Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
First Nine Weeks Scope and Sequence
August 24th – September 11, 2015 Simplify Expressions, Solve Linear Equations (one variable), Solve Linear Inequalities (one variable)
Vocabulary
English
Distribute Property
Algebraic Expression
Product
Perimeter
Combine Like Terms
Coefficient
No Solution
Is
All Real Numbers
Turnaround Words (to,
from, than)
Solution
Order of Operations
Spanish
Expression Algebraica
Perimetro
Coeficiente
Solucion
Is Greater Than
Is At Most
Is No Less Than
English
Difference
Variable
Constant
Evaluate
Sum
Area
Literal Equation
Triple
Less Than
Spanish
Variable
Area
English
Numerical Expression
Quotient
Equation
Term
Quantity
Solve
Equal To
Inverse Operations
More Than
Reciprocal
Twice
Zero Pair
Inequality
Is Less Than or Equal
To
Is At Least
Power
Simplify
Is Less Than
Is Greater Than or
Equal To
Is No More Than
Identity
Potencia
Spanish
Ecuacion
Termino
Operaciones Inversos
Identidad
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
1
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Unit 1: Expression, Linear Equations (one variable) and Linear Inequalities (one variable)
Readiness
Supporting
Standard Clarification
TEKS/SEs
TEKS/SEs
(A.5)Linear
functions,
equations, and
inequalities.
The student
applies the
mathematical
process
standards to
solve, with and
without
technology,
linear equations
and evaluate the
reasonableness
of their
solutions. The
student is
expected to
(A) solve linear
equations in
one variable,
including
those for
which the
application of
the
distributive
property is
necessary and
for which
variables are
included on
both sides;
(A.10) Numbe
r and algebraic
methods. The
student applies
the
mathematical
process
standards and
algebraic
methods to
rewrite in
equivalent forms
and perform
operations on
polynomial
expressions. The
student is
expected to
(A) add and
subtract
polynomials
of degree one
and degree
two;
(D) rewrite
polynomial
expressions
of degree one
and degree
two in
equivalent
forms using
the
distributive
property;
1. TSWBAT simplify numerical expressions by
using Order of Operations.
2. TSWBAT simplify algebraic expressions by
combining like terms (of degree one and
degree two) and using the distributive
property.
3. TSWBAT evaluate rational and irrational
numbers in algebraic expressions to find the
solution.
4. TSWBAT solve one-variable equations
including those with the variables being on
both sides of the equals sign; also with
distributive property on both sides.
5. TSWBAT recognize that the solution to the
equation is the value(s) of the variable,
which make a true equality when
substituted back into the equation.
Equations shall include rational numbers,
Questions
Essential:
1. How can expressions and
equations help us to generalize
and describe patterns in our
world?
2. How can we use expressions
and equations to model and
solve real-world problems?
3. How does solving a linear
equation compare to solving a
linear inequality?
4. Why do we want to compare
rather than get an exact
answer?
Guiding:
1. What is the process to order of
operations?
2. Why does the order matter
when simplifying expressions
and solving equation?
3. How are terms considered to
be “like” or “unlike”?
4. How are inverse operations
used to solve equations?
5. What is the difference between
expression and equation?
6. What are zero pairs?
7. What is the difference between
evaluate, simplify, and solve?
2
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
(A.12) Numbe
r and
algebraic
methods.
distributive property and combining like
terms.
The student
applies the
mathematical
process
standards and
algebraic
methods to
write, solve,
analyze, and
evaluate
equations,
relations, and
functions. The
student is
expected to
(E) solve
mathematical
and scientific
formulas,
and other
literal
equations,
for a
specified
variable.
6. TSWBAT use common literal equations
(mathematical geometric formula and
scientific formulas) in real life situations.
7. TSWBAT translate stated linear expressions
into algebraic symbols and vice versa.
(A.5)Linear
functions,
equations,
and
inequalities.
The student
10. TSWBAT identify the solution set for
inequalities.
8. TSWBAT solve one-variable inequalities
including those with the variables being on
both sides and distributive property on both
sides of the inequality sign. Inequalities
shall include rational numbers, distributive
property and combining like terms
including.
Questions
8. What is the process in solving
an equation?
9. How are the characteristics of
an equation that is considered
“no solution”?
10. What is the purpose of a literal
equation?
11. What are some similarities and
differences between equations
and inequalities?
12. What is the difference between
at least and at most?
13. How do you solve an
inequality?
14. How do you determine the
reasonableness of solution set?
9. TSWBAT graph solutions on a number line.
11. TSWBAT justify solution sets of
3
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
applies the
mathematical
process
standards to
solve, with and
without
technology,
linear equations
and evaluate
the
reasonableness
of their
solutions. The
student is
expected to
(B) linear
inequalities in
one variable,
including
those for
which the
application of
the
distributive
property is
necessary and
for which
variables are
included on
both sides;
and
Standard Clarification
Questions
inequalities.
12. TSWBAT translate verbal inequality
statements to algebraic symbols.
13. TSWBAT to explain the solution to an
inequality as it pertains to a given problem.
4
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
First Nine Weeks Scope and Sequence
September 14 – October 1, 2015 Functions and Relations
Vocabulary
English
Function
Range
Mapping Diagram
Undefined Slope
Linear Model
Continuous
Input
Independent
x-axis
Cartesian Coordinate
Plane
Parent Function
Point-slope Form
Spanish
English
Graph
Vertical Line Test
Relation
Function Notation
Slope
Origin
Output
Vertical
y-axis
Spanish
English
Domain
Ordered Pair
Zero Slope
Correlation
Discrete
Table
Dependent
Horizontal
Non-linear Functions
Quadrants
Rate of Change
Standard Form
Slope-intercept Form
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
5
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Unit 2: Functions and Relations
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.2) Linear
functions,
equations, and
inequalities.
The student
applies the
mathematical
process
standards when
using properties
of linear
functions to
write and
represent in
multiple ways,
with and without
technology,
linear equations,
inequalities, and
systems of
equations. The
student is
expected to
(A) determine the
domain and
range of a
linear function
in
mathematical
problems;
determine
reasonable
domain and
(A.3) Linear
functions,
equations, and
inequalities.
