# Algebra I TIA Pacing Guide by tyndale

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```									   Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                        Objective                                 Task Analysis                      Vocabulary                           21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                       *teacher word

1st Nineweeks
1. Enduring Understanding - Statistics are used to make inferences and predictions.
1a. Essential Question - How can the results of a statistical investigation be used to support an argument?
DIP.5.AI.6                                    Analyze real life situations by constructing   Prerequisite Skills:                          axis             graphing calculator   Use the internet to find
Construct and interpret a cumulative          and interpreting cumulative frequency          ♦construct histograms                         histograms       district data of      a stock price daily.
frequency histogram in real-life situations   histograms                                     ♦interpret a histogram                        intervals        school age            Use this data to make
students              an ongoing histogram
*construct and interpret a cumulative                                                and cumulative
analyze        real life situations     frequency histogram in real-life situations                                          frequency histogram.

cumulative
construct /
frequency
interpret
histogram

DIP.5.AI.5                                    Analyze real-life situations by constructing   Prerequisite Skills:                       bar graph           graphing calculator Compare the number
Use two or more graphs to compare data        and using scatter plots and line of best fit   ♦interpret various representations of data box-and-whisker     excel program       of Girl Scout cookies
sets                                                                                         sets                                       plots               stock journal       sold over a two-year
Ex.                                                                                                                                     histograms                              span. Compare the
box-and-whisker, histograms, scatter plots                                                   *use two or more graphs to compare data line graph                                 data. Make
two or more           sets                                       scatter plot                            suggestions for the
analyze                                                                            stem-and-leaf                           upcoming year.
graphs
display

compare              data sets

rev. 05-2009                                                                                                                                                                               1 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                       Objective                                 Task Analysis                       Vocabulary                          21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                       *teacher word

DIP.5.AI.11                                   Explain and cite examples as justification    Prerequisite Skills:                           bias             http://mathforum.or
Explain how sampling methods, bias, and       how sampling methods, bias, and phrasing      ♦define biased and unbiased data               conclusions      g/library/view/7884
phrasing of questions in data collection      of questions in data collection impact the    sampling                                       data             .html
impact the conclusions                        conclusions                                   ♦describe methods of data collection           sampling
♦examine misleading graphs and                                  This lesson uses
questions                                                       decision-making
♦use sampling methods                                           ideas from
data collection                                                                         statistics in the
evaluation          impacts                                                                              science classroom.
conclusion             *explain how sampling methods, bias,
Students make
and phrasing of questions in data                               use of sampling to
collection impact the conclusions                               back up a
sampling                                                                              claim, and design
explain        methods, bias                                                                           (with teacher
and phrasing                                                                            assistance) a
statistical
experiment to
study a problem.

DIP.5.AI.1                                    Construct and use scatter plots and line of   Prerequisite Skills:                        axis
Construct and use scatter plots and line of   best fit to make inferences in real-life      ♦graph on a coordinate plane                coordinate
best fit to make inferences in real-life      situations                                    ♦construct scatter plots and draw lines of  system
situations                                                                                  best fit                                    extrapolate
♦write equation of a line in slope-interceptinferences
form                                        interpolate
line of best fit
*construct and use scatter plots and line regression
of best fit                                 scatter plot
*make inferences in real-life situations    x-axis
using the constructed scatter plot and line y-axis
of best fit

rev. 05-2009                                                                                                                                                                            2 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                      Objective                                   Task Analysis                     Vocabulary                           21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                      *teacher word

DIP.5.AI.4                                   Comprehension of measures of central            Prerequisite Skills:                     central              http://www.casioed
Determine the effects of changes in the data tendency by describing the effects of           ♦use mean, median, mode, and range       tendencies           ucation.com/resour
set on the measures of central tendency      changes in data sets                                                                     data                 ce/pdfs/compariso
*determine the effects of changes in the mean                 n/FX-9750
data set on measures of central tendency median
measure of                                                       mode                 Given a set of
comprehension
central tendency                                                   range                data, the students
will be able to
enter it into the
effects of changes                                                                       Statistics Menu of
describe
in data sets                                                                         the
calculator, graph
the data using a
scatter plot, find
the Line of Best Fit
for the scatter
plot, and calculate
the measures of
central tendency.

DIP.5.AI.12                                 Analyze arguments based on data by               *differentiate correlation and causation     causation        data from a crime
Recognize when arguments based on data      recognizing correlation with causation           *recognize when arguments based on           correlation      scene
confuse correlation with causation                                                           data confuse correlation and causation

arguments based
analyze
on data

correlation with
recognize
causation

1b. Essential Question - How can matrices organize and display data?
DIP.5.AI.3                                  Apply real-life situations to construct simple   *compare matrices written literally and in   array            determine number
Construct simple matrices for real-life     matrices                                         context (with labeling)                      matrices         of store sales for a
situations                                                                                   *construct simple matrices for real-life                      product
situations
application      real life situations

construct            matrices

rev. 05-2009                                                                                                                                                                            3 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                       Objective                                Task Analysis                 Vocabulary                 21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                *teacher word

