Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(2) Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand
the relationship between a function and its inverse. The student is expected to:
2A.2(A) graph the
Graph the functions:
Absolute value function,
Make and describe a
Big Ideas Algebra 2
Graph
parent
function,
chart
of
the
parent
Ch. 1.2

f(x)=√x
functions f(x)=√x,
transformation,
functions including

f(x)=1/x
f(x)=1/x, f(x)=x3,
Now, graph its parent function. Describe translation, reflection,
linear, quadratic,
 f(x)=x3
TEXTEAMS
f(x)= 3√x, f(x)=bx,
3
the
transformation.
Identify
the
domain
vertical
stretch,
vertical
exponential and
Algebra 2/Pre-Cal

f(x)=
√x,
f(x)=|x|, and f(x)=logb (
x
and range.
shrink
logarithmic functions.
Student Activity
f(x)=b
x) where b is 2, 10,
Matching Parent

f(x)=|x|
and e, and, when
Correct Answer:
Have
students
Functions

f(x)=log
(x)
where
applicable, analyze the
b
investigate and describe Google Drive
b is 2, 10, and e
key attributes such as
transformations.
College Board
For each function
domain, range,
Springboard
analyze key attributes:
intercepts, symmetries,
Practice with
 domain
asymptotic
transformations,
behavior, and maximum  range
charades, filling out a
and minimum given an  intercepts
chart that students’
interval.
 symmetries
graph and describe all
Readiness Standard
 asymptotic behavior
Domain: (-∞,∞)
changes.
 maximum
Range: (-∞, -3]
 minimum
Misconceptions:
 The student may confuse domain and range.
 The student may confuse the different types of symmetry (with respect to the
origin, or with respect to an axis.)
 The student may confuse the equations for horizontal and vertical
asymptotes.
2016-2017
Page 1
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(3) Systems of equations and inequalities. The student applies mathematical processes to formulate systems of equations and inequalities, use a variety of methods
to solve, and analyze reasonableness of solutions. The student is expected to:
2A.3(A) formulate
Formulate systems of An amphitheater charges $75 for each seat in System
Students should be
Big Ideas Algebra 2
systems of equations,
linear equations in
Section A, $55 for each seat in Section B,
Linear
able to formulate a
Ch 2.1
including systems
three variables.
and $30 for each law seat. There are three
Variable
system of three
consisting of three
times as many seats in Section B as in
Quadratic
equations in three
Google Drive
linear equations in
Section A. The revenue from selling all
Solution
variables based on
Formulate system of
three variables and
23,000 seats is $870,000. Write a system of
Ordered pair
verbal descriptions.
Springboard
equations with linear
systems consisting of
equations for the situation.
Ordered triple
and quadratic
two equations, the first
College Board
function.
linear and the second
Correct Answer:
quadratic.
a=Section A seats, b=Section B seats, c=lawn
seats;
Readiness Standard
Misconceptions:
75a  55b  30c  870,000
 The student may have trouble setting up system from a verbal description
b  3a
(such as defining variables, or deciding which coefficients match up with
the given variables.)
a  b  c  23,000
 The student may incorrectly identify the equation of a line from a graph by
misreading the slope and/or y-intercept.
 The student may incorrectly identify the equation of parabola from a graph
by misreading the intercepts, vertex or direction of the opening.
2016-2017
Page 2
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
2A.3(B) solve systems
of three linear
equations in three
variables by using
Gaussian elimination,
technology with
matrices, and
substitution.
Readiness Standard
System
Linear
Solution
Elimination(Gaussian)
Substitution
Matrix (Matrices)
Dimension of a matrix
(rows, columns)
Inverse of a matrix
Ordered triple
Augmented matrix
Elements
Solve systems of three
linear equations in three
variables using :
 Gaussian elimination
 Substitution
 Technology with
matrices.
1. Solve the following using Gaussian
elimination:
x  2 y  2 z  14
2 x  3 y  2 z  5
x  2 y  z  3
Correct Answer:
x=-2, y=3, z=5
2. What is the y-value of the solution to
the matrix equation below?
1  x  2 
1 1
2 3
1   y    3 