The student
applies the
mathematical
process
standards when
using graphs of
linear functions,
key features, and
related
transformations
to represent in
multiple ways
and solve, with
and without
technology,
equations,
inequalities, and
systems of
equations. The
student is
expected to
(A) determine
the slope of
a line given
a table of
values, a
graph, two
points on the
line, and an
equation
written in
Standard Clarification
1. Compare the following functions to determine
which has the greater rate of change.
Function 1: y = 2x + 4
Function 2:
Questions
Essential:
1. How can patterns be used to
describe relationships in
mathematical situations?
2. How can data be organized and
represented to provide insight
into the relationship between
quantities?
Guiding:
Solution: The rate of change for function 1 is 2;
the rate of change for function 2 is 3. Function
2 has the greater rate of change.
Example 2:
Compare the two linear functions listed below
and determine which has a negative slope.
Function 1: Samantha starts with $20 on a gift
card for the bookstore. She spends $3.50 per
week to buy a magazine. Let y be the amount
remaining as a function of the number of
weeks, x
Function 2: Calculator rental
The school bookstore rents graphing
1. What is the coordinate plane
and its components?
2. How do you graph an ordered
pair?
3. How do you find the domain
and range of a discrete graph?
4. How do you find the domain
and range of a continuous
graph?
5. How do you identify the
independent and dependent
quantity in an linear equation
and in a real world problem?
6. What are the different
representations of ordered
pairs?
7. How do you know when a
graph is not a function? A set
of points?
8. What is the difference between
“f(x)= 2” and “f(2)=” ?
6
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
range values
for real- world
situations,
both
continuous
and discrete;
and represent
domain and
range using
inequalities;
(A.3) Linear
functions,
equations, and
inequalities. The
student applies
the mathematical
process standards
when using
graphs of linear
functions, key
features, and
related
transformations
to represent in
multiple ways and
solve, with and
without
technology,
equations,
inequalities, and
systems of
equations. The
student is
expected to
Supporting
TEKS/SEs
Standard Clarification
various
forms,
including
𝑦 = 𝑚𝑥 + 𝑏,
𝐴𝑥 + 𝐵𝑦 = 𝐶
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 );
(E) determine the
effects on the
graph of the
parent
function f(x)
= x when f(x)
is replaced by
af(x), f(x) +
d, f(x – c),
f(bx) for
specific
values of a,
b, c, and d;
(A.4) Linear
functions,
equations,
and
inequalities.
The student
applies the
mathematical
process
standards to
formulate
statistical
relationships
and evaluate
their
2.
3.
4.
5.
6.
calculators for $5 per month. It also collects a
non-refundable fee of $10.00 for the school
year. Write the rule for the total cost (c) of
renting a calculator as a function of the
number of months (m). c = 10 + 5m
Solution: Function 1 is an example of a
function whose graph has a negative slope.
Both functions have a positive starting amount;
however, in function 1, the amount decreases
3.50 each week, while in function 2, the
amount increases 5.00 each month.
Find slope and/or rate change given two points
and/or a table.
Write rule for a pattern, given next term
(arithmetic sequences)
Evaluate function rules to obtain domain or range
given a set of the latter.
Write the function rule for graphs using rise over
run.
Write the function rule given a real-life situation;
use rate of change (cost per item, monthly fee)
and initial value/initial fee.
Questions
9. How do you graph a linear
equation?
10. How do you change a linear
equation from standard form
to slope intercept form?
11. What are the four types of
slope?
12. How do domain and range
relate to independent and
dependent variables?
13. How is the “input” and
“output” in a relation related
to the x-values and y-values on
a table?
14. For any given line or table, how
does the rate of change relate
to its set of points?
15. How can the calculator be used
to help find the function of a
table?
16. What is an example of a
relation that is not a function?
7
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
(B) calculate the
rate of change
of a linear
function
represented
tabularly,
graphically, or
algebraically
in context of
mathematical
and realworld
problems;
(C) graph linear
functions on
the coordinate
plane and
identify key
features,
including xintercept, yintercept,
zeros, and
slope, in
mathematical
and realworld
problems;
(A.6) Quadratic
functions and
equations. The
student applies
the mathematical
process
Supporting
TEKS/SEs
reasonablenes
s based on
real-world
data. The
student is
expected to
(C) write, with
Standard Clarification
7. Represent in the form of an inequality.
and without
technology,
linear
functions
that provide
a reasonable
fit to data to
estimate
solutions
and make
predictions
for realworld
problems.
(A.12)
Number and
algebraic
methods. The
student applies
the
mathematical
process
standards and
algebraic
methods to
write, solve,
analyze, and
evaluate
Questions
Domain: All real numbers or all real solutions
Range: 𝑦 ≥ 6.2 𝑜𝑟 {𝑦|𝑦 ≥ 6.2}
Identify the domain and range of a real-life
problem using inequalities: Discrete – making x
number of fruit baskets and selling for $10
each, Continuous – driving at 20 mph on a path
that is 10 miles long.
8. Students will need to manipulate equations,
tables, or models to find rate of change (m).
a. Compare the following functions to
determine which has the greater rate of
change.
8
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
standards when
using properties
of quadratic
functions to write
and represent in
multiple ways,
with and without
technology,
quadratic
equations. The
student is
expected to
(A) determine the
domain and
range of
quadratic
functions and
represent the
domain and
range using
inequalities;
equations,
relations, and
functions. The
student is
expected to
(A) decide
whether
relations
represente
d verbally,
tabularly,
graphically
, and
symbolicall
y define a
function;
(B) evaluate
functions,
expressed
in function
notation,
given one
or more
elements
in their
domains;
(D)write a
formula for
the nth term
of arithmetic
and
geometric
sequences,
given the
value of
Standard Clarification
Questions
Function 1: y = 2x + 4
Function 2:
9. The school bookstore rents graphing calculators
for $5 per month. It also collects a nonrefundable fee of $10.00 for the school year.
Write the rule for the total cost (c) of renting a
calculator as a function of the number of months
(m).
10.
1. If you have a keen ear and some crickets,
can the cricket chirps help you predict the
temperature? What does 20 cricket chirps tell
you?
2. The model is used to draw conclusions: The
line estimates that, on average, each added
9
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[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
several of
their terms;
and
Standard Clarification
Questions
chirp predicts an increase of about 3.29
degrees Fahrenheit. What does this represent?
