynomial identities to the
complex number
complex numbers. For example, rewrite x2 + 4 as (x +
Complex conjugate
2i)(x – 2i).
Polynomials
(1 day)
(A) A.REI.7 Solve a simple system consisting of a
linear equation and a quadratic equation in two
variables algebraically and graphically.
A.CED.3 Represent constraints by equations or
inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or
nonviable options in a modeling context.
2 days
Review and Test
Students will solve and graph systems of
linear and quadratic equations.
Students will solve and graph systems of
quadratic inequalities.
Algebra 2
Common
Core
Sec 4.9
Unit 4: Polynomials
Quarter 2
Suggested Instructional Days: 9
1 day
(S) F.IF.7 c Graph functions expressed symbolically
Students will classify polynomials.
Monomial
Algebra 2
and show key features of the graph, by hand in simple
Students will graph polynomial functions Degree of a
Common
cases and using technology for more complicated
and describe end behavior.
monomial
Core
cases. Graph polynomial functions, identifying zeros
Polynomial
Sec 5.1
when suitable factorizations are available, and
Degree of a
showing end behavior
polynomial
(M) F.IF.4 For a function that models a
Polynomial
relationship between two quantities, interpret key
function
features of graphs and tables in terms of the
Standard form of a
quantities, and sketch graphs showing key features
polynomial
given a verbal description of the relationship. Key
function
features include: intercepts; intervals where the
Turning point
Algebra II Quarter 2 p. 4
Algebra II Quarter 2 Curriculum Map
2013-2014
function is increasing, decreasing, positive, or
End behavior
negative; relative maximums and minimums;
symmetries; end behavior; and periodicity.
A.SSE.1a Interpret expressions that represent a
quantity in terms of its context. Interpret parts of an
expression, such as terms, factors, and coefficients.
HS Task N07: Building Functions http://map.mathshell.org/materials/tasks.php?taskid=295&subpage=novice
HS FAL: Representing Polynomials http://map.mathshell.org/materials/lessons.php?taskid=436&subpage=concept
HS FAL: Sorting Equations and Identities http://map.mathshell.org/materials/lessons.php?taskid=218&subpage=concept
2 days
(M) F.BF.1 Write a function that describes a
Students will analyze the factored form
Factor theorem
relationship between two quantities. Combine
of the polynomial.
Multiple zero
standard function types using arithmetic
Students will write a polynomial function Multiplicity
operations.
from its zeros.
Relative maximum
A.SSE.1a Interpret expressions that represent a
Relative minimum
quantity in terms of its context. Interpret parts of an
expression, such as terms, factors, and coefficients.
(M) 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.
(A) A.APR.4 Prove polynomial identities and use
them to describe numerical relationships. For example,
the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2
can be used to generate Pythagorean triples.
HS Task A17: Cubic Graph http://map.mathshell.org/materials/tasks.php?taskid=265&subpage=apprentice
1 day
(M) A.REI.11 Explain why the x-coordinates of the Students will solve polynomial equations Sum of cubes
points where the graphs of the equations y = f(x)
by factoring and graphing.
Difference of cubes
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.
(M) 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).
(M) F.IF.4 For a function that models a
relationship between two quantities, interpret key
Algebra 2
Common
Core
Sec 5.2
Algebra 2
Common
Core
Sec 5.3
Algebra II Quarter 2 p. 5
Algebra II Quarter 2 Curriculum Map
2013-2014
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.
(S) 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.
2 days
A.APR.1 Understand that polynomials form a system
Students will divide polynomials using
Synthetic division
Algebra 2
analogous to the integers, namely, they are closed
long division and synthetic division.
Remainder
Common
under the operations of addition, subtraction, and
theorem
Core
multiplication; add, subtract, and multiply
Sec 5.4
polynomials.
(S) 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.
(M) 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).
HS Task N03: Arithmetic with Polynomials and Rational Expressions http://map.mathshell.org/materials/tasks.php?taskid=291&subpage=novice
1 day
(A) F.BF.3 Identify the effect on the graph of
Students will solve equations using the
Rational root
Algebra 2
replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
Rational Root Theorem.
theorem
Common
specific values of k (both positive and negative); find
Students will use the Conjugate Root
Conjugate root
Core
the value of k given the graphs. Experiment with cases Theorem.
theorem
Sec 5.9
and illustrate an explanation of the effects on the graph
Descartes’ rule of
using technology. Include recognizing even and odd
signs
functions from their graphs and algebraic expressions
for them.
(S) F.IF.8 a Write a function defined by an expression
in different but equivalent forms to reveal and explain
different properties of the function. Use the process of
Algebra II Quarter 2 p. 6
Algebra II Quarter 2 Curriculum Map
2013-2014
factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry
of the graph, and interpret these in terms of a context.
(S) F.IF.9 Compare properties of two functions each
represented in a different way (algebraically,
graphically, numerically in tables, or by verbal
descriptions).
(S) 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.
2 days
Review and Quarter 2 Test
NOTES/REFLECTIONS:
Algebra II Quarter 2 p. 7