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Algebra 2 Year-at-a-Glance
Leander ISD
1st Six Weeks
Content Topics
Essential
Unit of
Study
TEKS
2nd Six Weeks
6 weeks
3 weeks
01
Linear Functions
02
Polynomials &
Polynomial
Functions
Solve linear
equations, model
data using linear
functions,
scatterplots/regressi
on. Graph/write
abs value functions
w/ transformations,
solve abs value
equations/inequaliti
es. Solve 2 & 3
variable system of
linear equations.
Graph system of
linear inequalities.
Focus
2A.1AB, 2A.2A,
2A.3ABC, 2A.4AB
6 weeks
03
Quadratic Functions &
Factoring
Use properties of Graph quadratics functions in
standard, vertex, or intercept
exponents to
form. Solve quadratic
simplify
equations by factoring, finding
expressions.
square roots, completing the
Add, subtract,
square, and the quadratic
multiply
formula. Use imaginary and
polynomials.
Factor and solve complex numbers. Graph and
polynomial
solve quadratic inequalities.
equations.
Write quadratic functions and
models.
Evaluate nth
roots and use
rational
exponents. Apply
properties of
rational
Focus
Focus t
2A.2A
2A.2AB, 2A.6ABC, 2A.7AB,
2A.8BD
Support
a.1, a.2, 2A.1A
Support
2A.4AB
4th Six Weeks
5th Six Weeks
6th Six Weeks
3 weeks
3 weeks
6 weeks
4 weeks
04
Inverses &
Square Root
Functions
05
Rational
Functions
06
Exponential & Log
Functions
07
Conics
Explore the
relationship
between a
function and its
inverse. Find the
inverse of a
linear, quadratic,
cubic, and power
function. Graph
square root
functions. Solve
square root and
other simple
radical equation
by a variety of
methods.
Write and graph
direct variation
equations. Model
inverse and joint
variation. Graph
rational functions.
Multiply, divide,
add, and subtract
rational
expressions.
Solve rational
equations.
Graph exponential
growth and decay
functions. Use functions
involving e . Evaluate
logarithms and graph
logarithmic functions.
Apply properties of
logarithms. Solve
exponential and
logarithmic equations.
Use the graphing
calculator to model
exponential and power
functions.
Focus
2A.4AC,
2A.9ABCDEFG
Focus
Focus
2A.10ABCDEFG 2A.11ABCDEF
Focus
2A.5ABCDE
Support
Support
a.5, 2A.1B, 2A.2A 2A.4AC
Support
a.5
Graph and write
the equations of
circles ellipses,
hyperbolas, and
parabolas.
Identify the
important
characteristics of
conics. Use
completing the
square to write
conics in (h,k)
form.
McDougal
Text
Resources
Alg 2
Resources
Support
A.1D, A.6D, A.7A
3 weeks
3rd Six Weeks
2007-08
McDougal 1.1, 1.2, McDougal 5.1,
1.3, 2.1, 2.2, 2.3,
5.3, 5.4, 6.1,.6.2
2.4, 2.6, 2.7, 1.7,
2.8, 3.1, 3.2, 3.3,
3.4
McDougal 4.1, 4.2, 4.3, 4.4,
4.5, 4.6, 4.7
McDougal 6.4,
6.5, 6.6
McDougal 2.5,
McDougal 7.1, 7.2, 7.3, McDougal 9.1,
8.1, 8.2, 8.3, 8.4, 7.4, 7.5, 7.6, 7.7
9.2, 9.3, 9.4, 9.5,
8.5, 8.6
9.6
10 Aug 2007
Algebra 2 Essential Units of Study 2007-08
01 EUS - Linear Functions (6 Weeks)
Focus TEKS
(2A.1) Foundations for functions: uses properties and
attributes of functions and applies functions to problem
situations. The student is expected to:
(A) identify the mathematical domains and ranges of
functions and determine reasonable domain and range
values for continuous and discrete situations.
(B) collect and organize data, make and interpret
scatterplots, fit the graph of a function to the data, interpret
the results, and proceed to model, predict, and make
decisions and critical judgments.
(2A.2) Foundations for functions: understands the
importance of the skills required to manipulate symbols in
order to solve problems and uses the necessary algebraic
skills required to simplify algebraic expressions and solve
equations and inequalities in problem situations. The
student is expected to:
(A) use tools including factoring and properties of exponents
to simplify expressions and transform and solve equations.
Content Description
1.1
Evaluate and simplify expressions involving real numbers.