10
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
First Nine Weeks Scope and Sequence
October 2 – October 23, 2015 Graphing Linear Equations (two variables) and Linear Inequalities (two variable)
Vocabulary
English
Linear Parent Function
Y-intercept
Solution
Slope-point Form
Parameter Changes
Shaded Region
Perpendicular
Inclusive
Spanish
English
Intercept
Slope
Vertical Shifts
Point-slope Form
Dash line
Solution Set
Reciprocal
Exclusive
Spanish
English
X-intercept
Steepness
Standard Form
Coefficient
Solid Line
Parallel
Trend Line
Reasonable Values
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 3: Graphing Linear Equations (two variables) and Linear Inequalities (two variables)
Readiness
Supporting
Standard Clarification
TEKS/SEs
TEKS/SEs
(A.3)Linear
functions,
equations, and
inequalities. The
student applies
the mathematical
1. A) Students identify the rate of change (slope)
and initial value (y-intercept) from tables, graphs,
equations or verbal descriptions to write a
function (linear equation).
Questions
Essential:
3. How can we utilize
equations to solve
problems?
4. What types of relationships
11
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
process standards
when using
graphs of linear
functions, key
features, and
related
transformations
to represent in
multiple ways and
solve, with and
without
technology,
equations,
inequalities, and
systems of
equations. The
student is
expected to
(C)graph linear
functions on
the coordinate
plane and
identify key
features,
including xintercept, yintercept,
zeros, and
slope, in
mathematical
and real-world
problems;
Supporting
TEKS/SEs
Standard Clarification
B) Students understand that the equation
represents the relationship between the x-value
and the y-value; what math operations are
performed with the x-value to give the y-value.
Slopes could be undefined slopes or zero slopes.
Tables:
Students recognize that in a table the y-intercept
is the y-value when x is equal to 0. The slope can
be determined by finding the ratio y/x between
the change in two y-values and the change
between the two corresponding x-values.
2.
A) Students build on their work with unit rates
from 6th grade and proportional relationships in 7th
grade to compare graphs, tables and equations of
proportional relationships.
B) Students identify the unit rate (or slope) in
graphs, tables and equations to compare two
proportional relationships represented in
different ways.
Example: Compare the scenarios to determine
which represents a greater speed. Explain your
choice including a written description of each
scenario. Be sure to include the unit rates in your
explanation.
Questions
can be modeled by linear
graphs?
5. How can I analyze, model,
and solve mathematical
situations using algebraic
symbols?
Guiding:
6. What is the rate of change
in the linear parent
function?
7. For any set of points, how
does the function for the
line relate to the set of
points?
8. How many points are on a
line?
9. If you increase the yintercept of a line what
happens to the line?
10. If you multiply the slope of
a line by -1, what happens
to the line?
11. If you double the slope of a
line, what happens to line?
12. How is direct variation
similar to linear parent
function?
13. If two lines intersect, are
the perpendicular lines?
14. How do you know is two
line are parallel?
15. How can the properties of
12
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
16.
17.
Solution: Scenario 1 has the greater speed since
the unit rate is 60 miles per hour. The graph
shows this rate since 60 is the distance traveled in
one hour. Scenario 2 has a unit rate of 55 miles
per hour shown as the coefficient in the equation.
Given an equation of a proportional relationship,
students draw a graph of the relationship.
Students recognize that the unit rate is the
coefficient of x and that this value is also the slope
of the line.
18.
19.
parallel and perpendicular
lines be used?
How do you identify the x
and y intercepts of a graph?
How do the coordinates of
x and y intercept relate to
the graph?
What is the difference
between perpendicular
lines and intersecting lines?
How can the properties of
parallel and perpendicular
lines be used?
3.
Students use their
knowledge of parallel and
perpendicular slopes and
their knowledge of linear
equations to write an
equation of a line that is
either parallel or
perpendicular to the X or
Y axis.
What would be the slope of a line that is
perpendicular to the x-axis?
13
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
2. Students will use knowledge of graphing linear
equations to graph linear inequalities.
Example 1:
Determine the linear inequality that is graphed
above.
14
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Second Nine Weeks Scope and Sequence
October 26 – November 13, 2015 Writing Linear Equations and Linear Inequalities
Vocabulary
English
Direct Variation
Standard Form
y-intercept
Parallel
Linear Regression
Inclusive
Spanish
English
Slope-Intercept form
Slope formula
Rate of change
Perpendicular
Correlation
Exclusive
Spanish
English
Point-slope form
Rise over Run
Initial value/fee
Scatter Plot
Shaded Region
Reasonable Values
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 4: Writing Linear Equations and Linear Inequalities
Readiness
Supporting
Standard Clarification
TEKS/SEs
TEKS/SEs
(A.2) Linear
functions,
equations, and
inequalities.
The student
applies the
mathematical
process
standards when
(A.2) Linear
functions,
equations, and
inequalities.
The student
applies the
mathematical
process
1. The graph below represents the cost of gum packs
as a unit rate of $2 dollars for every pack of gum.
The unit rate is represented as $2/pack.
Represent the relationship using a table and an
equation.
Questions
Essential:
1. How can we utilize
equations to solve
problems?
2. What types of relationships
can be modeled by linear
graphs?
3. How can I analyze, model,
15
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
using properties
of linear
functions to
write and
represent in
multiple ways,
with and without
technology,
linear equations,
inequalities, and
systems of
equations. The
student is
expected to
(A) write linear
equations in
two
variables
given a
table of
values, a
graph, and
a verbal
description;
standards when
using properties
of linear
functions to
write and
represent in
multiple ways,
with and without
technology,
linear equations,
inequalities, and
systems of
equations. The
student is
expected to
(B)write linear
equations in
two variables
in various
forms,
including
𝑦 = 𝑚𝑥 + 𝑏,
Ax + By = C,
and
y–y1 = m(x–x1),
given one
point and
the slope
and given
two points;
(D)write and
solve
equations
involving
direct
variation;
Standard Clarification
Equation: d = 2g, where d is the cost in dollars and g
is the packs of gum.
2. Compute (using technology) and interpret the
correlation coefficient of a linear fit. Use a
calculator or computer to find the correlation
coefficient for a linear association. Interpret the
meaning of the value in the context of the data.