DIP.5.AI.2                                    Apply simple matrices to compute addition,   *use simple matrices in addition,        array
Use simple matrices in addition, subtraction, subtraction, and scalar multiplication       subtraction, and scalar multiplication   matrices
and scalar multiplication                                                                                                           scalar
multiplication

application       simple matrices

compute          on, and scalar
multiplication

rev. 05-2009                                                                                                                                                            4 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                       Objective                              Task Analysis                Vocabulary                        21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                             *teacher word

1c. Essential Question - How is probability used to make decisions?
DIP.5.AI.8                                  Apply simple probability to compute with and Prerequisite Skills:                    chance              dice            Monitoring one's own
Compute simple probability with and without without replacement                          ♦apply concepts of simple probability   probability         cards           understanding and
replacement                                                                                                                      theoretical         spinner         learning.
*compute simple probability with and    probability                         Create a project that
without replacement                     probability without                 demonstrates content
simple                                                    replacement                         knowledge and
application                                                                    probability with                    conceptual
probability
replacement                         understanding in
different content areas.
Demonstrate problem
with and without                                                                                   solving ability and
compute
replacement                                                                                       ability to draw
conclusions.

rev. 05-2009                                                                                                                                                                  5 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                      Objective                                Task Analysis                    Vocabulary                           21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                  *teacher word

1d. Essential Question - How can statistics be used to model, analyze, and communicate real-world applications?
DIP.5.AI.10                                   Comprehend real-world problems by           *identify key information                   units of measure   graphing calculator Ability to identify,
Communicate real-world problems               communicating algebraically, numerically,   *determine the format in which the          unit rates                             analyze, and problem
graphically, algebraically, numerically and   and verbally                                solution should be written                  vocabulary                             solve.
verbally                                                              real-world          *represent and/or solve the situation       specific to                            Apply appropriate
comprehension                            *label solution with appropriate unit(s),   problems                               strategies to solve
problems
when necessary                                                                     problems both
algebraically, nu      *communicate real-world problems                                                   individually and in
communicating                            graphically, algebraically, numerically                                            groups.
merically and
Identify a potential
community issue that
can be analyzed using
a wide range of
mathematical tools
and develop an
analysis plan.

rev. 05-2009                                                                                                                                                                        6 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                          Objective                            Task Analysis                    Vocabulary                     21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                  *teacher word

2. Enduring Understanding - Mathematical rules and representations are used to provide consistency.
2a. Essential Question - Why are mathematical rules necessary?
LA.1.AI.1                                       Apply order of operations by evaluating    Prerequisite Skills:                       additive inverse
Evaluate algebraic expressions, including       algebraic expressions including radicals   ♦apply order of operations                 algebraic
radicals, by applying the order of operations                                                                                         expressions
*recognize an expression, including        algorithms
order of
application                           *substitute values in place of variables   Property
operations
*simplify numerical expressions using the Commutative
order of operations                        Property
algebraic        *evaluate algebraic expressions, including constant
evaluate          expressions
radicals, by applying the order of         difference
operations                                 Distributive
Property
evaluate
integers
irrational numbers
natural numbers
number sense
expressions
rational numbers
whole numbers

2b. Essential Question - How are variables used in algebraic expressions?
LA.1.AI.2.                                    Knowledge of expressions, equations, and     *recognize expressions, equations &        algebraic
Translate word phrases and sentences into inequalities by translating word phrases and     inequalities                               expressions
expressions, equations, and inequalities, and sentences (and vice versa)                   *recognize basic operations as words and   difference
vice versa                                                                                 symbols                                    equations
*translate word phrases and sentences      expressions
expressions, equ       into expressions, equations, and           inequalities
knowledge          ations, and         inequalities, and vice versa
inequalities

word phrases
translating
and sentences

rev. 05-2009                                                                                                                                                                  7 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                         Objective                                Task Analysis                     Vocabulary                   21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                      *teacher word

3. Enduring Understanding - Practical problems can be interpreted, represented, and solved using equations and
inequalities.
3a. Essential Question - How are formulas, equations and inequalities useful in solving practical problems?
SEI.2.AI.1                                      A. Apply algebraic methods to solve multi-   Prerequisite Skills:                         rational numbers
Solve multi-step equations and inequalities step equations with rational coefficients        ♦apply solving one- and two-step             coefficient
with rational coefficients numerically,                                                      equations and check solutions                Distributive
algebraically, graphically, and technologically                                              ♦apply Distributive Property                 Property
(continued below)                                                      algebraic             ♦apply the addition, subtraction,            evaluate
application
method               multiplication, and division properties of   no solution
equality to multi-step equations with        rational numbers
rational coefficients                        coefficient
multi-step
evaluate
equations with
solve                               *solve multi-step equations and                no solution
rational
coefficients         inequalities with rational coefficients        x-y table
numerically, algebraically, graphically,
B. Apply numbers, graphs, and technology to and technologically
solve multi-step equations with rational
coefficients

numbers, graphs
application
and technology

multi-step
equations with
solve
rational
coefficients

rev. 05-2009                                                                                                                                                                    8 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                          Objective                                 Task Analysis                     Vocabulary                    21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                        *teacher word

