Download 27 - Fort Bend ISD

PAP Algebra 2– 1st 9 weeks Pacing Guide 2016 – 2017
The following calendar represents a suggested pacing guide.
Monday
August 22
First day of school
Tuesday
Wednesday
23
24
Thursday
25
Formulate absolute value equations and
inequalities (2A.6D): Formulate the definition of
absolute value from a number line to model both
mathematical and real world situations.
Friday
26
Solving absolute value equations and
inequalities (2A.6E)

Absolute Value Functions
Formulate absolute value linear
29
30 equations to model31both
September 1
Solving absolute value equations and
inequalities (2A.6E,
2A.6F): Write and solve
mathematical
and real-world
Summative
absolute value equations and inequalities in connection with the definition in real
Assessment
situations.
(2A.6D)
world and mathematical contexts; identify
extraneous
solutions; write and graph
solutions as compound inequality statements in both interval and inequality notation.
Include connections to solving linear equations.
5
Absolute Value Functions
7
8
6
Holiday
Labor Day
Graph and write abs value equations (2A.2A, 2A.6C,
2A.6E, 2A.7I): Graph with and without transformations;
identify D&R (using ineq, interval, and set notation),
intercepts, symmetry, and max & min values (including
intervals); make connections between the multiple
representations and linear and quad functions.
2
Graph and write abs
value equations (2A.2A,
2A.6C, 2A.6E, 2A.7I):
9
Graph and write abs value inequalities (2A.6F)):
Graph an absolute value inequality of 2 variables;
compare to solving absolute value inequalities with 1
variable graphically (include problems with variables
on both sides of the inequality as well as absolute
value on both sides of the inequality).
Absolute Value Functions
12
13
14
15
Graph, Write and Solve systems of abs value and
linear equations (2A.6E) Graph systems from
multiple reps; write systems from a graph; solve
systems (include using systems as a method for
solving absolute value equations graphically)
16
Summative
Assessment
Write and Solve
systems of inequalities
(2A.3E):
Absolute Value Functions
19
20
21
22
23
Write and Solve systems of inequalities (2A.3E, 2A.3F, 2A.3G): Write and solve systems of two or more
linear inequalities in both mathematical and real-world contexts; make connections to the graph of the system
and the possible solutions of the system, include geometric shapes; include from a system of ineq from a table.
Holiday
Fair Day
Linear Systems of Equations and Inequalities
26
27
28
Write systems of three linear equations (2A.3A):
Formulate systems of 3 linear equations with 3
variables to model mathematical and real-world
situations. Note: not from a graph.
29
30
Write and Solve systems of three linear equations (2A.3A, 2A.3B): Write systems
and solve using substitution and Gaussian elimination for 3 variables; Introduce and
define matrices to solve ; Include systems where there is exactly 1 solution, infinitely
many solutions, and no solution; Determine the reasonableness of the solution(s).
Linear Systems of Equations and Inequalities
October 3
4
5
Write and Solve systems of three linear equations
(2A.3A, 2A.3B):
Systems of Equations and Inequalities
6
7
Summative
Assessment
Quadratic Relations:
Parabola (2A.4B): Write
equations of a parabola
using the def as a conic
section (spiral circle).
10
Quadratic Relations:
Parabola (2A.4B): use
information to determine
if horizontal or vertical;
include mathematical
and real world situations.
11
12
13
14
Complex Numbers (2A.7A): Define complex number system and the imaginary number
as the square root of -1; define and analyze the effects of finding powers of i.; simplify
square roots of negative numbers; solve quadratics having imaginary square roots using
the square root method; add, subtract, multiply, and divide complex numbers.
Quadratic Relations and Functions
Elementary Conf.