3. The correlation coefficient measures the
“tightness” of the data points about a line fitted
to data, with a limiting value of 1 (or -1) if all
points lie precisely on a line of positive (or
negative) slope. For the line fitted to cricket
chirps and temperature
(figure 1), the
correlation is 0.84, and
for the line fitted to
boys’ height (figure 2), it
is about 1.0. However,
the quadratic model for
tree growth (figure 3) is
Questions
and solve mathematical
situations using algebraic
symbols?
4. How can expressions,
equations, and inequalities
help us to generalize and
describe patterns in our
world?
5. How can we use
expressions, equations, and
inequalities to model and
solve real-world problems?
6. How do you represent
relationships between
quantities that are not
equal?
Guiding:
1. Can inequalities that
appear to be different be
equivalent?
2. Why should we know
different forms of linear
equations?
3. How do the words “and”
and “or” affect the
outcome of an inequality?
4. How does the solution set
of a line differ from the
solution set of a linear
inequality?
5. How is direct variation
similar to linear parent
function?
16
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9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
(E)write the
equation of a
line that
contains a
given point
and is
parallel to a
given line;
(F)write the
equation of a
line that
contains a
given point
and is
perpendicula
r to a given
line;
(G) write an
equation of a
line that is
parallel or
perpendicula
r to the
xor y-axis and
determine
whether the
slope of the
line is zero
or
undefined;
(A.4) Linear
functions,
equations, and
inequalities.
The student
applies the
Standard Clarification
non-linear, so the value of its correlation
coefficient has no direct interpretation
4. In situations where the correlation coefficient
of a line fitted to data is close to or 1, the two
variables in the situation are said to have a
high correlation. Students must see that one of
the most common misinterpretations of
correlation is to think of it as a synonym for
causation. A high correlation between two
variables (suggesting a statistical association
between the two) does not imply that one
causes the other. It is not a cost increase that
causes calories to increase in pizza, and it is not
a calorie increase per slice that causes cost to
increase; the addition of other expensive
ingredients cause both to increase
simultaneously. Students should look for
Questions
6. If two lines intersect, are
the perpendicular lines?
7. How do you know is two
line are parallel?
8. How do you draw the line
best fit on a paper graph?
Calculator?
9. What information do you
need to write the equation
of a line?
10. What are other names for
the equation of a line?
11. Why does the data on a
scatterplot “hover” around
the line of best fit?
12. If we calculate the line best
fit by hand, why will we not
get the same answer as the
calculator?
13. How do you identify the x
and y intercepts of a graph?
14. How do the coordinates of
x and y intercept relate to
the graph?
15. What is the difference
between perpendicular
lines and intersecting lines?
17
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
mathematical
process
standards to
formulate
statistical
relationships
and evaluate
their
reasonableness
based on realworld data. The
student is
expected to
(A)calculate,
using
technology,
the
correlation
coefficient
between two
quantitative
variables and
interpret this
quantity as a
measure of
the strength
of the linear
association;
(B)compare and
contrast
association
and causation
in real-world
problems;
and
(C)write, with
Standard Clarification
Questions
examples of correlation being interpreted as
cause and sort out why that reasoning is
incorrect. Examples may include medications
versus disease symptoms and teacher pay or
class size versus high school graduation rates.
One good way of establishing cause is through
the design and analysis of randomized
experiments.
5. A) Create a scatter plot from two quantitative
variables.
B) Describe the form, strength and direction of
the relationship.
C) Categorize data as linear or not. Use algebraic
methods and technology to fit a linear function
to the data. Use the function to predict values.
D) Explain the meaning of the slope and yintercept in context.
Example:
18
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
and without
technology,
linear
functions that
provide a
reasonable fit
to data to
estimate
solutions and
make
predictions for
real-world
problems.
Standard Clarification


Questions
If you have a keen ear and some crickets, can
the cricket chirps help you predict the
temperature? What does 20 cricket chirps tell
you?
The model is used to draw conclusions:
The line estimates that, on average, each added chirp
predicts an increase of about 3.29 degrees
Fahrenheit. What does this represent?
6. Tracy is selling purses and shoes to make at
least $300.00 to put towards her summer trip.
The purses cost $15.00 each and a pair of
shoes cost $12.00. Write a linear inequality
that represents the amount of purses and
shoes that Tracy needs to sell.
Solution: 15x+12y ≥ 300
19
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Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Second Nine Weeks Scope and Sequence
November 16 – December 18, 2015 Systems of Linear Equations and Linear Inequalities
Vocabulary
English
Linear equations
Inclusive
Point of Intersection
Solution
Intersecting Lines
Dependent
Y-intercept
Gauss Elimination
method
Profit Function
Spanish
English
Linear Inequalities
Exclusive
No Solution
Parallel Lines
Inconsistent
Independent
Standard form
Spanish
Substitution method
English
Solution set
Reasonableness
Infinitely Many Solution
Coinciding Lines
Consistent
Slope
Slope-intercept form
Spanish
Break-even
Cost Function
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 5: Systems of Linear Equations and Linear Inequalities
Readiness
Supporting
Standard Clarification
TEKS/SEs
TEKS/SEs
(A.2)
Linear
functions,
equations, and
(A.3) Linear
functions,
equations, and
inequalities. The
1. Solve systems of equations using tables, graphs,
substitution method and elimination method.
2. Solve systems of linear equations using graphs,
Questions
Essential:
1. How can a system of
equations and inequalities
support you in solving real-
20
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Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
inequalities. The
student applies
the mathematical
process standards
when using
properties of
linear
functions to write
and represent in
multiple ways,
with and without
technology, linear
equations,
inequalities, and
systems of
equations. The
student is
expected to
(I) write
systems of two
linear equations
given a table of
values, a graph,
and a verbal
description.
student applies
the mathematical
process standards
when using
graphs of linear
functions, key
features, and
related
transformations
to represent in
multiple ways and
solve, with and
without
technology,
equations,
inequalities, and
systems of
equations. The
student is
expected to
(F) graph
systems of
two linear
equations in
two variables
on the
coordinate
plane and
determine
the solutions
if they exist;
(G) estimate
graphically
the solutions
to systems of
two linear
equations
(A.5)Linear
functions,
equations, and
inequalities. The
student applies
the mathematical
process standards
to solve, with and
without
technology, linear
equations and
Standard Clarification
identify the solution set and reasonable values in
solution set.