SEI.2.AI.1                                      C. Apply simple equations to solve multi-step   Prerequisite Skills:                         rational numbers
Solve multi-step equations and inequalities inequalities with rational coefficients             ♦apply the Distributive Property to solve    coefficient
with rational coefficients numerically,                                                         inequalities                                 Distributive
algebraically, graphically, and technologically                                                 ♦solve one- and two-step inequalities,       Property
emphasizing the reversing of the             evaluate
application       simple equations         inequality symbol, and checking solutions    no solution
rational numbers
*solve multi-step inequalities with rational coefficient
multi-step           coefficients numerically, algebraically,     evaluate
inequalities with       graphically, and technologically             no solution
solve                                                                                 x-y table
rational
coefficients

D. Apply numbers and technology to solve
multi-step inequalities with rational
coefficients

numbers and
application
technology

multi-step
inequalities with
solve
rational
coefficients

rev. 05-2009                                                                                                                                                                       9 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                        Objective                              Task Analysis                      Vocabulary                          21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                    *teacher word

SEI.2.AI.4                                    A. Solve and graph simple absolute value    Prerequisite Skills:                          absolute value
Solve and graph simple absolute value         equations                                   ♦recognize absolute value symbol              absolute value
equations and inequalities                    B. Solve and graph simple absolute value    ♦find absolute value                          equation
Ex.                                           inequalities                                                                              absolute value
|x| = 5, |x| ≤5, |x| > 5                                                                  *analyze an absolute value equation to        absolute value
determine if it has no solution, one          inequality
solution, or two solutions
application       simple equations     *solve simple absolute value equations
*graph solutions on a number line

absolute value
solve and graph
equations

SEI.2.AI.8                                    Apply real-world problem solving by         *identify key information in a real-world     vocabulary       graphing calculator
Communicate real-world problems               communicating graphically, algebraically,   problem                                       specific to      graph paper
graphically, algebraically, numerically and   numerically, and verbally                   *determine the format (graphically,           problem given
verbally                                                                                  algebraically, numerically, or verbally) to
represent the problem and its solution
*evaluate the reasonableness of the
real-world        solution
apply                               *communicate real-world problems
problem solving
graphically, algebraically, numerically or
verbally
graphically, algebr
communicating      aically, numericall
y, and verbally

rev. 05-2009                                                                                                                                                                        10 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                         Objective                                   Task Analysis                 Vocabulary                              21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                     *teacher word

SEI.2.AI.3                                      Apply the linear form of a lateral equation to   Prerequisite Skills:                    linear formulas     http://www.knowle
Solve linear formulas and literal equations for solve for a specified variable                   ♦apply steps for solving an equation    literal equations   dge.state.va.us/cgi-
a specified variable                                                                                                                     variable            bin/lesview.cgi?idl
Ex.                                                                                              *recognize a literal equation                               =238
solve for p in I = prt                                                  linear form of a         *solve for a specified variable
application
lateral equation         *demonstrate multiple versions of the
result if necessary                                         The purpose of
this activity is to
integrate Earth
solve         specified variable                                                                    Science with
Algebra I in a
activity that will
incorporate the
use of a computer
to research
information of
each planet, use
calculations to
help understand
why we need to
know how to use
very large
numbers, and how
to graph those
numbers.

rev. 05-2009                                                                                                                                                                             11 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                      Objective                                Task Analysis                    Vocabulary                              21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                  *teacher word

2nd Nineweeks
1. Enduring Understanding - Functions are relationships that can be determined by their unique characteristics.
1a. Essential Question - What are the characteristics of a function?
LF.3.AI.1                                   Comprehend function and non-function          Prerequisite Skills:                        domain
Distinguish between functions and non-      relationships by inspecting graphs, ordered   ♦identify the domain of relations           functions
functions/relations by inspecting graphs,   pairs, mapping diagrams and/or tables of                                                  graph of a
ordered pairs, mapping diagrams and/or      data                                          *apply the vertical line test               function
tables of data                                                                            *express relations as tables, mapping       mapping diagram
diagrams, ordered pairs, and graphs         ordered pair
function and non-      *distinguish between functions and non-     range
comprehension           function          functions/relations by inspecting graphs,   relations
relationships
ordered pairs, mapping diagrams and/or      table
tables of data                              vertical line test
graphs, ordered
pairs, mapping
inspecting
diagrams and/or
tables of data

LF.3.AI.2                                    Knowledge of algebraic expressions, graphs, Prerequisite Skills:                         coordinate           http://alex.state.al. Develop and
Determine domain and range of a relation     sets of ordered pairs by identifying domain ♦identify x- and y-coordinate of ordered     domain               us/lesson_view.ph communicate ideas to
from an algebraic expression, graphs, set of and range                                   pairs                                        ordered pair         p?id=5104             others.
ordered pairs, or table of data                                                                                                       range                                      Use graphing
*identify domain and range of a relation     x-coordinate                               calculators and probes
algebraic                                                                           This lesson is a
expressions, grap    from algebraic expressions, graphs, sets     y-coordinate                               to collect and analyze
knowledge                                                                                                technology-based
hs, sets of      of ordered pairs, or tables of data                                                     environmental data or
activity in which
ordered pairs                                                                         students extend      contextual data.
graphing of linear
functions to the
use of
software.