Secondary PD
End of Grading
Period
PAP Algebra 2 FBISD 2nd Grading Period
2016-2017
Monday
October 17
Student Holiday
District PD
Tuesday
18
Wednesday
19
Thursday
20
Writing Quadratic Equations (2A.4A, 2A.4D, 2A.4E, 2A.7I): Write from standard
form to vertex form; apply completing the square; ID domain, range, axis of
symmetry, vertex, max or min; Find the equation given 3 points from multiple
representations; analyze 2nd differences, and regression of exact data; include
writing equations with imaginary roots,
Friday
21
Solve Quadratic
Equations and
Inequalities (2A.4F,
2A.4H)
Quadratic Relations and Functions
24
25
Checkpoint 1 window
26
27
28
Solve Quadratic Equations and Inequalities (2A.4F, 2A.4H) Solve quadratic
equations with complex solutions; spiral factoring, taking square roots,
completing the square and the quad formula; analyze the discriminant and best
method of solving;
Quadratic Relations and Functions
31
November 1
2
3
4
Write and Solve systems of two equations (one linear and one quadratic, extension with 2 quadratic)
(2A.3A, 2A.3C, 2A.3D)Write systems of two equations with one linear and one quadratic function (either
parabola or circle) to model mathematical and real-world situations; solve systems of 1 linear and 1 quadratic
including horizontal, 2 or 3 quadratics (circles and parabolas together), check for reasonableness or extraneous
solutions.
Summative
Assessment
Quadratic Relations and Functions
7
8
9
10
11
Solve systems of 2 inequalities (ext. with 1 linear and 1 quadratic, or 2
quadratic) (ext to 2A.4H): Write & solve systems of 2 inequalities in both math
and real-world contexts.; Make connections to the graph of the system and the
possible solutions of the system.
Summative
Assessment
Quadratic Relations and Functions
14
15
16
17
18
Inverses of Quadratic/ Square Root Functions (2A.2B, 2A.2C, 2A.2D, 2A.7I): Define an inverse and inverse function graphically and
algebraically; include inverse notation; analyze functions with and without inverse functions, reflection over the line y = x; analyze D and R;
make connections to solving quadratics with positive and negative roots and square roots with extraneous solutions. As an extension, find the
inverse to an absolute value function.
Quadratic and Square Root Functions
21
22
Holiday
23
Holiday
24
Holiday
25
Holiday
Thanksgiving Day
28
29
30
December 1
Solve Square Root Equations (2A.4F,2A.4G, 2A.7H): Solve square root
equations algebraically using its inverse function, the quadratic; include square
roots in exponential form; include equations with square roots on both sides;
check for extraneous solutions; solve graphically with technology; include math
and real world situations.
2
Graph and Write Square Root Functions (2A.2A,
2A.4C, 2A.4E, 2A.4F, 2A.7I): Use the sq root graph as
an inverse to the quad parent graph when x  0 to define
the parent sq root function and its attributes, define D and
R and intercepts algebraically and graphically; include max
and min on an interval; graph with transf. and ID changes in
attributes; write using tech and regression
Quadratic and Square Root Functions
5
Graph and Write
Square Root
Functions: Spiral
linear, quad, abs
value
6
7
8
9
Summative
Assessment
Graph Systems and Inequalities: Graph a square
root inequality in 2 variables; Solve systems of
equations and inequalities that contain a
square root function.
Quadratic and Square Root Functions
12
13
14
Exams
15
Exams
16
Exams
HS/MS Early
Dismissal
Exams
All Early Dismissal
End 1st Semester
PAP Algebra 2 FBISD 3rd Grading Period
2016-2017
Monday
January 2
Tuesday
3
Wednesday
4
Thursday
5
Friday
6
Graph Cubic Functions (2A.2A, 2A.7I, 2A.6A): Define cubic in terms of
polynomial; graph & ID key features (D,R, ints, symmetry) and transformations
with the cubic parent graph ;compare/spiral cubic with quadratic, linear, abs value,
and sq root functions
Campus
Prof. Development
Inverses of Cubic/
Cube Root Functions
(2A.2C,
Cubic and Cube Root Functions
9
10
11
Inverses of Cubic/ Cube Root: (2A.2C, 2A.2B, 2A.2D):
12
13
Solve Cube Root Equations Including Applications (2A.6B, 2A.7G, 2A.7H):
Simplify square and cube roots inc. variables, solve cube root equations using
radicals and exponent forms, include mathematical and real world situations.
Determine cubic inverses graphically and algebraically, D, R,
one-to-one, composition. Spiral quadratic and square roots.