1.2
1.3
2.1
2.2
2.3
2.4
2.6
2.7
1.7
2.8
3.1
3.2
3.3
3.4
Solve linear equations.
Represent relations and graph linear functions.
Find slopes of lines and rates of change.
Graph linear equations in slope-intercept form. Discuss domain/range.
Write linear equations in standard, slope-intercept, & point-slope form.
Fit lines to data in scatter plots using linear regression.
Graph and write absolute value functions with simple transformations.
Solve absolute value equations and inequalities.
Graph linear inequalities in two variables.
Solve systems of linear equations by graphing.
Solve systems of linear equations by algebraically.
Graph system of linear inequalities.
Solve system of equations in three variables
(2A.3) Foundations for functions: formulates systems of equations and inequalities from problem situations, uses a variety of methods to
solve them, and analyzes the solutions in terms of the situations. The student is expected to:
(A) analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems.
(B) use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities for given contexts.
(C) interpret and determine the reasonableness of solutions to systems of equations or inequalities.
(2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to:
(A) identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2), exponential (f(x) = ax), and logarithmic
(f(x) = logax) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = √x), and reciprocal of x (f(x) = 1/x)
(B) parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions.
A.1D Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations,
and inequalities. (TAKS 1)
Support TEKS
Textbook
Use properties of real numbers.
A.6D Graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept.
(TAKS 3)
Resources
Key Vocabulary
- Equivalent equations
- Absolute value
- Extraneous solutions
- Domain, range
- Parent function
- Slope-intercept form
- Point-slope form
- Correlation coefficient
- Best-fitting line
- Absolute value function
- Transformation
- Linear inequality in two variables
- Substitution method
- Elimination method
- System of linear inequalities
- System of three linear equations
- Ordered triple
Common Assessment
A.7A Analyze situations involving linear functions and formulate linear equations or inequalities to solve problems. (TAKS 4)
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
02 EUS - Polynomials and Polynomial Functions (3 Weeks)
Focus TEKS
Content Description
Textbook
Simplify expressions involving properties of exponents such as product of
powers, power of a power, power of a product, negative exponent, zero
exponent, quotient of powers, and power of a quotient.
5.1
Add, subtract, and multiply polynomials. Become familiar with the product of
conjugates, square of a binomial, and cube of a binomial.
5.3
Factor (including a common monomial factor, difference of two squares and
(A) use tools including factoring and properties of exponents factoring by grouping) and solve polynomial equations.
to simplify expressions and transform and solve equations.
Evaluate expressions with nth roots and rational exponents with and without
a calculator.
5.4
(2A.2) Foundations for functions: understands the
importance of the skills required to manipulate symbols in
order to solve problems and uses the necessary algebraic
skills required to simplify algebraic expressions and solve
equations and inequalities in problem situations. The
student is expected to:
Us properties of rational exponents to simplify expressions.
Resources
6.1
6.2
Support TEKS
Key Vocabulary
- polynomial
- polynomial function
- end behavior
- factored completely
- factor by grouping
- quadratic form
- nth root of ‘a”
- index of a radical
a.1 Foundations for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation,
quantitative reasoning,; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are - simplest form of a radical
- like radicals
essential foundations for all work I high school mathematics. Students continue to build on this foundation as they expand their
- power function
understanding through other mathematical experiences.
- inverse relation
a.2 Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways - inverse function
- radical function
to represent mathematical situations and to express generalizations. Students study algebraic concepts and the relationship
- radical equation
among them to better understand the structure of algebra.
Common Assessment
(2A.1) Foundations for functions: uses properties and attributes of functions and applies functions to problem situations. The
student is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous
and discrete situations.
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
03 EUS - Quadratic Functions and Factoring (9 Weeks)
Focus TEKS
(2A.2) Foundations for functions: understands the importance of
the skills required to manipulate symbols in order to solve problems
and uses the necessary algebraic skills required to simplify
algebraic expressions and solve equations and inequalities in
problem situations. The student is expected to:
(A) use tools including factoring and properties of exponents to
simplify expressions and transform and solve equations.
(B) Use complex numbers to describe the solutions of quadratic
equations.
Content Description
Textbook
Graph quadratic functions in standard form.
4.1
Graph quadratic functions in vertex form and intercept form.
4.2
4.3
4.4
4.5
4.6
Use factoring to solve a quadratic with a leading coefficient of 1.
Use factoring to solve a quadratic with a leading coefficient of 'a'.
Solve quadratic equations by finding square roots. Solutions may be
complequadratic
n mbers
b t no operations
or plotting
comple No
n mbers
Solve
equations
with complex
numberofsolutions.
complex
numbers operations or plotting.
