Download Algebra I CP

Algebra One CP—Scope and Sequence—Year at a Glance
Three Weeks
Topics/Concepts
Algebra 1—First Semester
1st Three
2nd Three
Weeks
Weeks
Foundations
Functions
for Algebra
3rd Three
Weeks
Functions
4th Three
Weeks
Linear
Functions
5th Three
Weeks
Systems of
Equations
6th Three
Week
Systems of
Equations
Linear
Functions
Equations
Resource: Holt
Algebra One
Chapter 1,
Chapter 2
Chapter 2,
Chapter 4
Chapter 4,
Chapter 5
Chapter 5
Chapter 6
Chapter 6
TEKS
8.6B, 8.7A,
8.7B, 8.7D,
8.8A, 8.8B,
8.14A,
8.14C, 8.15A
8.1B, 8.3B,
8.6A, 8.6B,
8.7A, 8.7B,
8.7C, 8.7D,
8.8A, 8.8B,
8.14A
A.1A, A.1B,
A.1C, A.1D,
A.1E, A.2A,
A.2B, A.2D,
A.3A, A.3B,
A.6B, 8.14A,
8.15A
A.7A, A.7B,
A.7C, A.8A,
A.8B, A.8C
TAKS Objectives
EOC Objectives
6, 7, 8, 9, 10
6, 7, 8, 9, 10
1, 2, 3, 10
1, 2, 3
A.1A, A.1B,
A.1C, A.1D,
A.1E, A.2A,
A.2C, A.2D,
A.3B, A.4A,
A.4C, A.5A,
A.5C, A.6A,
A.6B, A.6C,
A.6D, A.6E,
A.6F, A.6G,
8.15A, 8.16A
1, 2, 3, 10
1, 2, 3
A.7A, A.7B,
A.7C, A.8A,
A.8B, A.8C,
8.8A, 8.8B,
8.8C, 8.9A,
8.9B, 8.10A,
8.10B,
8.11A,
8.11B,
8.12A,
8.12C, 8.13B
4, 6, 7, 8, 9
4
Page 1 of 16
Revised 4/28/09
4, 8, 9
4
Three Weeks
Topics/Concepts
Algebra 1—Second Semester
7th Three
8th Three
9th Three
Weeks
Weeks
Weeks
Inequalities
Quadratic
Exponents
Functions
and
Systems of
and
Polynomials
Inequalities
Equations
Resource: Holt
Algebra One
TEKS
Chapter 3,
Chapter 6
A.1C, A.1D,
A.7A, A.7C,
8.16B
TAKS Objectives
EOC Objectives
1, 2, 4, 5, 10
1, 4
11th Three
Weeks
Quadratic
Functions
and
Equations
12th Three
Weeks
Exponential
Functions
Chapter 9
Chapter 7
Chapter 8
Chapter 9
A.1E, A.2A,
A.2B, A.4C,
A.9A, A.9B,
A.9C, A.9D,
A.10A, A.10B
1, 2, 5
1, 2, 5
A.4A, A.4B,
A.11A, 8.16B
A.3A, A.4A,
A.4B, A.11A,
A.11B, A.11C
A.2A, A.9B,
A.9C, A.9D,
A.10A, A.10B
Inverse
Variation
Functions
Chapter 11
Chapter 12
A.1C, A.1D,
A.3B, A.4A,
A.11B, A.11C
2, 5, 10
2, 5
2, 5, 10
2, 5
2, 5
2, 5
1, 2, 5
1, 2, 5
Page 2 of 16
Revised 4/28/09
10th Three
Weeks
Factoring
Polynomials
Algebra I CP
Foundations for Algebra and Equations
Essential Learning Outcomes
TEKS
Topics (not in sequential order)
The learner will:
 simplify integers raised to a
power;
 simplify multi-operation
numerical expressions using
the correct order of
operations;
 compare and order integers in
real-life situations;
 use the correct notation to
compare integers;
 create or match an expression
to an equivalent expression;
 verbalize multi-operation
expressions;
 use appropriate operations to
solve an equation or simplify
an expression to solve a
problem involving integers;
 use symbols (write an
algebraic expression) to
represent situations;
 define what a variable(s)
represents in a problem
situation;
 connect equation notation with
function notation
8.6B
8.7A
8.7B
8.7D
8.8A
8.8B
8.14C
8.15A
8.14C
8.14A
Translate between words and
algebra
Evaluate algebraic expressions
Add real numbers
Subtract real numbers
Multiply real numbers
Divide real numbers
Evaluate expressions containing
exponents
Evaluate expressions containing
square roots
Classify numbers within the real
number system
Use the order of operations to
simplify expressions
Use Commutative, Associative and
Distributive properties to symplify
expressions
Combine like terms
Graph ordered pairs in the
coordinate plane
Graph functions from ordered pairs
Page 3 of 16
Revised 4/28/09
Approximate Time: 3 weeks (1st Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook – Chapter 1 Summative
TAKS:
Assessments
6
7
Formative
8
Assessments
9
10
Algebra I CP
Functions
Essential Learning Outcomes
The learner will:
 solve one- and two-step
equations;
 write an expression to
represent a problem situation;
 when given an equation in a
problem situation, substitute
the appropriate value(s) in
order to solve the problem;
 justify solution to one- and
two-step equations;
 distinguish between
independent and dependent
quantities;
 complete a table of data from
an equation, a graph, concrete
models, or a given situation;
 identify range when given