Cubic and Cube Root Functions
16
17
Holiday
MLK Day
18
19
Checkpoint 2 window
Summative
Assessment
20
Simplify Radical Expressions and Solve
Equations with Rational Exponents (2A.7G,
2A.7H): Simp all radical expressions with variables;
solve all equations involving rational exponents.
Cubic and Cube Root Functions
23
24
25
26
27
Systems and Inequalities with Cubic and Cube
Root Functions (2A.2A, 2A.6B): Solve systems
involving any of the functions studied up to this
point both graphically and algebraically when
possible; include inequalities of cubic and cube root
both graphically and algebraically (when possible)
Graph Cube Root Functions (2A.2A, 2A.7I,
2A.6A): Graph and identify key features (D,R, ints,
symmetry) and transformations with the cube root
parent graph. Verify intercepts algebraically.
Cubic and Cube Root Functions
30
31
February 1
Add, subtract, Multiply Polynomials (2A.7B):
Includes all polynomials, binomial expansion and
Pascal’s triangle, and applications such as
perimeter and area.
Summative
Assessment
2
3
Divide Polynomials (2A.7C, 2A.7D): Includes
degree 3 and 4 polynomials divided by degree 1 and
2 polynomials, long division, synthetic division,
quotient/remainder and divisor and connections to
factoring with a remainder of 0.
Operations of Polynomial and Rational Functions
6
7
Divide Polynomials
(2A.7C, 2A.7D):
8
9
10
Factor Polynomials (2A.7D, 2A.7E): Factor degree 3 and 4 polynomials, and make connections to the graph of
polynomials, its zeroes and x-intercepts (Note: graphing and solving polynomials is not a TEKS, only done in
connection with understanding factors), Extension: Factor (not solve) polynomials of any degree, graph and solve
any degree 3 polynomial equations and inequalities. Include spiral discussion about inverses of cubic functions
and revisit one-to one.
Operations of Polynomial and Rational Functions
13
14
Student Holiday
District PD
15
Factor Polynomials (2A.7D, 2A.7E) include
factoring using synthetic division, sum and
difference of cubes, and grouping, and include
polynomials that require factoring completely.
16
17 Elementary Conf.
Secondary PD
Summative
Assessment
Operations of Polynomial and Rational Functions
20
21
Student Holiday
District PD
22
23
Multiply and Divide Rational Expressions
(2A.7F, 2A.7I): Factor and simplify rational
expressions in order to multiply and divide, divide
by multiplying by the reciprocal and include all
domain restrictions.
24
Add and Subtract Rational Expressions: (2A.7F,
2A.7I): Include rational expressions with like and
unlike denominators, and include domain
restrictions on rational expressions.
Operations of Polynomial and Rational Functions
27
28
March 1
Add and Subtract
Rational Expressions:
(2A.7F, 2A.7I):
2
3
Solve Rational Equations (2A.6I, 2A.6J, 2A.6K,
2A.7I: Include addition and subtraction of rational
expressions within the equations and equations
equal to a constant or another rational expression.
Summative
Assessment
Operations of Polynomial and Rational Functions
6
7
8
Rational Functions
9
Solve Rational Equations (2A.6I, 2A.6J, 2A.6K, 2A.7I: Restrict the domain,
check reasonableness of solutions, and include mathematical and real world
situations. Extension: Include graphs of all rational functions using technology,
discussion of inverses, systems and connect to solving rational equations, and
inequalities from the graph. Note that solving rational inequalities is a pre-cal
TEKS.
10
End 3rd Nine Weeks
Graph and Transform Rational Functions
(2A.2A, 2A.6G, 2A.6K, 2A.7I): Graph and identify
key features (Asymptotes, D,R, intercepts,
symmetry) and transformations with the rational
parent graph. Include finding the intercepts both
graphically and algebraically.
Rational Functions
Spring Break—March 13- 17
Algebra 2 FBISD 4th Grading Period
2016-2017
Monday
March 20
Tuesday
Wednesday
21
Graph and Transform
Rational Functions
(2A.2A, 2A.6G, 2A.6K,
2A.7I):
Thursday
22
23
Friday
24
Writing and Solving Rational Functions (including inverse variation) (2A.6L 2A.6H, 2A.6J, 2A.6K): Use
direct var. for comparison, write and solve equations involving inverse variation in math and real world
situations. Check reasonableness, and define meanings of key features.