1  1  2  z   6
Correct Answer:
y=1
2016-2017
Vocabulary
Instructional
Strategies
See Field Guide for
detail instructional
implications.
Teach students to use
the graphing
calculator to enter
matrices.
Resources/
Weblinks
Big Ideas Algebra 2
Ch 2.1
Ch 2.2
Ch 2.3
Google Drive
Springboard
College Board
https://www.youtube.co
m/watch?v=FlLsxlWD6
a8
https://www.youtube.co
m/watch?v=7e1uywDt
Onc
Misconceptions:
 The student may make common algebraic or arithmetic mistakes when
solving equations, such as sign errors or errors in combining like terms.
 When using matrices to solve a system, the student may not correctly
rewrite equations into standard form (Ax+By+Cz=D). For example, the
equation x=3y would need to be rewritten as x-3y+(0)z=0.
Page 3
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
2A.3(E) formulate
systems of at least two
linear inequalities in
two variables.
System of linear
inequalities
Constraints
Supporting Standard
Connects: 2A.3A
Formulating systems of
linear inequalities based
on situations or verbal
descriptions of real-world
scenarios.
You can spend at most $60 on beads. A
bag containing red beads costs $2 per
bag. A bag containing blue beads costs
$3 per bag. You need more bags of blue
beads than bags of red beads. You need
a minimum of 4 red bags. Write a
system of linear inequalities for the
situation.
Vocabulary
Instructional
Strategies
Have students identify
the variables, then
describe and relate
them using two or
more inequalities.
Resources/
Weblinks
Big Ideas Algebra 2
Ch 2.4
Google Drive 2.4
College Board
Springboard
Correct answer:
x= red beads, y= blue beads
2 x  3 y  60

y  x
x  4

2016-2017
Page 4
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
2A.3(F) solve systems
of two or more linear
inequalities in two
variables.
System
Inequality
Linear inequality
Boundary
Slope
y-intercept
dotted (open)
solid (closed)
Feasible (shaded)
region
Solve the linear
inequalities by graphing
the solution set (or
feasible region) on a
coordinate grid.
Supporting Standard
Connects: 2A.3A
2A.3(G) determine
possible solutions in the
solution set of systems
of two or more linear
inequalities in two
variables.
Supporting Standard
Connect 2A.3A
Solve the system of inequities.
x  6