rev. 05-2009                                                                                                                                                                           12 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                         Objective                                Task Analysis                   Vocabulary                    21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                    *teacher word

LF.3.AI.3                                      Apply function notation to evaluate given     Prerequisite Skills:                       domain
Know and/or use function notation, including values in a domain                              ♦substitute for values for a variable      evaluate
evaluating functions for given values in their                                               ♦simplify expressions using the order of   function notation
domain                                                                                       operations                                 substitution
functions
application
notations          *evaluate functions for given values in
their domain
*know and/or use function notation,
given values in a      including evaluating functions for given
evaluating
domain             values in their domain

2. Enduring Understanding - Functions and their representations are used to model and analyze real-world applications
and quantitative relationships.
2a. Essential Question - How are patterns of change represented in functions?
LF.3.AI.4                                     Knowledge of independent and dependent         Prerequisite Skills:                       dependent
Identify independent variables and            variables to identify words, symbols, and/or   ♦use variables, literally and in context   variable
dependent variables in various                graphs                                         ♦identify independent and dependent        independent
representational modes: words, symbols,                                                      variables                                  variable
and/or graphs                                                                                                                           variable
*identify independent and dependent
independent and        variables in various representational
knowledge            dependent           modes: words, symbols, and/or graphs
variables

words, symbols
identify
and/or graphs

rev. 05-2009                                                                                                                                                                  13 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                         Objective                                    Task Analysis                       Vocabulary                              21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                            *teacher word

LF.3.AI.6                                       Apply two points, graph of a line, the           Prerequisite Skills:                           line                 http://www.okea.or
Calculate the slope given                       equation of a line to calculate the slope of a   ♦apply slope formula and determine             coordinate point     g/otimms/lessonpl
•two points                                     line                                             coordinate points                              slope                ans/enid/Alg1Enid
•the graph of a line                                                                             ♦apply slope as a ratio of change in y         slope-intercept      LessonWatchOutF
•the equation of a line                                                                          (rise) over a change in x (run)                form                 orTheStairs.pdf
two points, graph          ♦recognize when a ratio is undefined
apply           of a line, the           ♦recognize and write slope-intercept form
equation of a line         of a line
The students
must prepare a
*calculate slope using two points, the                               written and oral
graph of a line, and the equation of a line                          presentation
calculate         slope of a line                                                                               stating if the
stairs in their
building are safe
according to the
research
provided.

LF.3.AI.7                                       Comprehend parallel, perpendicular or            Prerequisite Skills:                           opposite                                  Acting responsibly with
Determine by using slope whether a pair of      neither lines by describing slope                ♦recognize pairs of fractions as opposite      parallel line                             the interests of the
lines are parallel, perpendicular, or neither                                                    reciprocals                                    perpendicular line                        larger community in
♦recognize/calculate the slope of a line       reciprocal                                mind demonstrating
parallel, perpendi         ♦describe a pair of lines as being parallel,   slope                                     ethical behavior in
comprehension
cular or neither          perpendicular, or neither                      slope-intercept                           personal, community,
form                                      workplace.
*determine by using slope whether a pair                                                 Identify a community
of lines are parallel, perpendicular or                                                  issue that can be
describe         slope of a line           neither                                                                                  analyzed using a wide
range of tools.

rev. 05-2009                                                                                                                                                                                     14 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                         Objective                               Task Analysis                    Vocabulary                     21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                    *teacher word

LF.3.AI.8                                      Apply linear equations to represent slope    Prerequisite Skills:                        literal equation                 Ability to identify,
Write an equation in slope-intercept, point-   intercept, point-slope, and standard form:   ♦use slope-intercept, point-slope, and      point-slope form                 analyze and solve
slope, and standard forms given                •two points                                  standard forms of a line, and apply their   slope                            problems.
•two points                                    •a point and y-intercept                     associated formulas                         slope-intercept                  Apply a strategy to
•a point and y-intercept                       •x-intercept and y-intercept                 ♦solve literal equations for a given        form                             solve problems in
•x-intercept and y-intercept                   •a point and slope                           variable                                    standard form                    groups.
•a point and slope                             •a table of data                             ♦substitute for a given variable            x-intercept                      Use physical and
•a table of data                               •the graph of a line                                                                     y-intercept                      digital models to
•the graph of a line                                                                        *write an equation of a line in slope-                                       demonstrate concepts.
intercept form, point-slope form, and                                        Use presentation
standard form                                                                software to present
findings.
application        linear equations

slope-
intercept, point-
represented
slope and
standard form

LA.1.AI.7                                  Knowledge of expressions to recognize            *determine that dividing by zero is         undefined          The purpose
Recognize when an expression is undefined undefined values                                  undefined                                   expression
*recognize when an expression is
undefined
knowledge          expression

recognize        undefined values

rev. 05-2009                                                                                                                                                                   15 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                            Objective                                  Task Analysis                        Vocabulary                             21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                              *teacher word

