Download Algebra I Pre-AP

Algebra One Pre-AP Scope and Sequence Year at a Glance
Three Weeks
Topics/Concepts
Algebra 1—First Semester
1st Three
2nd Three
Weeks
Weeks
Foundations
Solving
for Algebra
equations
3rd Three
Weeks
Rates
Ratios
Proportions
4th Three
Weeks
Inequalities
5th Three
Weeks
Introduction
to Functions
6th Three
Weeks
Linear
Functions
Resource: Holt
Algebra One
Chapter 1
Chapter 2.1
to 2.5
Chapter 2.6
to 2.10
Chapter 3
Chapter 4
Chapter 5
TEKS
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1F,1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
5B
2A
2A,2B,2C,2D
2E,2F,2G
5A
12E
12A,12B,12C
12D
3A,3B,3C,3E
4A,4B,4C
STAAR Readiness
Standards
A.3.A,A.3.B
A.3.A
A.4.B
A.4.B
A.3.A
A.1.D,A.1.E
A.1.A,A.1.B
A.1.C
A.3.A
A.4.B
12E
A.1.A,A.1.B
A.1.C,A.1.D
A.1.E
A.2.A,A.2.B,A.2.C
A.2.D
A.2.A,A.2.B
A.3.A,A.3.B
A.3.A,A.3.B
A.4.C
A.5.A,A.5.B
A.5.C
A.5.A,A.5.B
A.6.A,A.6.B
A.6.C,A.6.D
A.6.E,A.6.F
A.6.G
A.7.A,A.7.B
A.7.C
Page 1 of 16
Revised 12/10/2013
Algebra One Pre-AP Scope and Sequence Year at a Glance
Three Weeks
Topics/Concepts
Algebra 1—Second Semester
7th Three
8th Three
9th Three
Weeks
Weeks
Weeks
Systems of
Quadratic
Exponents
Equations
Functions
and
and
Polynomials
Systems of
Equations
Inequalities
10th Three
Weeks
Factoring
Polynomials
11th Three
Weeks
Solving
Quadratic
Functions
and
Equations
12th Three
Weeks
Exponential
Functions
Inverse
Variation
Functions
Resource: Holt
Algebra One
Chapter 6
Chapter 9.1
to 9.4
Chapter 7
Chapter 8
Chapter 9.5
to 9.9
Chapter 11.1
to 11.4
Chapter 12.1
TEKS
1A,1B,1C,1D
1E,1F,1G
1A,1C,1D,1E
1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
1A,1B,1C,1D
1E,1F,1G
2A,2H,2I
6A,6B
10A,10B
10C,10D,10E
10F
7A,7B
11A,11B
3C,3D,3F,3G
3H
7A,7C
8A,8B
12A,12B,12C
12D
12A,12B
10E,10F
5C
STAAR Readiness
Standards
A.3.A
A.5.A,A.5.B
A.5.C
A.1.A,A.1.B
A.1.C,A.1.D
A.4.B
A.3.A
12F
A.1.E
A.11.A
A.4.AA.4.B
A.2.C
A.1.A,A.1.B
A.1.C,A.1.D
A.1.E
A.2.A,A.2.B
A.2.C
A.3.A
A.2.B,A.2.C
A.3.A,A.3.B
A.4.A,A.4.C
A.3.A,A.3.B
A.4.C
A.9.A,A.9.D
A.4.C
A.9.A,A.9.B
A.9.C,A.9.D
A.10.A,A.10.B
A.11.A,A.11.B
A.11.C
A.6.A,A.6.B
A.7.A
A.8.A,A.8.B
A.8.C
Page 2 of 16
Revised 12/10/2013
Algebra I Pre-AP
Foundations for Algebra
Essential Learning Outcomes
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;
TEKS
Objectives (not in sequential
order)
1A
1B
1C
1D
1E
1F
1G
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 12/10/2013
Approximate Time: 3 weeks (1st Three Weeks)
Suggested Resources Assessments STAAR
Readiness
Standards
HOLT Textbook –
Summative
A.3.A
Chapter 1
Assessments
A.3.B
LTF Diagnostics
Formative
Assessments
A.4.B
Algebra I Pre-AP
Solving equations and formulas
Essential Learning Outcomes
TEKS
The learner will:
 Solve one-step equations by
using addition, subtraction,
multiplication, or division
 Solve two-step and multistep
equations
 Solve multistep equations
involving fractions
 Solve Multistep equations with
variables on both sides
 Solve equations with special
solutions
 Solve for variables in formulas
1A
1B
1C
1D
1F
1G
5A
12E
Approximate Time: 3 weeks (2nd Three Weeks)
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Solve one-step equations involving the 4 HOLT Textbook –
Summative
A.3.A
basic operations
Chapter 2.1 to 2.5
Assessments
Solve equations in one variable that
A.4.B
contains more than one operation
LTF Diagnostics
Formative
Solve equations in one variable that
Assessments
contain variable terms on both sides
Solve an equation in two or more
variables for one of the variables
Solve equations that either have infinite
solutions or no real solutions
Solve a formula for a given variable
Page 4 of 16
Revised 12/10/2013
Algebra I Pre-AP
Solving equations : Ratios, Rates, Proportions and Percents
Essential Learning Outcomes
TEKS
Objectives (not in sequential order)
The learner will:
 Write and use ratios, rates,
and unit rates
 Convert rates to other
units
 Write and solve
proportions
 Write and solve percent
problems
 Find percent increase or
decrease over time
1A
1B
1C
1D
1E
1F
1G
Approximate Time: 3 weeks (3rd Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Write and use ratios, rates and unit rates Holt Chapter 2.5 to