Solve quadratic equations by completing the square.
(2A.6) Quadratic and square root functions: understands that
Solve quadratic equations using the quadratic formula.
quadratic functions can be represented in different ways and
translates among their various representations. The student is
Graph and solve quadratic inequalities.
expected to:
Write quadratic functions and models given a graph or description.
(A) determine the reasonable domain and range values of
quadratic functions, as well as interpret and determine the
reasonableness of solutions to quadratic equations and
inequalities.
(B) relate representations of quadratic functions, such as algebraic,
tabular, graphical, and verbal descriptions.
(C) determine a quadratic function from its roots or a graph.
(2A.7) Quadratic and square root functions: interprets and describes the effects of changes in the parameters of quadratic functions in applied
and mathematical situations.
The student is expected to:
(A) use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^2 + bx + c and the y = a(x h)^2 + k symbolic representations of quadratic functions.
(B) use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)2 + k form of a
function in applied and purely mathematical situations.
Resources
4.7
4.8
4.9
4.10
Key Vocabulary
- standard form of a quadratic
function
- parabola
- vertex form
- intercept form
- root of an equation
- zero of a function
- square root
- imaginary number
- complex number
- completing the square
- quadratic formula
- discriminant
Common Assessment
Support TEKS
(2A.8) Quadratic and square root functions: formulates equations and inequalities based on quadratic functions, uses a variety of methods to
solve them, and analyzes the solutions in terms of the situation. The student is expected to:
(A) Analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems.
(B) Analyze and interprets the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula.
(2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to:
(A) identify and sketch graphs of parent functions, including linear, quadratic, exponential, and logarithmic functions, absolute value of x, square root of x , and reciprocal of x.
(B) parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
04 EUS - Inverses and Square Root Functions (3 Weeks)
Focus TEKS
(2A.4) Algebra and geometry: connects algebraic and
geometric representations of functions. The student is
expected to:
(A) identify and sketch graphs of parent functions, including
square root of x.
(C) describe and analyze the relationship between a
function and its inverse.
(2A.9) Quadratic and square root functions: formulates
equations and inequalities based on square root functions,
uses a variety of methods to solve them, and analyzes the
solutions in terms of the situation. The student is expected
to:
Content Description
Explore the relationship between a function and its inverse.
Textbook
6.4 activity (p. 437)
Find the inverse of a linear, quadratic, cubic, and power function of the form
y = a x^n + c
6.4
Graphs of square root functions including parameter change and
domain/range.
6.5
Solve and determine the reasonableness of solutions for square root and
other simple radical equations using algebraic, tabular, graphical, and verbal
representation
6.6
6.6 extension (p. 460)
(A) Use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions
and describe limitations on the domains and ranges.
(B) Relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions.
(C) Determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness
of solutions to square root equations and inequalities.
(D) Determine solutions of square root equations using graphs, tables, and algebraic methods.
(E) Determine solutions of square root inequalities using graphs and tables.
(F) Analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems.
Resources
Key Vocabulary
-inverse relation
- inverse function
- radical function
- radical equation
- extraneous solution
Support TEKS
Common Assessment
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
05 EUS - Rational Functions (3 Weeks)
Focus TEKS
Content Description
Write and graph direct variation equations from verbal descriptions. Apply
(2A.10) Rational functions: formulates equations and
a model for direct variation from verbal description.
inequalities based on rational functions, uses a variety of
methods to solve them, and analyzes the solutions in terms
Use inverse variation and joint variation models.
of the situation.
Support TEKS
(A) use quotients of polynomials to describe the graphs of
Graph simple rational functions and be able to describe vertical/horizontal
rational functions, predict the effects of parameter changes,
asymptotes and domain/range of those functions.
describe limitations on the domains and ranges, and
examine asymptotic behavior.
Graph rational functions with higher-degree polynomials. Include end(B) analyze various representations of rational functions with behavior in description.
respect to problem situations.
(C) determine the reasonable domain and range values of Multiply and divide rational expressions and then simplify.
rational functions, as well as interpret and determine the
reasonableness of solutions to rational equations and
Add, subtract and then simplify rational expressions.
inequalities.
(D) determine the solutions of rational equations using
graphs, tables, and algebraic methods.
Solve rational equations by multiplying by the LCD. Check for extraneous
(E) determine solutions of rational inequalities using graphs solutions.
and tables.
(F) analyze a situation modeled by a rational function,
formulate an equation or inequality composed of a linear or
quadratic function, and solve the problem.