LF.3.AI.5                                        Interpret the rate of change/slope and           Prerequisite Skills:                            slope
Interpret the rate of change/slope and           intercepts within the context of everyday life   ♦identify and find slope, x-intercept, and y-   slope as a rate of
intercepts within the context of everyday life   Ex.                                              intercept                                       change
Ex.                                              telephone charges based on base rate (y-         ♦apply slope-intercept form                     slope-intercept
telephone charges based on base rate (y-         intercept) plus rate per minute (slope)          ♦calculate the rate of change                   form
intercept) plus rate per minute (slope)                                                                                                           x-intercept
*interpret the rate of change                   y-intercept
*interpret the intercepts
slope (rate of           *interpret the rate of change/slope and
analyze
change)               intercepts within the context of everyday
life
everyday
interpreting
situation

2b. Essential Question - Why are linear functions useful?
DIP.5.AI.1                                       Apply inferences in real-life situations to      Prerequisite Skills:                            axis                 graphing calculator Accessing and
Construct and use scatter plots and line of      construct and use scatter plots and line of      ♦graph on a coordinate plane                    coordinate           cell phone bill with managing information.
best fit to make inferences in real-life         best fit                                         ♦construct scatter plots and draw lines of      system               minutes used         Integrating and
situations                                                                                        best fit                                        extrapolate                               creating information.
♦write equation of a line in slope-intercept    inferences                                Evaluating and
form                                            interpolate                               analyzing information.
line of best fit                          Find and analyze data
inferences in real        *construct and use scatter plots and line       regression                                sets and collection
application
life situations                                                         scatter plot                              processes with respect
of best fit
*make inferences in real-life situations        x-axis                                    to the authenticity of
using scatter plots and line of best fit        y-axis                                    the data.
scatter plots
construct and use       and line of
best fit

rev. 05-2009                                                                                                                                                                                      16 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                     Objective                               Task Analysis                Vocabulary                          21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                            *teacher word

DIP.5.AI.11                                Explain and cite examples as justification    Prerequisite Skills:                   bias             http://mathforum.or
Explain how sampling methods, bias, and    how sampling methods, bias, and phrasing      ♦define biased and unbiased data       conclusions      g/library/view/7884
phrasing of questions in data collection   of questions in data collection impact the    sampling                               data             .html
impact the conclusions                     conclusions                                   ♦describe methods of data collection   sampling
This lesson uses
Focus on scatter plots and line of best fit   questions
decision-making
♦use sampling methods                                   ideas from
data collection                                                                statistics in the
*explain how sampling methods, bias,                    science classroom.
evaluation          impacts
conclusion            and phrasing of questions in data                        Students make
collection impact the conclusions                       use of sampling to
back up a
sampling                                                                    claim, and design
explain          methods, bias                                                                 (with teacher
and phrasing                                                                  assistance) a
statistical
experiment to
study a problem.

rev. 05-2009                                                                                                                                                                 17 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                       Objective                                 Task Analysis                     Vocabulary                          21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                     *teacher word

New Application: DIP.5.AI.10                  Communicate real-world problems               *identify key information                    units of measure   graph calculator   Exercise personal
Communicate real-world problems               graphically, algebraically, numerically and   *determine the format in which the           unit rates         graph paper        responsibility and
graphically, algebraically, numerically and   verbally                                      solution should be written                   vocabulary                            flexibility in various
verbally                                                                                    *represent and/or solve the situation        specific to                           contexts.
Focus on scatter plots and line of best fit   *label solution with appropriate unit(s),    problems                              Setting and meeting
when necessary                                                                     high standards and
*communicate real-world problems                                                   goals for one's self and
graphically, algebraically, numerically                                            others.
real-world                                                                                             Use the internet to
synthesis
problems
present findings that
can be shared with
other schools that
graphically, algebr
communicating                                                                                                                 focus on real-world
aically, numericall
y and verbally                                                                                           demonstrations.

2c. Essential Question - What makes a relationship linear?
DIP.5.AI.7                                    Knowledge of tables and graphs to recognize Prerequisite Skills:                           linear function
Recognize linear functions and non-linear     linear functions                            ♦identify linear functions and non-linear      x-y table
functions by using a table or a graph                                                     functions

tables and           *recognize linear functions and non-linear
knowledge
graphs             functions by using a table or a graph

recognize        linear functions

rev. 05-2009                                                                                                                                                                          18 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                          Objective                                 Task Analysis                      Vocabulary                     21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                         *teacher word