3. The Anytime long-distance plan charges $4.80 per
month plus 5¢ a minute. The Talk More plan
charges 9¢ a minute and no monthly fee. For what
number of minutes are the charges for the two
plans the same?
 Write a system of two equations to model this
situation.
 Solve the system by creating a table.
2.
Students need to understand that the solution
to a system of two linear equations is their point of
intersection.
3. Systems of linear equations can also have one
solution, infinitely many solutions or no solutions.
Students will discover these cases as they graph
Questions
life world problems?
Guiding:
1. What are the advantages
and disadvantages of
solving a system of linear
equations graphically
versus algebraically?
2. How can systems of
equations be used to
represent situations and
solve problems?
3. How can you tell if you
have solved a linear system
of equations?
4. What is the difference
between the x-intercept, yintercept, and point of
intersection?
5. What is the solution to a
linear system of equations
if the lines never intersect?
6. If the solution to a linear
system of equations only
“works” for one equation,
what can you conclude
about that point?
7. In problem situations, like
revenue and cost, what
does the point of
intersection represent?
What can you conclude
prior to the point of
21
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9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
evaluate the
reasonableness of
their solutions.
The student is
expected to
(C) solve systems
of two linear
equations with
two variables for
mathematical and
real-world
problems.
with two
variables in
real-world
problems;
and
(H)
graph the
solution set of
systems of two
linear inequalities
in two variables
on the coordinate
plane.
Standard Clarification
systems of linear equations and solve them
algebraically. Students graph a system of two
linear equations, recognizing that the ordered
pair for the point of intersection is the x-value
that will generate the given y-value for both
equations. Students recognize that graphed lines
with one point of intersection (different slopes)
will have one solution, parallel lines (same slope,
different y-intercepts) have no solutions, and
lines that are the same (same slope, same yintercept) will have infinitely many solutions. By
making connections between algebraic and
graphical solutions and the context of the system
of linear equations, students are able to make
sense of their solutions. Students need
opportunities to work with equations and context
that include whole number and/or
decimals/fractions. Students define variables and
create a system of linear equations in two
variables

Questions
intersection? After?
Plant A and Plant B are on different watering
schedules. This affects their rate of growth.
Compare the growth of the two plants to
determine when their heights will be the same.
Let W = number of weeks
22
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
Let H = height of the plant after W weeks
4.
Students will need to graph the solution set of
two inequalities, but they should also be able to read
a graph of the solution set. Students will need to
graph the solution set of two inequalities, but they
should also be able to read a graph of the solution
set.
23
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Curriculum & Instruction
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Third Nine Weeks Scope and Sequence
January 19 – January 26,2016 Exponents
Vocabulary
English
Base
Cubic
Standard Form
Product Rule
Coefficient
Rational Exponents
Spanish
English
Term
Square
Ascending
Exponent
Zero Power
Power to Power
Spanish
English
Reciprocal
Descending
Quotient Rule
Power of
Negative Power
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 6: Exponents
Readiness
TEKS/SEs
Supporting
TEKS/SEs
(A.11) Number
and algebraic
methods. The
student applies
the mathematical
process standards
(A.10) Number
and algebraic
methods. The
student applies
the mathematical
process
Standard Clarification
1. Use patterns to generate the laws of exponents
with whole number exponents and apply in
problem solving situations including but not
limited to area and volume.
Questions
Essential:
1. Why do you think
exponents are important to
mathematicians and
scientist?
2. How does using scientific
24
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
and algebraic
methods to
rewrite algebraic
expressions into
equivalent forms.
The student is
expected to
(B) simplify
numeric and
algebraic
expressions
using the
laws of
exponents,
including
integral and
rational
exponents.
standards and
algebraic
methods to
rewrite in
equivalent forms
and perform
operations on
polynomial
expressions. The
student is
expected to
(B) multiply
polynomials of
degree one
and degree
two;
Standard Clarification
2. Use rational exponents. Demonstrate how
rational exponents are written in radical form and
visa versa. Show how to use the product rule and
power rule to make rational exponents become
1
2
1
2
integer exponents. Example: 𝑥 ∙ 𝑥 = 𝑥
3. Zero Power rule , negative exponents, power to a
power, product rule and quotient rule.The area of
a triangle is 30m4n3 and the base is 10m2 . Find
the height.
4. Which expression describes the area in square
units of rectangle that has a length of 10x4y5 units
and a width of 2xy?
A. 12xy
B. 20x5y6
C. 20x4y5
D. 12x5y6
5. How many seconds does it take sunlight to reach
the earth if the speed of the light is 186,000 miles
per second and the average distance from the sun
to the earth is 9.3 x 107 miles?
Questions
notation help scientists to
make good decisions?
Guiding:
1. What is the difference
between x5y7 and x5 + y7 ?
2. How do you identify the
degree of a polynomial?
3. How is combining like
terms similar to adding and
subtracting polynomials?
4. What is the difference
between 3x and x3?
5. How can show numerically
that -x3 and (-x)3 are not the
same?
6. Why is x0 equivalent to
25/25 ?
25
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Third Nine Weeks Scope and Sequence
January 27 – March 1, 2016 Polynomials
Vocabulary
English
Product
Quotient
Multiply
Distributive Property
GCF (Greatest
Common Factor)
Variable
Standard Form
Monomial
Polynomial
Cubic
Constant
Spanish
English
Factors
Dividend
Polynomial
Box Method
Spanish
English
Dimensions
Long Division
FOIL method
Exponents
Product Rule
Quotient Rule
Coefficient
Ascending order
Binomial
Linear
Nth degree
Base
Descending order
Trinomial
Quadratic
Term
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
26
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Curriculum & Instruction
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Unit 7: Polynomials
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.10) Numbe
r and algebraic
methods. The
student applies
the
mathematical
process
standards and
algebraic
methods to
rewrite in
equivalent forms
and perform
operations on
polynomial
expressions. The
student is
expected to
(E)factor, if
possible,
trinomials
with real
factors in the
form
ax2 + bx + c,
including
perfect
square
trinomials of
degree two;
and
(A.10) Numbe
r and algebraic
methods. The
student applies
the
mathematical
process
standards and
algebraic
methods to
rewrite in
equivalent forms
and perform
operations on
polynomial
expressions. The
student is
expected to
(A) add and
subtract
polynomials
of degree one
and degree
two;
(B) multiply
polynomials
of degree one
and degree
two;
(C) determine the
quotient of a
polynomial of
degree one
and
polynomial of
degree two
Standard Clarification
Questions
1.