domain and a function;
 identify domain when given
range and a function;
 identify an appropriate and
reasonable domain and range
for a given situation;
 identify domain and range of
both a function and a situation
as continuous or discrete;
 formulate a linear equation to
solve a problem;
 use data to determine if a
relation is a function
Revised 4/28/09
TEKS
Topics (not in sequential order)
8.6A
8.6B
8.7A
8.7B
8.7C
8.7D
8.8A
8.8B
8.1B
8.3B
8.14A
A.7B
A.4A
A.6G
A.4A
A.1D
Solve one-step equations in one
variable using addition,
subtraction, multiplication or
division
Solve equations in one variable that
contains more than one operation
Solve equations in one variable that
contain variable terms on both
sides
Solve a formula for a given variable
Solve an equation in two or more
variables for one of the variables
Write and use ratios, rates and unit
rates
Write and solve proportions
Use proportions to solve problems
involving geometric figures
Use proportions and similar figures
to measure objects indirectly
Solve problems involving percents
Use common applications of
percents
Estimate with percents
Find percent increase and decrease
Match simple graphs with situations
Graph a relationship
Identify functions
Find the domain and range of
relations and functions
Identify independent and dependent
variables
Write an equation in function for
given input values
Graph functions given a limited
domain
Graph functions given a domain of
all real numbers
Page 4 of 16
Approximate Time: 3 weeks (2nd Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook – Chapter 2 Summative
TAKS:
Assessments
6
7
Formative
8
Assessments
9
10
Algebra I CP
Functions and Linear Functions
Essential Learning Outcomes
TEKS
The learner will:
 identify the linear parent
function;
 sketch the linear parent
function y = x;
 create ordered pairs that
would fall on the graph of the
line y = x;
 complete a table of data from
a linear equation, a graph,
concrete models, or a given
situation;
 determine the x and y
intercepts of a linear function;
 determine the zeroes of a
linear function;
 verbalize functional
relationships;
 make and/or interpret
decisions, predictions, and
critical judgments from
functional relationships;
 related questions when given
a real-world situation;
 determine if situations are
represented by a linear
function;
 analyze a situation involving
linear functions;
 determine if the solution to a
linear equation is reasonable
in terms of the situation;
 describe the relationship
among quantities;
A.1A
A.1B
A.1C
A.1D
A.1E
A.2A
A.2B
A.2D
A.3A
A.3B
A.6B
8.14B
8.15A
Topics (not in sequential order)
Create and interpret scatter plots
Use trend lines to make predictions
Recognize and extend an arithmetic
sequence
Find a given term of an arithmetic
sequence
Identify linear functions and linear
equations
Graph linear functions that
represents real-world situations
and give their domain and range
Find x- and y-intercepts and
interpret their meanings in realworld situations
Use x- and y-intercepts to graph
lines
Find rates of change and slopes
Relate a constant rate of change to
the slope of a line
Find slope by using the slope
formula
Identify, write, and graph direct
variation
Page 5 of 16
Revised 4/28/09
Approximate Time: 3 weeks (3rd Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook – Chapter 4 Summative
TAKS:
and Chapter 5
Assessments
1
2
Formative
3
Assessments
10
EOC:
1
2
3
Algebra I CP
Functions and Linear Functions
Essential Learning Outcomes
TEKS










Topics (not in sequential order)
create a graph from an
equation, table of data,
concrete models, or a given
situation;
create a graph that fits a given
situation;
interpret a situation in terms
of given information;
create and/or interpret
scatterplots from problem
situations;
sketch a trend line for
scatterplots to make
predictions, decisions, and
critical judgments;
determine if a set of data has
a positive, negative, or no
correlation;
compare and contrast linear
and non-linear situations