(G) use functions to model to and make predictions in
problem situations involving direct and inverse variation.
Textbook
Resources
2.5
8.1
8.2
8.3
8.4
8.5
8.6
Key Vocabulary
- direct variation
- constant of variation
- inverse variation
a.5 Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying - joint variation
relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and - rational function
technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model - horizontal asymptote
mathematical situations to solve meaningful problems.
- vertical asymptote
- simplified form of a rational
(2A.1) Foundations for functions: uses properties and attributes of functions and applies functions to problem situations. The
expression
student is expected to:
- complex fraction
(B) collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and
- cross multiplying
proceed to model, predict, and make decisions and critical judgments.
- least common denominator
- extraneous solutions
(2A.2) Foundations for functions: understands the importance of the skills required to manipulate symbols in order to solve
problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities
in problem situations. The student is expected to:
(A) use tools including factoring and properties of exponents to simplify expressions and transform and solve equations.
Common Assessment
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
06 EUS - Exponential and Log Functions (6 Weeks)
Focus TEKS
(2A.11) Exponential and logarithmic functions: formulates
equations and inequalities based on exponential and
logarithmic functions, uses a variety of methods to solve
them, and analyzes the solutions in terms of the situation.
The student is expected to:
(A) Develop the definition of logarithms by exploring and
describing the relationship between exponential functions
and their inverses.
(B) Use the parent functions to investigate, describe, and
predict the effects of parameter changes on the graphs of
exponential and logarithmic functions, describe limitations
on the domains and ranges, and examine asymptotic
behavior.
(C) Determine the reasonable domain and range values of
exponential and logarithmic functions, as well as interpret
and determine the reasonableness of solutions to
exponential and logarithmic equations and inequalities.
(D) Determine the solutions of exponential and logarithmic
equations using graphs, tables, and algebraic methods.
Content Description
Textbook
Graph and use exponential growth functions with base b > 1.
7.1
Graph and use exponential decay functions with base 0 > b >1.
7.2
Study functions involving the natural base "e" .
7.3
Evaluate logarithms and graph logarithmic functions of base "b".
7.4
Apply properties of logarithms (product property, quotient property, and
power property) to rewrite logarithmic expressions.
7.5
Solve exponential and logarithmic equations.
7.6
Use the regression feature on the graphing calculator to model exponential
and power functions.
7.7
Resources
(E) Determine solutions of exponential and logarithmic inequalities using graphs and tables.
(F) Analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.
Support TEKS
Vocabulary
- exponential function
- exponential growth
- growth factor
- exponential decay
- decay factor
- logarithm of y with base b
(2A.4) Algebra and geometry: connects algebraic and geometric representations of functions. The student is expected to:
- natural base e
(A) identify and sketch graphs of parent functions, including linear, quadratic, exponential, and logarithmic functions, absolute value - common logarithm
of x, square root of x , and reciprocal of x.
- natural logarithm
(C) describe and analyze the relationship between a function and its inverse.
- exponential equation
- logarithmic equation
Common Assessment
Aug 8, 2007
Algebra 2 Essential Units of Study 2007-08
07 EUS - Conics (4 Weeks)
Focus TEKS
Content Description
Explore the intersections of planes and cones.
(2A.5) Algebra and geometry: knows the relationship
between the geometric and algebraic descriptions of conic
sections.
(A) Describe a conic section as the intersection of a plane
and a cone.
(B) Sketch graphs of conic sections to relate simple
paramerter changes in the equation to corresponding
changes in the graph.
(C) Identify symmetries from graphs of conic sections.
(D) Identify the conic section from a given equation.
(E) Use the method of completing the square.
Textbook
9.6 Activity (p. 649)
Graph and write the equations of circles centered at the origin. Determine
the equation of a circle given its center and a point on the circle.
9.3
Graph and write the equation of an ellipse in standard form. Identify the
vertices, foci, major, and minor axes.
9.4
Graph and write equations of hyperbolas. Identify vertices, foci, and
asymptotes.
9.5
Graph and write the equations of parabolas that open up/down or left/right.
9.2
Graph and write equations of translated conics and identify the important
characteristics of the graphs. Complete the square to write conics in (h,k)
form.
9.6
Resources
Support TEKS
Key Vocabulary
- conic sections
- ellipse
- focus, foci
- directrix
- vertices
- major axis
a.5 Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. - minor axis
- hyperbola
Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools and technology (including, but
- transverse axis
not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve
- circle equation
meaningful problems.
- general second degree equation
Common Assessment
Aug 8, 2007