Classify polynomials by degrees and number of Essential:
1. When could a non-linear
terms
function be used to model a
2.
Add and subtract two or more given
real-world situation?
2. What factors can affect good
polynomials modeling perimeter where a figure or
decision making?
expression is given.
Simplify: 2(x+1)(x-3) - 3(x2 +5x +7)
Guiding:
3.
Multiply binomial by a binomial and a binomial 1. How is calculating area similar
to multiplying polynomials?
by a trinomial; use geometric applications of area and
2. How are the factors similar to
volume to apply skills.
the products of a polynomial?
4.
Divide a polynomial by a monomial using
3. Compare and Contrast y=x and
algebra tiles, pictures, and written expressions.
y=x2
2 7
5 3
2 2
Simplify 10x y + 20x y divided by 2x y
5.
Factor trinomials in which a=1 and 1< a<10;
use box method or factor by grouping; use geometric
applications of area to find factors (dimensions).
6.
Factor completely by using GCF; use geometric
applications of volume to find factors (dimensions).
7.
Factor difference of squares and perfect square
trinomials (refer to dimensions of a square or radius).
8.
Find the quotient of a polynomial of degree
two when divided by a polynomial of degree one; use
long division. Reinforces multiplying polynomials and
refer to long division from prior grades.
27
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Curriculum & Instruction
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Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
when divided
by a
polynomial of
degree one
and
polynomial of
degree two
when the
degree of the
divisor does
not exceed
the degree of
the dividend;
(D) rewrite
polynomial
expressions
of degree
one and
degree two
in equivalent
forms using
the
distributive
property;
(F) decide if a
binomial can
be written as
the difference
of two
squares and,
if possible,
use the
structure of a
difference of
two squares
to rewrite the
binomial.
28
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Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Third Nine Weeks Scope and Sequence
March 2 – March 11, 2016 Quadratic Functions
Vocabulary
English
Roots
X-intercepts
Spanish
Parameter Changes
Vertical Shifts
Vertex
Upward
Domain
Parent Function
Completing the square
English
Solutions
Y-intercepts
Wider (vertically
compressed)
Horizontal Shifts
Minimum
Downward
Range
Vertex Form
Quadratic Regression
Spanish
English
Zeros
Axis of Symmetry
Narrow (vertically
stretched)
Reflection
Maximum
Radical
Zero Product Property
Standard Form
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
29
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Unit 8: Quadratic Functions
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.6) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
when using
properties of
quadratic
functions to write
and represent in
multiple ways,
with and without
technology,
quadratic
equations. The
student is
expected to
(A) determine
the domain
and range of
quadratic
functions and
represent the
domain and
range using
inequalities;
(A.7) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
when using
graphs of
(A.6) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
when using
properties of
quadratic
functions to write
and represent in
multiple ways,
with and without
technology,
quadratic
equations. The
student is
expected to
(B) write
equations of
quadratic
functions
given the
vertex and
another point
on the graph,
write the
equation in
vertex form
Standard Clarification
1. Represent domain and
range in the form of an
inequality.
Domain: All real numbers or all
real solutions
Range: y≥6.2 or {y|y≥6.2}
𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘,
and rewrite
the equation
from vertex
form to
standard
form
2. The vertex of a quadratic function is (3,4) and
another point on the graph is (1,12), determine
the equation in:
a)vertex form
b)standard form
 Connect all quadratic graphs to the parent
function.
𝑏
 Connect the x-value of the vertex (h) to − .
2𝑎
 Recognize that c is the y-intercept.
 Use completing the square to transform the
standard form (𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐) to vertex
form (𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘).
2
 Square the binomial in 𝑦 = 𝑎 (𝑥 − ℎ) + 𝑘 and
simplify to find the standard form as shown
above.
 Connect the x-value of the vertex to h and the
y-value of the vertex with k.
 Identify the line of symmetry and write its
Questions
Essential:
1. Why do we use different
methods to solve math?
Guiding:
1. On a graphical model, how can
you determine the solutions to
a quadratic equation?
2. What are the different names
for solutions to a quadratic?
3. Why do we set a quadratic
equation equal to 0 when
solving for the x-intercepts?
4. How do the graphs of y=x2 and
y=-x2 compare to each other?
5. How does the maximum and
minimum relate to the vertex
of a parabola?
6. How does the domain of
the linear parent function
relate to the domain of the
quadratic parent function?
7. How are the parameter
changes to a line and a
parabola similar? How are they
different?
8. In a table, how do the values of
a quadratic function compare
to the values of linear
function?
9. How can the characteristics of
a parabola help in identifying
other points?
30
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
quadratic
functions and
their related
transformations
to represent in
multiple ways and
determine, with
and without
technology, the
solutions to
equations. The
student is
expected to
(A) graph
quadratic
functions on
the coordinate
plane and use
the graph to
identify key
attributes, if
possible,
including xintercept, yintercept,
zeros,
maximum
value,
minimum
values,
vertex, and
the equation
of the axis of
symmetry;
(C) determine
the effects on
the graph of
Supporting
TEKS/SEs
𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 ;
and
(C) write
quadratic
functions
when given
real solutions
and graphs of
their related
equations.
(A.7) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
when using
graphs of
quadratic
functions and
their related
transformations
to represent in
multiple ways and
determine, with
and without
technology, the
solutions to
equations. The
student is
expected to
(B) describe the
relationship
between the
linear factors
of quadratic
Standard Clarification
Questions
equation.
 Use the value of “a” to determine whether the
function opens up or down (reflection).
 Use the value of “h” to determine the number
of units the graph will shift horizontally (left or
right); explain how to determine given the
equation.
 Use the value of “k” to determine the number
of units the graph will shift vertically (up or
down); explain how to determine given the
equation.
 Use the value of “h” and “k” to identify the
domain and range of the function.
 Connect the y-value of the vertex as the
maximum or minimum value of the function.
3.
Create a scatter plot from two quantitative
variables.
 Describe the form, strength and direction of
the relationship.
 Categorize data as quadratic or not. Use
algebraic methods and technology to fit a
quadratic function to the data. Use the
function to predict values.
 Explain the meaning of the x-intercepts in
concept.
