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Arkansas Algebra I Arch Ford/Northwest Arkansas Instructional Alignment Algebra I AR Department of Education Essential Materials/ CONTENT STANDARD/ Objective Task Analysis Vocabulary 21st Century skills Resources Student Learning Expectations (SLE) *teacher word 1st Nineweeks 1. Enduring Understanding - Statistics are used to make inferences and predictions. 1a. Essential Question - How can the results of a statistical investigation be used to support an argument? DIP.5.AI.6 Analyze real life situations by constructing Prerequisite Skills: axis graphing calculator Use the internet to find Construct and interpret a cumulative and interpreting cumulative frequency ♦construct histograms histograms district data of a stock price daily. frequency histogram in real-life situations histograms ♦interpret a histogram intervals school age Use this data to make students an ongoing histogram *construct and interpret a cumulative and cumulative analyze real life situations frequency histogram in real-life situations frequency histogram. cumulative construct / frequency interpret histogram DIP.5.AI.5 Analyze real-life situations by constructing Prerequisite Skills: bar graph graphing calculator Compare the number Use two or more graphs to compare data and using scatter plots and line of best fit ♦interpret various representations of data box-and-whisker excel program of Girl Scout cookies sets sets plots stock journal sold over a two-year Ex. histograms span. Compare the box-and-whisker, histograms, scatter plots *use two or more graphs to compare data line graph data. Make two or more sets scatter plot suggestions for the analyze stem-and-leaf upcoming year. graphs display compare data sets rev. 05-2009 1 of 30 Arkansas Algebra I Arch Ford/Northwest Arkansas Instructional Alignment Algebra I AR Department of Education Essential Materials/ CONTENT STANDARD/ Objective Task Analysis Vocabulary 21st Century skills Resources Student Learning Expectations (SLE) *teacher word DIP.5.AI.11 Explain and cite examples as justification Prerequisite Skills: bias http://mathforum.or Explain how sampling methods, bias, and how sampling methods, bias, and phrasing ♦define biased and unbiased data conclusions g/library/view/7884 phrasing of questions in data collection of questions in data collection impact the sampling data .html impact the conclusions conclusions ♦describe methods of data collection sampling ♦examine misleading graphs and This lesson uses questions decision-making ♦use sampling methods ideas from data collection statistics in the evaluation impacts science classroom. conclusion *explain how sampling methods, bias, Students make and phrasing of questions in data use of sampling to collection impact the conclusions back up a sampling claim, and design explain methods, bias (with teacher and phrasing assistance) a statistical experiment to study a problem. DIP.5.AI.1 Construct and use scatter plots and line of Prerequisite Skills: axis Construct and use scatter plots and line of best fit to make inferences in real-life ♦graph on a coordinate plane coordinate best fit to make inferences in real-life situations ♦construct scatter plots and draw lines of system situations best fit extrapolate ♦write equation of a line in slope-interceptinferences form interpolate line of best fit *construct and use scatter plots and line regression of best fit scatter plot *make inferences in real-life situations x-axis using the constructed scatter plot and line y-axis of best fit rev. 05-2009 2 of 30 Arkansas Algebra I Arch Ford/Northwest Arkansas Instructional Alignment Algebra I AR Department of Education Essential Materials/ CONTENT STANDARD/ Objective Task Analysis Vocabulary 21st Century skills Resources Student Learning Expectations (SLE) *teacher word DIP.5.AI.4 Comprehension of measures of central Prerequisite Skills: central http://www.casioed Determine the effects of changes in the data tendency by describing the effects of ♦use mean, median, mode, and range tendencies ucation.com/resour set on the measures of central tendency changes in data sets data ce/pdfs/compariso *determine the effects of changes in the mean n/FX-9750 data set on measures of central tendency median measure of mode Given a set of comprehension central tendency range data, the students will be able to enter it into the effects of changes Statistics Menu of describe in data sets the calculator, graph the data using a scatter plot, find the Line of Best Fit for the scatter plot, and calculate the measures of central tendency. DIP.5.AI.12 Analyze arguments based on data by *differentiate correlation and causation causation data from a crime Recognize when arguments based on data recognizing correlation with causation *recognize when arguments based on correlation scene confuse correlation with causation data confuse correlation and causation arguments based analyze on data correlation with recognize causation 1b. Essential Question - How can matrices organize and display data? DIP.5.AI.3 Apply real-life situations to construct simple *compare matrices written literally and in array determine number Construct simple matrices for real-life matrices context (with labeling) matrices of store sales for a situations *construct simple matrices for real-life product situations application real life situations construct matrices rev. 05-2009 3 of 30 Arkansas Algebra I Arch Ford/Northwest Arkansas Instructional Alignment Algebra I AR Department of Education Essential Materials/ CONTENT STANDARD/ Objective Task Analysis Vocabulary 21st Century skills Resources Student Learning Expectations (SLE) *teacher word DIP.5.AI.2 Apply simple matrices to compute addition, *use simple matrices in addition, array Use simple matrices in addition, subtraction, subtraction, and scalar multiplication subtraction, and scalar multiplication matrices and scalar multiplication scalar multiplication application simple matrices 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

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posted: | 3/22/2010 |

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