based on tables, graphs,
verbal descriptions, scenarios
and equations;
apply vocabulary such as flat
rate, initial fee, rate of
change, service fee, etc. when
given a situation;
create a graph from a linear
equation (by finding ordered
pairs), table of data, concrete
models, or a given situation;
given data having a constant
rate of change, find an
equation for a table of data,
graph, concrete models, or a
given situation;
Page 6 of 16
Revised 4/28/09
Approximate Time: 3 weeks (3rd Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
Algebra I CP
Functions and Linear Functions
Essential Learning Outcomes
TEKS



Topics (not in sequential order)
use accurate trend line and/or
its equation to make
predictions;
determine the slope or the
rate of change given an
ordered pair, a table of values,
a graph, or an equation;
connect proportional change
to direct variation (y = kx)
function
Page 7 of 16
Revised 4/28/09
Approximate Time: 3 weeks (3rd Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
Algebra I CP
Linear Functions
Essential Learning Outcomes
The learner will:
 write the equation of a line;
 translate equations from
standard form to slopeintercept form;
 interpret the meaning of slope
in situations using data,
symbolic representations, or
graphs;
 interpret the meaning of
intercepts (both x and y) in
situations using data, symbolic
representations, or graphs;
 describe and predict the
effects of changes in m and b
on the graph of y = mx + b;
 interpret and/or predict the
effects of changing slope and
y-intercept in applied
situations;
 determine if lines are parallel
 represent a line that is parallel
to a given line;
 write equations of parallel
lines;
 write equation of a line parallel
to a given line through a given
point
TEKS
Topics (not in sequential order)
A.1A
A.1B
A.1C
A.1D
A.1E
A.2A
A.2B
A.2D
A.3A
A.3B
A.6B
8.14B
8.15A
A.2C
A.4A
A.4C
A.5A
A.5C
A.6A
A.6C
A.6D
A.6E
A.6F
A.6G
8.16A
Write a linear equation in slopeintercept form
Graph a line using slope-intercept
form
Graph a line and write a linear
equation using point-slope form
Write a linear equation given two
points
Identify and graph parallel and
perpendicular lines
Write equations to describe lines
parallel or perpendicular to a given
line
Describe how changing slope and yintercept affect the graph of a
linear function
Graph absolute-value functions
Identify characteristics of absolutevalue functions and their graphs
Page 8 of 16
Revised 4/28/09
Approximate Time: 3 Weeks (4th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook – Chapter 4 Summative
TAKS:
and Chapter 5
Assessments
1
2
Formative
3
Assessments
10
EOC:
1
2
3
Algebra I CP
Systems of Equations
Essential Learning Outcomes
The learner will:
• formulate a system of linear
equations (two unknowns)
from a given situation;
• solve two-variable systems of
equations using a variety of
methods;
• determine if an ordered pair is
the solution to a system of
equations
TEKS
Topics (not in sequential order)
A.7A
A.7B
A.7C
A.8A
A.8B
A.8C
Identify solutions of systems of
linear equations into variables
Solve systems of linear equations in
two variables by graphing
Solve systems of linear equations in
two variables by substitution
Solve systems of linear equations in
two variables by elimination
Page 9 of 16
Revised 4/28/09
Approximate Time: 3 Weeks (5th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook - Chapter 6
Summative
TAKS:
(Lessons 6.1 to 6.4)
Assessments
4
8
Formative
9
Assessments
EOC:
4
Algebra I CP
Systems of Equations
Essential Learning Outcomes
The learner will:
 choose an appropriate method
for solving a system of
equations;
 interpret the solution to a
system of equations in terms
of the situation;
 determine the reasonableness
of the solution to a system of
equations in terms of the
situation
TEKS
Topics (not in sequential order)
A.7A
A.7B
A.7C
A.8A
A.8B
A.8C
Compare and choose an appropriate
method for solving systems of
linear equations
Solve special systems of linear