Summative
A.3.A
Convert from one rate’s units to another
2.10
Assessments
Write and solve proportions
Use proportions to solve problems
Formative
involving geometric figures
Assessments
Use proportions and similar figures to
measure objects indirectly
Solve problems involving percents
Use common applications of percents
(Find simple interest, commission, tip,
and tax)
Find percent increase and decrease
Page 5 of 16
Revised 12/10/2013
Algebra I Pre-AP
Inequalities
Essential Learning Outcomes
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;
TEKS
1A
1B
1C
1D
1E
1F
1G
5B
Approximate Time: 3 Weeks (4th Three Weeks)
Objectives (not in sequential order) Suggested
Assessment STAAR
Resources
s
Readiness
Standards
Identify solutions of inequalities with
Holt Textbook—
Summative
A.1.D
one variable
Chapter 3
Assessments
A.1.E
Write and graph inequalities with one
variable
LTF Diagnostics
Formative
A.3.A
Solve inequalities using the operations
Assessments
of addition, subtraction, multiplication,
A.4.B
and division
Solve compound inequalities in one
variable
Graph solution sets of compound
inequalities in one variable
Page 6 of 16
Revised 12/10/2013
Algebra I Pre-AP
Introduction to functions
Essential Learning Outcomes
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;
 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;
 create a graph from an
equation, table of data,
concrete models, or a given
situation;
(continued next page)
TEKS
1A
1B
1C
1D
1E
1F
1G
2A
12A
12B
12C
12D
Approximate Time: 3 Weeks (5th Three Weeks)
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Match simple graphs with situations
HOLT Textbook –
Summative
A.1.A
Differentiate between discrete and
Chapter 4
Assessments
A.1.B
continuous graphs
A.1.C
Identify a function
LTF (Algebra I)
Formative
Find the domain and range of a function
-Introduction to
Assessments
A.2.A
Identify independent and dependent
Function Notation
A.2.B
variables
-Connecting a
A.2.C
Write and evaualte a function in function
Verbal Description
A.2.D
notation
to Table and Graph
Graph a function given a limited domain
-Use Tables and
A.3.A
Graph a function given a domain of all
graphs to
A.3.B
real numbers
Determine the
Create and interpret scatter plots
Better Deal
A.4.C
Use trend lines to make predictions
-Connecting Table,
Recognize and extend an arithmetic
Graph, and
A.5.A
sequence
Function Notation
A.5.B
Identify linear functions and linear
-Discrete and
equations
Continuous Data
Graph linear functions that represent
-Rate of Change
real-world situations and give their
-Slope Investigation
domain and range
LTF Diagnostics
Page 7 of 16
Revised 12/10/2013
Algebra I Pre-AP
Introduction to functions
Essential Learning Outcomes








TEKS
Objectives (not in sequential order)
create a gr-aph 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;
create a graph from a linear
equation (by finding ordered
pairs), table of data, concrete
models, or a given situation;
use accurate trend line and/or
its equation to make
predictions;
Page 8 of 16
Revised 12/10/2013
Approximate Time: 3 Weeks (5th Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Algebra I Pre-AP
Linear functions
Essential Learning Outcomes
The learner will:
 Identify linear functions
 Sketch the parent function f(x)
= x (or y = x)
 create a table of data from a
linear equation, a graph,
concrete models, or a situation
 determine and interpret the
zeroes of a linear function
 verbalize functional
relationships
 make and/or interpret
decisions, predictions, and
critical judgments from
functional relationships
 determine and interpret the xand y-intercepts of a linear
function (the zeros)
 Graph a linear function by
using the x- and y-intercepts
 Determine the slope of a line
given ordered pairs, a table of
values, a graph, or an
equation
 Connect proportional change
to direct variation (y=kx)
function
 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;
(continued next page)
TEKS
Objectives (not in sequential order)
1A
1B
1C
1D
1E
1F
1G
Identify linear functions and equations