10. Without a graphic model, how
can you tell from a quadratic
equation if a parabola has a
maximum or minimum?
11. What role does the y-intercept
play when solving a quadratic
equation?
12. What do the solutions look like
if there are no real solutions?
13.How do you identify the roots
to a quadratic from a table of
values?
31
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
the parent
function f(x) =
x2 when f(x) is
replaced by
af(x), f(x) +
d, f(x – c),
f(bx) for
specific values
of a, b, c, and
d.
Supporting
TEKS/SEs
Standard Clarification
Questions
expressions
and the zeros
of their
associated
quadratic
functions;
and
(A.8) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
to solve, with and
without
technology,
quadratic
equations and
evaluate the
reasonableness of
their solutions.
The student
formulates
statistical
relationships and
evaluates their
reasonableness
based on realworld data. The
student is
expected to
(B) write, using
technology,
quadratic
functions
32
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
that provide
a reasonable
fit to data to
estimate
solutions and
make
predictions
for real-world
problems.
(A.12) Number
and algebraic
methods. The
student applies
the mathematical
process standards
and algebraic
methods to write,
solve, analyze,
and evaluate
equations,
relations, and
functions. The
student is
expected to
(B)evaluate
functions,
expressed in
function
notation,
given one or
more
elements in
their
domains;
33
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Fourth Nine Weeks Scope and Sequence
March 28 – April 12, 2016 Quadratic Equations
Vocabulary
English
Quadratic standard
form
Solutions
Radical
Root
Zero Product Property
Spanish
English
Spanish
English
Completing the Square
Quadratic Formula
Zeros
Square Roots
Vertex Form
X-intercepts
Double root
Factoring
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 9: Quadratic Equations
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.7) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
when using
(A.7)Quadratic
functions and
equations. The
student applies
the mathematical
process
standards when
Standard Clarification
1.
2.
Student is able to find the solution to a quadratic
equation by using a table or graphing; when f(x)
= 0 or another value.
Student can use the axis of symmetry to find the
other solution of a partial graph.
Questions
Essential:
1.
Describe how the value
of 𝑟 2 affects the reasonableness
and/or accuracy of the prediction.
2.
Why are roots, zeros, and
solutions commonly misinterpreted?
34
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
graphs of
quadratic
functions and
their related
transformations
to represent in
multiple ways and
determine, with
and without
technology, the
solutions to
equations. The
student is
expected to
(A) graph
quadratic
functions on
the
coordinate
plane and
use the
graph to
identify key
attributes, if
possible,
including xintercept,
y-intercept,
zeros,
maximum
value,
minimum
values,
vertex, and
the equation
of the axis of
symmetry;
using graphs of
quadratic
functions and
their related
transformations
to represent in
multiple ways
and determine,
with and without
technology, the
solutions to
equations. The
student is
expected to
(B) describe the
relationship
between the
linear factors
of quadratic
expressions
and the zeros
of their
associated
quadratic
functions; and
(A.8) Quadratic
functions and
equations. The
student applies
the mathematical
process
standards to
solve, with and
without
technology,
quadratic
Standard Clarification
3.
Student can find a solution using the vertex and
any point.
4. Student can graph a quadratic equation and
identify the number of solutions.
5. Student can find the vertex of a graph and axis
of symmetry using the quadratic equation.
𝑏
Student can find other points by using 𝑥 =
2𝑎
and the axis of symmetry.
6. Students will be able to estimate solutions by
looking at a graph and/or table (sign change on
the y values).
7. Students will solve difference of squares using
square roots.
8. Student s will solve perfect square trinomials in
factored form using square roots.
9. Students will solve quadratic equations by
factoring and using zero product property.
10. Students will solve quadratic equations by
completing the square and using square roots.
11. Students will solve quadratic so by using the
quadratic formula; equation must be in standard
form and/or be able to identify values of a, b,
and c. Students will also be able to simplify the
radical when solving with the quadratic formula.
12. Students will be able to create scatter plot of
real life data a use quadratic regression to find a
Questions
Guiding:
1.
How are roots, zeros, and
solutions similar and different?
2.
Explain how to solve a
quadratic function by graphing or
using a table?
3.
What are you finding when
you are asked for the value of x
when f(x)=0?
4.
When and how do you use
the zero product property?
5.
Give examples of real life
situations that model quadratic
equations.
6.
Explain how to simplify a
radical.
7.
Using the quadratic
formula, how can you determine
that there will be no solution?
8.
How many solutions does a
perfect square trinomial have?
9.
How many solutions does a
difference of squares trinomial
have?
10.
In what form must the
quadratic equation be in so that
you can use factoring to solve?
11.
In what form must the
quadratic equation be in so that
you can use the quadratic formula?
12.
Explain the steps to solve a
quadratic equation by completing
the square.
35
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
(A.8) Quadratic
functions and
equations. The
student applies
the mathematical
process standards
to solve, with and
without
technology,
quadratic
equations and
evaluate the
reasonableness of
their solutions.
The student
formulates
statistical
relationships and
evaluates their
reasonableness
based on realworld data. The
student is
expected to
(A) solve
quadratic
equations
having real
solutions by
factoring,
taking square
roots,
completing
the square,
and applying
the quadratic
Supporting
TEKS/SEs
equations and
evaluate the
reasonableness
of their solutions.
The student
formulates
statistical
relationships and
evaluates their
reasonableness
based on realworld data. The
student is
expected to
(B) write,
using
technology,
quadratic
functions
that provide
a reasonable
fit to data to
estimate
solutions and
make
predictions
for realworld
problems.
Standard Clarification
Questions
quadratic equation that best fits the model.
13. Students can evaluate quadratic regression
equation to make predictions.
14. Students will use the value of r squared to
determine if a prediction can be reasonable and
if model fits quadratic regression.
13.
Explain when is best to use
graphs/tables, square roots,
factoring, completing the square or
quadratic formula to solve a
quadratic equation.
(A.11) Number
and algebraic
methods. The
student applies
the mathematical
process standards
and algebraic
36
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
formula; and
Supporting
TEKS/SEs
Standard Clarification
Questions
methods to
rewrite algebraic
expressions into
equivalent forms.