Rational Functions
27
28
29
30
31
Graph Exponential Functions (2A.2A, 2A.5A, 2A.7I): Graph and
identify the domain and range, the intercepts, the asymptote and
asymptotic behavior. Identify transformations including vertical and
horizontal stretch and compression, reflections over the x-axis and yaxis, horizontal and vertical shifts. Identify and analyze changes in key
attributes including D and R, intercepts, and the asymptote. Verify the yintercept algebraically. Extension: include all bases
Summative
Assessment
Rational Functions
Exponential and Logarithmic Functions
April 3
Graph Exponential
Functions (2A.2A,
2A.5A, 2A.7I):.
Analyze the effects on
transf from the graph
of exp functions other
than the parent.
4
5
6
7
Inverse of Exponential/ Logarithmic Functions (2A.2B, 2A.2C,
2A.2D, 2A.5C, 2A.7I): Determine the inverse of the exp function
graphically and algebraically. Show one-to-one. Identify the domain and
ranges. Define logarithm at natural logarithm function. Recognize the
inverse as a reflection over the line y = x and show using composition.
Summative
Assessment
Exponential and Logarithmic Functions
10
11
12
13
14
Checkpoint 3 window
Holiday
Good Friday
Graph Logarithmic Functions (2A.2A, 2A.5A, 2A.7I): Graph and analyze. Identify the domain and
range, the intercepts, the asymptote and asymptotic behavior. Identify and analyze changes in key
attribute from transformations. Verify the x-intercept and y-intercept algebraically. Analyze the
effects on transformations from the graph of exponential functions other than the parent.
Exponential and Logarithmic Functions
17
18
19
Formulate exponential and log equations
(2A.5B, 2A.7I) Formulate exp and log
equations to model real-world situations.
Include exponential relationships in recursive
notation. Include situations involving growth
and decay. Include domain restrictions.
20
21
Solve exponential & logarithmic functions including applications
(2A.5D, 2A.5E, 2A.7I):
Solve exp equations algebraically using its inverse function, the log
function. Solve single log equations algebraically using its inverse function,
the exponential function.
Exponential and Logarithmic Functions
24
25
26
27
28
Systems and Inequalities of Exponential and
Log Functions (extension): While solving logs
was with single logs, students will make
connections to solving systems and solving
equations with a log on both sides.
Develop properties of logarithms using the inverse concept (Extension):
Students will explore and develop the properties of logarithms. (Note: this
is a discussion in terms of the inverse concept and not use of properties
which is a pre-calculus TEKS. Use of properties should be basic and in
terms of making the connections with exponential properties.
Exponential and Logarithmic Functions
May 1
2
3
Systems and Inequalities of Exponential and
Log Functions (extension): Discussions
should include number of solutions and graphic
representations. Inequalities include algebraic
and graphic representations in single and two
variables.
4
5
Function Families: A summation of the
functions studies in PAP Algebra 2. Compare
and contrast functions and their attributes.
Summative
Assessment
Functions and Data Analysis
Exponential and Logarithmic Functions
8
9
10
11
12
Regression Models (2A.8A, 2A.8B, 2A.8C): Access prior knowledge of
writing regression equations for linear, quadratic, and exponential
functions to choose the best model and write the equation using
regression. Use the regression equation to make predictions and critical
judgments. Note: Each function is not done in isolation.
Analyze data and choose best representation
(2A.8A): select the appropriate model, analyze
the data to determine which model would best
fit the situation. Extension: include all
functions studied.
Functions and Data Analysis
15
16
17
18
Regression Models (2A.8A, 2A.8B,
2A.8C)
19
Summative
Assessment
Data Analysis
22
23
24
25
26
Exams
Review for Exam
29
30
Holiday
Memorial Day
31
Exams
June 1
Exams
HS/MS Early
Dismissal
Exams
All Early
Dismissal
End of 2nd
Semester
2
Teacher Work Day