Docstoc

Algebra I TIA Pacing Guide

Document Sample
Algebra I TIA Pacing Guide Powered By Docstoc
					   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



                                                                   addition, subtracti
                                                   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
                                                                                           radicals                                   Associative
                                                                         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
                                                                     including radicals
                                                                                           operations                                 Distributive
                                                                                                                                      Property
                                                                                                                                      evaluate
                                                                                                                                      integers
                                                                                                                                      irrational numbers
                                                                                                                                      natural numbers
                                                                                                                                      number sense
                                                                                                                                      radical
                                                                                                                                      radical
                                                                                                                                      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
                                                    identify      domain and range                                                                         spreadsheet
                                                                                                                                                           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
                                                                                         ♦examine misleading graphs and
                                                                                                                                                 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
roots                                                                                                                                           radical
                                                                                                *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
                                                                                               rational coefficients using addition,
                                                                                               subtraction, multiplication (individually)
                                                                        polynomial
                                                  comprehension
                                                                        expressions



                                                                     addition, subtracti
                                                                     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
                                                                                       answers                                    greatest common
                                                                                                                                  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
                                                                                                                                                     answer all such
                                                                                                                                                     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
Simplify radical expressions, such as 3     simplifying radical expressions             ♦recognize perfect squares                   radical expression
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)
                                                                                        *simplify radical expressions
                                                                       radical
                                                 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
Add, subtract, and multiply simple radical   simplifying using addition, subtraction, and   ♦combine like terms                           prime number
expressions                                  multiplication radicals                                                                      radical
                                                                                            *perform operations with simplified           radical expression
                                                                                            radicals                                      radicand
                                                                       basic radical        *perform operations with non-simplified
                                                 comprehension
                                                                       expressions          radicals
                                                                                            *add, subtract, and multiply simple radical
                                                                                            expressions
                                                                     addition, subtracti
                                                     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
                                                                                               Prerequisite Skills:                                            solving quadratic
                                                                                               ♦recall standard form of polynomial                             equations.
                                                      application            factoring                                                                         Students will play
                                                                                               ♦use order of operations
                                                                                               ♦apply substitution                                             the game
                                                                                                                                                               "Chutes and
                                                                                                                                                               Ladders,"
                                                                            quadratic          *compute real number solutions using                            modified for
                                                         solve
                                                                            equations          quadratic formula                                               quadratic
                                                                                               *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




                                                                            quadratic
                                                         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




                                                                   quadratic, absolut
                                                                     e value, and
                                                   identify
                                                                      exponential
                                                                       functions




                                                                   quadratic, absolut
                                                                      e value, and
                                                 knowledge
                                                                      exponential
                                                                    function families



                                                                          vertical
                                                                    shifts, reflections
                                                                   over the x-axis of
                                                   identify        quadratics, absolu
                                                                      te value, and
                                                                       exponential
                                                                    function families




   rev. 05-2009                                                                                                                                                                              30 of 30

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:17
posted:3/22/2010
language:English
pages:30