1

y  x 1
2

 y  2 x  4
Correct answer:
The solution to the system of
inequalities would be the triangular
region shaded on the graph provided.
Identify possible solutions
from the graph of a
system of linear
inequalities.
Solution of a system of
linear inequalities
Determine possible solutions to the
graph above.
Possible answer:
(4, 1), because
46
True
2016-2017
Vocabulary
1
(4)  1
2
1  2 1
1 3
True
1
1  2(4)  4
1  8  4
1  4
Instructional
Strategies
Use a graphing organizer to
help student graph each line
individually.
Use different colored map
pencils to distinguish
between the different
sections.
Resources/
Weblinks
Big Ideas Algebra 2
Ch 2.4
Google Drive
Connect that where all line
shaded areas overlap is
where the solutions are
found.
Have students select points
within the constraints and
plug into the system to
check for mathematical
reasonableness.
Have students create tables
to help organize their work
and to communicate their
reasoning.
Big Ideas Algebra 2
Ch 2.4
Google Drive
Model selecting points on
the boundary lines to
support the open/solid line
meanings.
True
Page 5
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(2) Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand
the relationship between a function and its inverse.
2A.4(B) write the
Explore properties of
Write an equation of the parabola
Axis of symmetry,
Put roots back into
Big Ideas Algebra 2
equation of a parabola
parabolas.
shown.
standard form, minimum factor form and then
3.2
using given
value, maximum value,
multiply binomials to
3.3
attributes, including
Find maximum and
intercept form, focus,
put into standard form Google Drive
vertex, focus, directrix,
minimum values of
directrix
of a quadratic
College Board
axis of symmetry,
quadratic functions.
equation.
Springboard
and direction of
opening.
Graph quadratic functions
using x-intercepts.
Readiness Standard
Solve real-life problems
Correct Answer:
y  0.1x 2
2016-2017
Misconceptions:
Page 6
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(6) Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube
root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions.
2A.6(C) analyze the
Write functions
Absolute value function
Use a graphic organizer
Big Ideas Algebra 2
effect on the graphs
representing translations
Transformation
to help student
Ch 1.3
of f(x) = |x| when f(x) is and reflections.
Translation
understand the four basic
replaced by af(x),
Reflections
types of transformations
f(bx), f(x-c),
Write functions
Vertical stretch
when applied to absolute Google Drive:
and f(x) + d for specific representing stretches and
Vertical compression
value parent function.
Transformation
positive and negative
shrinks.
Horizontal stretch
Charades
real values of a, b,
Horizontal compression
Have student complete
Answer:
c, and d.
Write functions
transformation charades
Translated left 5 units and down 3
representing
combinations
to incorporate the
units,
and
reflected
over
the
x-axis.
Supporting Standard
of
transformations.
perceptual modes into
Connects: 2A.4C,
instruction.
2A.6E
2A.6(D)
Formulate absolute value
The graph of f(x) is provided below.
Absolute Value
Relate to distance on a
Big Ideas Algebra 2
formulate absolute
equations.
Distance
number line, which is
Ch 1.4, Example 3
value linear equations.
given by the formula
Google Drive:
d  x1  x2 when
Supporting Standard
formulating from
Connects: 2A.6C,
situation problems.
2A.6E
Also formulate from
Formulate the equation for f(x).
graphs in the form
Correct Answer:
f ( x)  a x  c  d , use
f ( x)  2 x  1  3
2016-2017
the vertex as points c and
d, select another point
from the graph for x and
y, then solve for a.
Page 7
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
2A.6(E) solve absolute
value linear equations.
Readiness Standard
Solve absolute value
equations.
Include some equations
with two absolute values.
Identify special solutions
of absolute value
equations.
2A.6(F) solve absolute
value linear inequalities.
Supporting Standard
Connect: 2A.6E
Solve Algebraically
Solve Graphically
Solve for k.
3k  2  2 k  2
Correct Answer:
k  0.4 , k  6
 3 2  4 x  5  13
Correct Answer:
Solve for x:
x>2 or x<-1
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Absolute value
Linear
Equation
Solution
Extraneous
Instructional
Strategies
1. Write the two related
linear equations, for a
positive solution and
negative solution.
2. Solve for both.
3. You will have two
solutions.
Resources/
Weblinks
Big Ideas Algebra 2
Ch 1.4
Ch 1.5
Google Drive
College Board
Springboard
Misconceptions:
The student may assume that the two solutions to an absolute value equation
are always opposites. For example, in the equation x  2  8 , since one
solution is x=6, a student may incorrectly assume that the other solution is
x=-6. (Instead, the other solution comes from solving x+2=-8, yielding x=-10)
Absolute value
Graph solutions on a
Big Ideas Algebra 2
Inequality
number line.
Ch 1.5
Inclusive
Union (“or”)
Check work by
Intersection (“and”)
substitution solution set
into the question.
Include no solution
situations.
2016-2017
Page 8
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(7) Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The
student is expected to:
2A.7(I) write the
Determine domain and
Write the following interval in interval
Set, set-builder
Practice reading graphs Big Ideas Algebra 2
domain and range of a
range in interval
notation, inequalities, and set notation.
notation, subset,
(both continuous and
Ch. 1.1
function in interval
notation, inequalities and
endpoints,
discrete) left to right to
notation, inequalities,
set notation.
bounded
find domain and bottom
and set notation.
intervals,
to top to find range.
Correct Answers:
unbounded
intervals
Supporting Standard
(-1,3],  1  x  3 , {x  1  x  3}
2016-2017
Page 9
Mathematics
Course: Pre-AP Algebra II
Unit 1: Absolute Value Functions
Unit 2: Linear Regression and Systems of Linear Equations
TEKS
Guiding Questions/
Assessment
Specificity
Designated Grading Period: 1st Six Weeks
Days to teach: 14
Vocabulary
Instructional
Strategies
Resources/
Weblinks
2A.(8) Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions.
2A.8(A) analyze data to
select the appropriate
model from among linear,
quadratic, and exponential
models.
Supporting Standard
Connect: 2A.8C
2A.8(B) use regression
methods available through
technology to write a linear
function, a quadratic
function, and an
exponential function from
a given set of data.
Supporting Standard
2A.8(C) predict and
make decisions and critical
judgments from a given set
of data using linear,
quadratic, and exponential
models
Readiness Standard
2016-2017
Determine if the data is
linear, quadratic or
exponential.
Write an equation for the
model.
Determine whether the data shows a
linear relationship. Estimate y when
x  15 and explain its meaning in the
context of the situation.
Days, x
Number of
tickets sold,
y
3
76
7
164
11
252
14
318
20
450
Line of fit
Line of best fit
Correlation coefficient
Use card sorts of data
sets and graphs to
match models to the
data.
https://www.youtube.c
om/watch?v=FlD3eD
RgiPI
Be sure to show
students how to turn
diagnostics on in the
graphing calculator.
https://www.youtube.co
m/watch?v=wQkHFqa
OU2w
y  22 x  10
y=87, so in 5 days, you can predict
that 87 tickets will have sold.
Big Ideas Algebra 2
Ch 1.6
Models may include
equations and graphs.
Correct answer:
Yes, linear relationship
Have students make
predictions for both
variables, not just always
y.
Provide students with
different sets of data to
create scatterplots to
analyze the data.
Misconceptions:
Focus on Linear in this
unit.
Page 10