3. Enduring Understanding - Algebra is a tool for describing and representing patterns and relationships.
3a. Essential Question - How are patterns of change represented in functions?
LF.3.AI.9                                       Comprehend graphs of linear functions by       Prerequisite Skills:                          horizontal shift
Describe the effects of parameter changes,      describing effects of parameter changes,       ♦graph lines                                  linear functions
slope and/or y-intercept, on graphs of linear   slopes and y-intercepts (and vice versa)       ♦apply slope-intercept form of a line         parameter
functions and vice versa                                                                                                                     change
*describe the effects of parameter            slope
changes, slope and/or y-intercept, on         vertical shift
graphs of linear functions and vice versa     y-intercept
graph of linear
comprehension
function

effects of
parameter
describing
changes, slope
and y-intercepts

DIP.5.AI.9                                      Knowledge of linear functions be recognizing *identify explicitly defined linear functions   consecutive
Recognize patterns using explicitly defined     explicitly defined and recursively defined   *identify recursively defined linear            explicitly defined
and recursively defined linear functions        patterns                                     functions                                       functions
*recognize patterns using explicitly            patterns
defined and recursively defined linear          recursively
knowledge         linear functions     functions                                       defined functions

explicitly defined
recognize        and recursively
defined patterns

rev. 05-2009                                                                                                                                                                        19 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                        Objective                                 Task Analysis                        Vocabulary                           21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                         *teacher word

3b. Essential Question - How is proportional reasoning used to solve problems?
SEI.2.AI.6                                     A. Apply rates of change to model problems    *identify a direct variation equation           constant
Solve problems involving direct variation and involving indirect or direct variation         *solve problems involving direct variation      direct variation
indirect (inverse) variation to model rates of                                               algebraically or graphically                    constant
change                                                                                       *explain how one variable affects the           indirect (inverse)
other variable, if applicable                   variation
application        rates of change        *identify an indirect variation equation
*solve problems involving indirect
variation and indirect (inverse) variation to
problems            model rates of change
model           involving indirect
or direct variation

B. Apply rates of change to solve indirect or
direct variation

application        rates of change

indirect or direct
solve
variation

SEI.2.AI.5                                   Apply real-world problems to solve rates,       Prerequisites Skills:                           percent              newspaper
Solve real-world problems that involve a     proportions and percents                        ♦apply rates, proportions, and percents         proportion           maps
combination of rates, proportions and                                                        ♦write equations to represent real-world        rates                credit card rate
percents                                                                                     problems                                        ratio                sheet
♦solve equations for specified information      scale
♦assess reasonableness of a solution
♦label solution with appropriate unit(s)
real world
application
problems             *solve real-world problems that involve
rates, proportions and percents

rates proportions
solve
and percents

rev. 05-2009                                                                                                                                                                              20 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                    Objective                                  Task Analysis                      Vocabulary                    21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                    *teacher word

3rd Nineweeks
1. Enduring Understanding - Linear functions are used to model and analyze real-world applications.
1a. Essential Question: How are systems of equations and their solutions used to represent real-world situations?

SEI.2.AI.2                                A. Application of systems of two linear          Prerequisite Skills:                         simultaneous
Solve systems of two linear equations     equations by solving numerically, graphically,   ♦graph lines                                 (systems of)
•numerically (from a table or guess and   and technologically                              ♦find points of intersection                 equations
check)                                    B. Application of systems of two linear          ♦create and complete a function table        substitution
•algebraically (including the use of      equations by solving algebraically by the                                                     method
manipulatives)                            substitution method                              *graph, with and without appropriate         standard form of
•graphically                              C. Application of systems of two linear          technology, two linear equations on one      a linear equation
•technologically                          equations by solving algebraically by the        set of coordinate axes                       elimination
elimination method                               *determine if a system of two linear         method
equations has one solution (intersecting
lines), no solution (parallel lines), or
infinitely many solutions (same line) and
give solution(s)
systems of two           *choose one equation and solve for a
application
linear equations          variable, in terms of the other variable
*use substitution method to solve for both
variables
*write solution in the proper form
numerically, graph         *write equation in standard form
ically, technologic        *use the elimination method to solve for
solving             ally, using           both variables
substitution and          *write solution in proper form
elimination            *solve systems of two linear equations
•numerically (from a table or guess and
check)
•algebraically (including the use of
manipulatives)
•graphically
•technologically

rev. 05-2009                                                                                                                                                                  21 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                          Objective                                  Task Analysis                        Vocabulary                      21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                            *teacher word

2. Enduring Understanding - Equivalent forms of algebraic expressions provide different information for solving problems.

2a. Essential Question - How are equivalent forms of expressions involving exponents found?
LA.1.AI.3                                       Comprehend laws of exponents and roots by Prerequisite Skills:                                  exponents
Apply the laws of (integral) exponents and      simplifying expressions                   ♦apply order of operations                            powers
*recognize exponents and roots                  radical expression
laws of exponents          *practice laws of exponents and roots           radicand
comprehension
and roots
individually
*simplify multi-step expressions using the
laws of exponents and roots
simplifying         expressions            *apply the expression

LA.1.AI.4                                       Comprehend scientific notation by               Prerequisite Skills:                            scientific notation
Solve problems involving scientific notation,   simplifying using multiplication and division   ♦distinguish between scientific notation
including multiplication and division                                                           and standard form
♦translate standard form into scientific
notation, and vice versa
comprehension       scientific notation
*explain uses of scientific notation in real-
world applications
multiplication and
simplifying
division

rev. 05-2009                                                                                                                                                                            22 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                          Objective                                 Task Analysis                     Vocabulary                 21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                        *teacher word