Give the domain and range of a linear
function
Find x- and y-intercepts of a line and
interpret their meanings
Graph a line using intercepts
Find rates of change (or slopes) given
ordered pairs, table, or the graph
Relate a constant rate of change to the
slope of a line
Find the slope of a line from an equation
Identify, write, and graph direct variation
Write a linear equation in slope-intercept
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
2A
2B
2C
2D
2E
2F
2G
3A
3B
3C
3E
4A
4B
4C
12E
Page 9 of 16
Revised 12/10/2013
Approximate Time: 3 weeks (6th Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
HOLT Textbook –
Summative
A.1.A
Chapter 5
Assessments
A.1.B
A.1.C
LTF (Algebra I)
Formative
A.1.D
- Parallel and
Assessments
A.1.E
Perpendicular
Lines: An
A.2.A
Investigation
A.2.B
- Write the
Equation of a Line:
A.3.A
Review
A.3.B
LTF Diagnostics
A.5.A
A.5.B
A.5.C
A.6.A
A.6.B
A.6.C
A.6.D
A.6.E
A.6.F
A.6.G
A.7.A
A.7.B
A.7.C
Algebra I Pre-AP
Linear functions
Essential Learning Outcomes







TEKS
Objectives (not in sequential order)
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
Page 10 of 16
Revised 12/10/2013
Approximate Time: 3 weeks (6th Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Algebra 1 Pre-AP
Systems of Equations and Inequalities
Essential Learning Outcomes
TEKS
The learner will:
• formulate a system of linear
equations (two unknowns)
from a given situation;
• determine if an ordered pair is
the solution to a system of
equations
 solve two-variable systems of
equations using a variety of
methods;
 choose an appropriate method
for solving a system of
equations;
 interpret the solution to a
system of equations in terms
of the situation;
 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 twovariable inequalities;
 determine the reasonableness
of the solution to linear
inequalities in terms of the
situation
1A
1B
1C
1D
1E
1F
1G
2A
2H
2I
3C
3D
3F
3G
3H
5C
Approximate Time: 3 Weeks (7th Three Weeks)
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Identify solutions of systems of linear
Holt Textbook—
Summative
A.3.A
equations in two variables
Chapter 6
Assessments
Solve systems of linear equations in two
A.5.A
variables by graphing
Formative
A.5.B
Solve systems of linear equations in two
Assessments
A.5.C
variables by the substitution method
LTF (Algebra I)
Solve systems of linear equations in two
-Find Area and
A.6.A
variables by the elimination method
Writing Equations
A.6.B
Compare and choose an appropriate
for Bounded
method for solving systems of linear
Regions
A.7.A
equations
-Painting the House
Solve special systems of linear equations -Solving Systems of
A.8.A
in two variables (that may have infinite Linear Equations
A.8.B
solutions or no real solutions)
-Graphing and
A.8.C
Classify systems of linear equations and
Finding Areas of
determine the number of solutions
Bounded Areas
Graph and solve linear inequalities in two
variables
LTF Diagnostics
Graph and solve systems of linear
inequalities in two variables
Page 11 of 16
Revised 12/10/2013
Algebra 1 Pre-AP
Introduction to Quadratic Functions and Equations
Essential Learning Outcomes
TEKS
Objectives (not in sequential order)
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;
1A
1C
1D
1E
1G
6A
6B
7A
7c
12A
12B
Approximate Time: 3 Weeks (8th Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Identify the quadratic parent function
Holt Textbook-Summative
A.1.A
Sketch the quadratic parent function
Chapter 9, sections
Assessments
A.1.B
Graph a quadratic function using a table
1-4
A.1.C
of values
Formative
A.1.D
Identify the vertex, axis of symmetry,
LTF
Assessments
and symmetric points for a quadratic
Investigation
A.2.A
function
Graphing Quadratic
A.2.B
Graph a quadratic function by finding the Functions
A.2.C
vertex, axis of symmetry and
symmetric points
Quadratic
A.3.A
Explore transformations of a quadratic
Optimization
A.3.B
function
Graphing Quadratic
A.4.C
Functions
A.9.A
LTF Diagnostics
A.9.B
A.9.C
A.9.D
Page 12 of 16
Revised 12/10/2013
Algebra 1 Pre-AP
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