The student is
expected to
(A) simplify
numerical
radical
expressions
involving
square roots;
and
37
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Fourth Nine Weeks Scope and Sequence
April 15 – April 22, 2016 Exponential Functions and other non-linear functions
Vocabulary
English
Inverse Variation
Exponential decay
Constant, k
Minimum
x-intercept
Spanish
English
Exponential Function
Growth rate
Asymptote
Domain
y-intercept
Exponential
Regression
Half-life
Spanish
English
Exponential growth
Decay rate
Maximum
Range
Steep
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 10: Exponential Functions
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.9)Exponentia
l functions and
equations. The
student applies
the mathematical
(A.9)Exponentia
l functions and
equations. The
student applies
the mathematical
Standard Clarification
Questions
1. Students will graph exponential functions and can
determine the domain and the range.
2. Will be able to interpret the meaning of a and b in
real-life problems.
Essential:
1. Compare and contrast linear,
quadratic and exponential
functions and/or equations.
38
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
process standards
when using
properties of
exponential
functions and
their related
transformations
to write, graph,
and represent in
multiple ways
exponential
equations and
evaluate, with
and without
technology, the
reasonableness of
their solutions.
The student
formulates
statistical
relationships and
evaluates their
reasonableness
based on realworld data. The
student is
expected to
(C) write
exponential
functions in
the form
f(x) = 𝑎 ∙ 𝑏 𝑥
(where b is
a rational
number) to
describe
problems
process standards
when using
properties of
exponential
functions and
their related
transformations
to write, graph,
and represent in
multiple ways
exponential
equations and
evaluate, with
and without
technology, the
reasonableness of
their solutions.
The student
formulates
statistical
relationships and
evaluates their
reasonableness
based on realworld data. The
student is
expected to
(A) determine
the domain
and range of
exponential
functions of
the form
f(x) = abx
and
represent
the domain
Standard Clarification
3. Will be able to describe the effects of a and b on a
graph. Students will be able to find the asymptote
of graphs and exponential equations.
4. Students will be able to determine if a table of
data is exponential.
5. Students will be able to write and evaluate
equations about exponential growth.
6. Students will be able to write and evaluate
equations about exponential decay.
7. Students will use exponential regression to
determine of real life data can have an
exponential equation.
8. Student will use r squared to determine if data is
exponential or not.
9. Student will also use r squared to determine if the
exponential equation will yield a reasonable
and/or accurate prediction.
10.Student will use the exponential equation to
evaluate and make predictions about the data.
11.Student will use exponential decay to represent
the half-life of substances.
12.Students will be able to determine the number of
half-lives that occur in a given time period.
Questions
Guiding:
1. Describe the effects of b on
the graphs of exponential
graphs.
2. Describe the effects of a on
the graphs of exponential
graphs.
3. Give examples of how to
use exponential equations
In real life situations.
4. Explain how to identify the
asymptotes of exponential
graphs.
5. What is the domain and
range of a exponential
growth graph?
6. How do you find the a and
b given a real life situation?
7. Describe the differences
between the graphs of
exponential growth and
exponential decay.
8. How do you determine the
number half lives that occur
over a period of time?
9. Describe the similarities
and differences between
exponential growth and
exponential decay.
39
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
arising from
mathematic
al and realworld
situations,
including
growth and
decay;
(D) graph
exponential
functions that
model growth
and decay and
identify key
features,
including yintercept and
asymptote, in
mathematical
and real-world
problems; and
Supporting
TEKS/SEs
Standard Clarification
Questions
and range
using
inequalities;
(B) interpret the
meaning of
the values
of a and b in
exponential
functions of
the form
f(x) = abx in
real-world
problems;
(D)write, using
technology,
exponential
functions
that provide
a reasonable
fit to data
and make
predictions
for realworld
problems.
40
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Fourth Nine Weeks Scope and Sequence
May 9 – May 27, 2016 Sequences (Arithmetic and Geometric)
Vocabulary
English
Arithmetic sequence
Common difference
Spanish
English
Sequence
Common ratio
Spanish
English
Geometric sequence
Recursive formula
Spanish
Integrated Process Skills:
(A.1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to
(A) apply mathematics to problems arising in everyday life, society, and the workplace;
(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving process and the reasonableness of the solution;
(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation,
and number sense as appropriate, to solve problems;
(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language
as appropriate;
(E) create and use representations to organize, record, and communicate mathematical ideas;
(F) analyze mathematical relationships to connect and communicate mathematical ideas; and
(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Unit 11: Sequences (Arithmetic and Geometric)
Readiness
Supporting
TEKS/SEs
TEKS/SEs
(A.12) Number
and algebraic
methods. The
student applies
the mathematical
process standards
and algebraic
methods to write,
solve, analyze,
and evaluate
Standard Clarification
1. Students will be able to determine if a table is
an arithmetic or geometric sequence using
common difference and common ratio.
2. Students will be able to write equations for
arithmetic sequences and make the connection
to linear equations.
3. Students will be able to find the nth term of an
Questions
Essential:
1. In your experience, what
makes a pattern true?
2. List some patterns that
model a rule. Will they work
for every integer?
Guiding:
1. Compare and contrast
arithmetic and geometric
41
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
equations,
relations, and
functions. The
student is
expected to
(A) decide
whether
relations
represented
verbally,
tabularly,
graphically,
and
symbolically
define a
function;
(C) identify
terms of
arithmetic
and geometric
sequences
when the
sequences are
given in
function form
using
recursive
processes;
(D) write a
formula for
the nth term
of arithmetic
and geometric
sequences,
given the
value of
several of
Standard Clarification
arithmetic sequence.
4. Students will be able to write equations for a
geometric sequence.
5. Students will able to find the nth term for a
geometric sequence.
6. Students will be able to write a recursive
formula given a sequence.
Questions
2.
3.
4.
5.
6.
7.
8.
sequences.
What is a sequence?
What is a arithmetic
sequence? Give an
example.
What is a geometric
sequence? Give an
example.
What is a common
difference?
What is a common ratio?
What is the difference
between an arithmetic and
geometric sequence?.
How do you write a
recursive formula?
42
Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016
Curriculum Guide – 2015-2016
9th Algebra I Regular
Aldine ISD
Readiness
TEKS/SEs
Supporting
TEKS/SEs
Standard Clarification
Questions
their terms;
and
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Contact:
[Program Director’s name]
[Grade level] Program Director [Subject] @ [PD office number]
[Program Director’s email address]
Curriculum & Instruction
2/6/2016