2b. Essential Question - How are equivalent forms of polynomials found?
LA.1.AI.5                                       Comprehend polynomial expressions by           Prerequisite Skills                          algorithm
Perform polynomial operations (addition,        simplifying addition, subtraction,             ♦apply order of operations, laws of          coefficient
subtraction, multiplication) with and without   multiplication and division with manipulatives exponents and like terms                     polynomial
manipulatives                                                                                                                               term
*simplify polynomial expressions with
subtraction, multiplication (individually)
polynomial
comprehension
expressions

on, multiplication,
simplifying
division with
manipulatives

rev. 05-2009                                                                                                                                                                   23 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                  Objective                                Task Analysis                    Vocabulary                            21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                              *teacher word

NLF.4.AI.1                              Apply the factoring strategy to solve          Prerequisite Skills:                       binomials          http://www.learner.
Factoring polynomials:                  polynomials and trinomials in the form ax² +   ♦apply concepts of greatest common         difference of      org/channel/works
•greatest common factor                 bx + c using greatest common factor,           factor, Distributive Property, and prime   squares            hops/algebra/work
•binomials (difference of squares)      difference of squares, and grouping            factorization                              factor             shop5/lessonplan1
•trinomials                                                                            ♦perform polynomial operations to check    factoring          c.html
factor (GCF)       The questions on
this site dealing
*identify special cases                    monomial
with factoring
application         factoring             Ex.                                        perfect square     polynomials have
difference of two squares and perfect      trinomials         been selected
square trinomials                          prime              from various state
factorization      and national
solving          polynomials                                                       standard form of   assessments.
a polynomial       Although the
trinomials         lesson may not
fully equip
students to
test questions
successfully, stud
ents who
participate in
active lessons like
this one will
eventually develop
the conceptual
understanding
needed to
succeed on these
and other state
assessment
questions.

rev. 05-2009                                                                                                                                                                    24 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                      Objective                              Task Analysis                     Vocabulary                     21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                 *teacher word

2c. Essential Question - How are algebraic fractions simplified?
LA.1.AI.6                                   Comprehend factoring by simplifying         Prerequisite Skills:                         algebraic fraction
Simplify algebraic fractions by factoring   algebraic fractions                         ♦simplify fractions                          coefficient
factor
*factor polynomials                          factoring
comprehension           factoring        *recognize when an expression is
undefined
*simplify algebraic fractions by factoring

simplifying      algebraic fractions

2d. Essential Question - When is an algebraic fraction undefined?
LA.1.AI.7                                 Knowledge of expressions by recognizing an *determine that dividing by zero is       undefined
Recognize when an expression is undefined undefined expression                       undefined                                 expression
*factor polynomials in the denominator to
find values where the denominator equals
knowledge         expression          0
*recognize when an expression is
undefined

recognize           undefined

3. Enduring Understanding - Radical expressions are useful in solving problems.
3a. Essential Question - How are radical operations performed?
LA.1.AI.8                                   Comprehend algebraic expressions by         Prerequisite Skills:                         radical
divided by the square root of 7                                                                                                      radicand
*simplify basic square roots (Ex. the
algebraic         square root of 24)
comprehension                            *rationalize the denominator (Ex. 3
expressions
divided by the square root of 7)
simplifying
expressions

rev. 05-2009                                                                                                                                                                25 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                        Objective                                Task Analysis                      Vocabulary                      21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                      *teacher word

LA.1.AI.9                                    Comprehend basic radical expressions by        Prerequisite Skills:                          number theory
*perform operations with simplified           radical expression
basic radical        *perform operations with non-simplified
comprehension
expressions
simplify             on, and
multiplications

3b. Essential Question - How are radicals used in coordinate geometry?
SEI.2.AI.7                                  Apply coordinate geometry to represent and *apply Pythagorean Theorem formula                 coordinate                        Use logical reasoning
Use coordinate geometry to represent and/or solve for missing segments using           *use coordinate geometry to represent              geometry                          skills.
solve problems (midpoint, length of a line  Pythagorean Theorem                        and/or solve problems                              distance between                  Skillful in using various
segment, and Pythagorean Theorem)                                                                                                         two points                        problem-solving
Focus only on Pythagorean theorem                                                             Pythagorean                       strategies.
Theorem                           Formulate, approach,
and solve problems
coordinate                                                                                          beyond those studied
application                                                                                                              using a variety of tools
geometry
such as the graphing
calculator and
geometry software.
represent and         Pythagorean
solve              Theorem

rev. 05-2009                                                                                                                                                                        26 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                           Objective                               Task Analysis                    Vocabulary                              21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                      *teacher word