equations in two variables
Classify systems of linear equations
and determine the number of
solutions
Page 10 of 16
Revised 4/28/09
Approximate Time: 3 weeks (6th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook - Chapter 6
Summative
TAKS:
(Lessons 6.1 to 6.4)
Assessments
4
6
Formative
7
Assessments
8
9
EOC:
4
Algebra 1 CP
Inequalities and Systems of Inequalities
Essential Learning Outcomes
TEKS
Topics (not in sequential order)
The learner will:
 formulate inequalities based
on linear functions;
 write a one-variable inequality
to solve an application
problem;
 solve one-variable inequalities
in problem situations;
 graph the solution of a onevariable inequality on a
number line;
 use a variety of methods to
solve a one-variable
inequality;
 analyze an inequality situation
involving linear functions;
 write a two-variable inequality
to solve an application
problem;
 solve two-variable inequalities
in problem situations using a
variety of methods;
 interpret the solution to oneand two-variable inequalities;
 determine the reasonableness
of the solution to linear
inequalities in terms of the
situation
A.1.C
A.1.D
A.2.B
A.3.A
A.4.B
A.7.B
A.7.C
A.8.C
Identify solutions of inequalities with
one variable
Write and graph inequalities with
one variable
Solve inequalities using the
operations of addition, subtraction,
multiplication, and division
Solve compound inequalities in one
variable
Graph solution sets of compound
inequalities in one variable
Graph and solve linear inequalities in
two variables
Graph and solve systems of linear
inequalities in two variables
Page 11 of 16
Revised 4/28/09
Approximate Time: 3 Weeks (7th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
Holt Textbook—Chapter 3
Summative
TAKS:
and Chapter 6, Sections 5
Assessments
Gr. 8
and 6
1
Formative
2
Assessments
6
Gr.9Exit
1
2
4
5
10
EOC:
1
4
Algebra 1 CP
Quadratic Functions and Equations
Essential Learning Outcomes
TEKS
The learner will:
 identify the quadratic parent
function;
 create ordered pairs that
would fall on the graph of
y = x2;
 sketch the quadratic parent
function;
 identify symmetric points on
the graph of y=x2;
 identify the vertex of y=x2;
 identify the axis of symmetry
of y=x2;
 determine the axis of
symmetry, symmetric pairs of
points, and vertex of a
quadratic function
 use a graphing calculator to
verify table of data, equation,
and /or graph
 describe and predict the effect
of changes in a and c on the
graph of y = ax2 + c;
 graph quadratic functions
using transformations;
A.2.A
A.4.A
A.9.A
A.9.B
A.9.D
A.10.B
Topics (not in sequential order)
Identify the quadratic parent
function
Sketch the quadratic parent function
Graph a quadratic function using a
table of values
Identify the vertex, axis of
symmetry, and symmetric points
for a quadratic function
Graph a quadratic function by
finding the vertex, axis of
symmetry and symmetric points
Explore transformations of a
quadratic function
Page 12 of 16
Revised 4/28/09
Approximate Time: 3 Weeks (8th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
Holt Textbook--Chapter 9,
Summative
TAKS:
sections 1-4
Assessments
Gr. 8
4
Formative
6
Assessments
Gr.9Exit
1
2
5
EOC:
1
2
5
Algebra 1 CP
Exponents and Polynomials
Essential Learning Outcomes
The learner will:
 Simplify integers raised to a
power;
 Develop and use the laws of
exponents to simplify
expressions;
 Simplify polynomials;
 Multiply polynomials
TEKS
Topics (not in sequential order)
A.4A,
A.4B,
A.11A,
8.16B
Evaluate expressions containing 0
and integer exponents
Simplify expressions containing 0
and integer exponents
Evaluate and multiply by powers of
10
Convert between standard notation
and scientific notation
Use multiplication properties of
exponents to evaluate and simplify
expressions
Use division properties of exponents
to evaluate and simplify
expressions
Classify polynomials and write
polynomials in standard form
Evaluate polynomial expressions
Add and subtract polynomials
Multiply polynomials
Find special products of binomials