Objectives (not in sequential order)
1A
1B
1C
1D
1E
1F
1G
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
10A
10B
Page 13 of 16
Revised 12/10/2013
Approximate time: 3 weeks (9th Three Weeks)
Suggested
Assessments STAAR
Resources
Readiness
Standards
HOLT Textbook –
Summative
A.4.B
Chapter 7
Assessments
A.11.A
LTF Lessons and
Formative
Diagnostics
Assessments
LTF Diagnostics
Algebra 1 Pre-AP
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
1A
1B
1C
1D
1E
1F
1G
10C
10D
10E
10F
Approximate time: 3 weeks (10th Three Weeks)
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
Write the prime factorization of numbers
HOLT Textbook –
Summative
A.3.A
Find the GCF of monomials;
Chapter 8
Assessments
Factor polynomials by using the greatest
A.4.A
common factor
LTF Lessons and
Formative
A.4.B
Factor quadratic trinomials of the form
Diagnostics
Assessments
x 2  bx  c
Factor quadratic trinomials of the form
ax  bx  c
2
Factor perfect square trinomials
Factor the difference of two squares
Page 14 of 16
Revised 12/10/2013
LTF Diagnostics
Algebra I Pre-AP
Solving Quadratic Functions and Equations
Approximate Time: 3 weeks (11th Three Weeks)
Essential Learning Outcomes
TEKS
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
The learner will:
1A
Solve quadratic equations by graphing
HOLT Textbook Summative
A.1.E
 determine if a set of data is
1B
Connect the solutions to a quadratic
Chapter 9, Sections Assessments
quadratic;
1C
equation to the roots of the equation,
5-9
A.2.C
 solve quadratic equations;
1D
the zeroes of the function, and the xFormative
 connect the roots (solutions)
1E
intercepts of the function
LTF Diagnostics
Assessments
A.3.A
of the equation, the zeroes of
1F
Solve quadratic equations by factoring
the related function, and the
1G
Solve quadratic equations using square
A.4.A
x-intercepts of the graph of
roots
A.4.C
the function;
7A
Solve quadratic equations using
 determine the zeroes of a
7B
completing the square
A.9.A
quadratic function;
Solve quadratic equations using the
A.9.D
 interpret points on the graph
8A
quadratic formula
of a quadratic function in a
8B
Determine the number of solutions of a
A.10.A
given situation;
quadratic equation by using the
A.10.B
 draw conclusions from the
10E
discriminant
graph of a quadratic function
10F
Determine the reasonableness of
in a given situation;
solutions to a quadratic function
12F
Page 15 of 16
Revised 12/10/2013
Algebra I Pre-AP
Exponential Functions and Inverse Variation Functions
Approximate Time: 3 weeks (12th Three Weeks)
Essential Learning Outcomes
TEKS
Objectives (not in sequential order)
Suggested
Assessments STAAR
Resources
Readiness
Standards
The learner will:
1A
Recognize and extend geometric
Holt Textbook-Summative
A.1.A
 apply exponent laws in
1B
sequences and find the nth term of a
Chapter 11.1 to
Assessments
A.1.B
problem-solving situations;
1C
geometric sequence
11.4
A.1.C
 represent situations involving
1D
Evaluate exponential functions and
Holt Textbook-Formative
A.1.D
exponential growth and decay; 1E
identify and graph exponential
Chapter 12.1
Assessments
A.1.E
 distinguish between a graph
1F
functions
representing exponential
1G
Solve problems involving exponential
LTF Diagnostics
A.2.B
growth and a graph
growth and decay
A.2.C
representing exponential
11A
Compare linear, quadratic and
decay;
11B
exponential models
A.3.A
 solve exponential growth and
Determine the type of function and write
A.3.B
decay application problems;
12A
an equation to describe it
 represent situations involving
12B
Identify and graph square-root functions
A.4.C
inverse variation;
12C
and their domains and ranges
 solve inverse variation
12D
Simplify and manipulate radical
A.11.A
application problems;
expressions
A.11.B
 identify the graph of the
Solve radical equations
A.11.C
rational function parent:
Identify, write, and graph inverse
variation problems
1
y 
Solve inverse variation application
x
problems
Identify excluded values of rational
functions
Identify and graph the rational function
parent function
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Revised 12/10/2013