4. Enduring Understanding - The characteristics of non-linear functions and their representations are useful in solving real-
world problems.
4a. Essential Question - How are quadratic equations solved?
NLF.4.AI.3                                      A. Solve quadratic equations with and          Prerequisite Skills:                       composite            http://www.learnnc.
Solve quadratic equations using the             without appropriate technology by factoring    ♦factor quadratics                         number               org/lessons/Michell
appropriate methods with and without            B. Solve, using quadratic formula, quadratic   ♦solve equations                           parabola             eLongest52320027
appropriate technology                          equations with real number solutions with      ♦apply zero product property               quadratic formula    01
•factoring                                      and without appropriate technology                                                        quadratic function
•quadratic formula with real number solutions                                                  *solve quadratic equations by factoring,   square root          This lesson is
with and without appropriate technology    real roots           designed as a
review lesson for
♦recall standard form of polynomial                             equations.
application            factoring                                                                         Students will play
♦use order of operations
♦apply substitution                                             the game
"Chutes and
quadratic          *compute real number solutions using                            modified for
solve
*solve quadratic equations with real                            equations, as
number solutions using the quadratic                            they review for
formula, with and without appropriate                           the test.
technology
application            factoring

solve          equations with real
number solutions

rev. 05-2009                                                                                                                                                                              27 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                       Objective                                 Task Analysis                      Vocabulary                            21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                      *teacher word

4b. Essential Question - How do quadratic functions model real-world problems and their solutions?
NLF.4.AI.2                                    Find the minimum, maximum, vertex, and         *recognize that a zero is where a graph      maximum
Determine minimum, maximum, vertex and        zeros (roots) of a given graph of a non-linear intersects the x-axis                        minimum
zeros given the graph                         function                                       *recognize the highest point as a            vertex
maximum and lowest point as a minimum        zeros
given a graph
*determine the minimum, maximum,
graphs of non-        vertex, and zeros (roots) of a given graph
comprehension
linear functions       of a non-linear function

minimum, maximu
finding         m, vertex and
zeros

NLF.4.AI.5                                    Synthesis real world nonlinear problems by    *identify key information                     units of measure   graphing calculator
Communicate real-world problems               communication graphically, algebraically,     *determine the format in which the            unit rates         graph paper
graphically, algebraically, numerically and   numerically and verbally                      solution should be written                    vocabulary
verbally                                                                                    *represent and/or solve the situation         specific to
*label solution with appropriate unit(s),     problems
when necessary
real world non
synthesis                               *communicate real-world problems
linear problems
graphically, algebraically, numerically

graphically, algebr
communicating     aically, numerically
and verbally

rev. 05-2009                                                                                                                                                                            28 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                        Objective                               Task Analysis                     Vocabulary                    21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                    *teacher word

4th Nineweeks
1. Enduring Understanding - Coordinate geometry can be used to solve problems.
1a. Essential Question - How can coordinate geometry help to solve problems?
SEI.2.AI.7                                  Apply coordinate geometry to represent and     *apply distance, midpoint, and               coordinate                      Use logical reasoning
Use coordinate geometry to represent and/or solve for midpoint, length of a line segment   Pythagorean Theorem formulas                 geometry                        skills.
solve problems (midpoint, length of a line  and Pythagorean Theorem                        *choose the appropriate formula to           distance between                Skillful in using various
segment, and Pythagorean Theorem)                                                          represent problems                           two points                      problem-solving
*use the appropriate formula to solve        midpoint                        strategies.
problems                                     Pythagorean                     Formulate, approach,
coordinate
application                             *use coordinate geometry to represent        Theorem                         and solve problems
geometry
and/or solve problems (midpoint, length of                                   beyond those studied
a line segment, and Pythagorean                                              using a variety of tools
Theorem)                                                                     such as the graphing
calculator and
midpoint, length
geometry software.
represent and       of a line segment
solve           and Pythagorean
Theorem

2. Enduring Understanding - Graphs of non-linear functions can be manipulated.
2a. Essential Question - How can the graphs of non-linear functions be identified and manipulated?
DIP.5.AI.7                                   Recognize linear functions and non-linear     Prerequisite Skills:                         linear function
Recognize linear functions and non-linear    functions by using a table or a graph         ♦identify linear functions and non-linear    x-y table
functions by using a table or a graph                                                      functions
Focus on non-linear
*recognize linear functions and non-linear
Linear addressed earlier in the year          functions by using a table or a graph

knowledge          table and graph

non-linear
recognize
functions

rev. 05-2009                                                                                                                                                                    29 of 30
Arkansas Algebra I

Arch Ford/Northwest Arkansas Instructional Alignment
Algebra I
AR Department of Education
Essential
Materials/
CONTENT STANDARD/                                     Objective                                     Task Analysis                      Vocabulary                            21st Century skills
Resources
Student Learning Expectations (SLE)                                                                                                        *teacher word

New Application: NLF.4.AI.4                A. Identify quadratic, absolute value, and         *recognize function families of quadratics,   absolute value     graphing calculator
Recognize function families and their      exponential function families                      absolute value, and exponential functions     functions
connections including vertical shift and   B. Identify vertical shifts and reflections over   *determine effects of parameter changes       exponential
reflection over the x-axis                 the x-axis of quadratics, absolute value, and      and reflections on graphs                     quadratic function
•quadratics (with rational coefficients)   exponential function families                      *recognize vertical shifts and reflections    reflections
•absolute value                                                                               over the x-axis of quadratics, absolute       vertical shift
•exponential functions                                                                        value, and exponential functions

knowledge          function families

e value, and
identify
exponential
functions

e value, and
knowledge
exponential
function families

vertical
shifts, reflections
over the x-axis of
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