Page 13 of 16
Revised 4/28/09
Approximate time: 3 weeks (9th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook –Chapter 7
Summative
TAKS:
Assessments
2
5
Formative
10
Assessments
EOC:
2
5
Algebra 1 CP
Factoring Polynomials
Essential Learning Outcomes
The learner will:
 factor polynomials using
various methods;
 factor various types of
polynomials;
 verify on the graphing
calculator that the original
polynomial expression is
equivalent to the factored
form of the expression;
 factor polynomials as
appropriate in problem
situations
TEKS
Topics (not in sequential order)
A.3A
A.4A
A.4B
A.11A
A.11B
A.11C
Write the prime factorization of
numbers
Find the GCF of monomials;
Factor polynomials by using the
greatest common factor
Factor quadratic trinomials of the
form x  bx  c
Factor quadratic trinomials of the
2
form ax  bx  c
Factor perfect square trinomials
Factor the difference of two squares
2
Page 14 of 16
Revised 4/28/09
Approximate time: 3 weeks (10th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook –Chapter 8
Summative
TAKS:
Assessments
2
5
Formative
10
Assessments
EOC:
2
5
Algebra I CP
Quadratic Functions and Equations
Essential Learning Outcomes
TEKS
The learner will:
 determine if a set of data is
quadratic;
 solve quadratic equations;
 connect the roots (solutions)
of the equation, the zeroes of
the related function, and the
x-intercepts of the graph of
the function;
 determine the zeroes of a
quadratic function;
 interpret points on the graph
of a quadratic function in a
given situation;
 draw conclusions from the
graph of a quadratic function
in a given situation;
A.2.A
A.9.D
A.10.B
A.9.B
A.9.C
A.10.A
Topics (not in sequential order)
Solve quadratic equations by
graphing
Connect the solutions to a quadratic
equation to the roots of the
equation, the zeroes of the
function, and the x-intercepts of
the function
Solve quadratic equations by
factoring
Solve quadratic equations using
square roots
Solve quadratic equations using
completing the square
Solve quadratic equations using the
quadratic formula
Determine the number of solutions
of a quadratic equation by using
the discriminant
Determine the reasonableness of
solutions to a quadratic function
Page 15 of 16
Revised 4/28/09
Approximate Time: 3 weeks (11th Three Weeks)
Suggested Resources
Assessments
TAKS/
EOC
Obj(s)
HOLT Textbook - Chapter 9, Summative
TAKS:
Sections 5 - 9
Assessments
2
5
Formative
Assessments
EOC:
2
5
Algebra I CP
Exponential Functions and Inverse Variation Functions
Approximate Time: 3 weeks (12th Three Weeks)
Essential Learning Outcomes
TEKS
Topics (not in sequential order)
Suggested Resources
Assessments
The learner will:
 apply exponent laws in
problem-solving situations;
 represent situations involving
exponential growth and decay;
 distinguish between a graph
representing exponential
growth and a graph
representing exponential
decay;
 solve exponential growth and
decay application problems;
 represent situations involving
inverse variation;
 solve inverse variation
application problems;
 identify the graph of the
rational function parent:
y 
1
x
TEKS – Recognize and extend geometric
A.3.B,
sequences and find the nth term of
A.4.A,
a geometric sequence
A.1.C, Evaluate exponential functions and
A.1.D,
identify and graph exponential
A.11B,
functions
A.11.C Solve problems involving
exponential growth and decay
Compare linear, quadratic and
exponential models
Determine the type of function and
write an equation to describe it
Identify and graph square-root
functions and their domains and
ranges
Simplify and manipulate radical
expressions
Solve radical equations
Identify, write, and graph inverse
variation problems
Solve inverse variation application
problems
Identify excluded values of rational
functions
Identify and graph the rational
function parent function
Page 16 of 16
Revised 4/28/09
Holt Textbook--Chapter 11
Holt Textbook--Chapter 12
Summative
Assessments
Formative
Assessments
TAKS/
EOC
Obj(s)
TAKS:
1
2
5
EOC:
1
2
5