GHS Curse Syllabus General Curse Infrmatin Curse Title: Accelerated Algebra 2 Year: 2015-2016 Department: Math Rm #: 112 Perids Taught: 3, 4, 6, 7 Resurces: Online editin f Algebra 2: Kanld, Burger, Dixn, Larsn, Leinwand; Hughtn Mifflin Harcrt ISBN 978-0-544-38591-7 Available at my.hrw.cm Curse Descriptin: Building n their wrk with linear, quadratic, and expnential functins, students extend their repertire f functins t include plynmial, ratinal, and radical functins. Students wrk clsely with the expressins that define the functins, and cntinue t expand and hne their abilities t mdel situatins and t slve equatins, including slving quadratic equatins ver the set f cmplex numbers and slving expnential equatins using the prperties f lgarithms. The 4 critical areas f fcus are: Plynmial, ratinal and radical relatinships, Trignmetry functins, mdeling with functins, and inferences and cnclusins frm data. The Mathematical Practice Standards apply thrughut the curse and, tgether with the cntent standards, prescribe that students experience mathematics as a cherent, useful, and lgical subject that makes use f their ability t make sense f prblem situatins. Accelerated Algebra 2 is mre rigrus than Algebra 2. Faculty Name: Office Hurs: Intrductin Cnnie Abel (BS Mathematics, MEd.) Mrs. Abel is available befre schl, during first lunch, and after schl. Appintments recmmended. Accelerated Algebra 2 is fr students wh are ready fr higher expectatins, and wuld like t take Pre- Calculus next year. Students shuld already have mastered prperties f negative numbers, fractins, expnents, radicals, slving ne and tw-step equatins, algebraic simplificatin t gather like terms, pltting tw-dimensinal crdinates, and graphing linear equatins. Level changes Students wh finish the curse with a grade f A r B will be recmmended fr Pre-Calculus. Students with a curse grade f C will be recmmended fr Technical Mathematics r Statistics and will be able t take Pre-Calculus fllwing Technical Math. Students with a curse grade f D r F will be recmmended t repeat the curse. Occasinally students wish t drp Accelerated Algebra 2 and finish the year with (nn-accelerated level) Algebra 2. Students wh change their status in this way will cntinue t have the same schedule and classrm. Mrs. Abel will differentiate the curriculum s that (nn-accelerated) Algebra 2 students will receive the same instructin but reduced rigr/expectatins in tests. NOTE: Students wh wish t make a level change must d s befre the end f the first quarter. Grading Hmewrk / frmative assessments 10% Tests / summative assessments-- 90% Grade scales regard C as prficient n unit standards, B as mastery and A as exceeding. D and F indicate failure t meet standards. Incmpletes/N-grades may be given at teacher discretin. Overall Averages A 90-100% B 80-89% C 70-79% D 60-69% F belw 60% I incmplete NG n grade Wrklad In additin t curse hurs in the classrm, students will be expected t spend 30 t 60 minutes utside f class fr hmewrk cmpletin fr every class meeting. T pass Accelerated Algebra 2, students must demnstrate prficiency in the skills listed n the last page f this dcument. These skills will be assessed in unit tests. In additin, they must either pass the state test in mathematics r pass tw wrk samples each frm a different mathematical strand. Wrk samples will be given as part f unit assessments.
Nte t Parents: Email at any time fr grade updates, questins, cncerns r cmments: abelc@hsd.k12.r.us and assignment details will be psted n www.schlgy.cm Students will need a graphing calculatr, and we recmmend TI-82, TI-83, TI 84. Students will be allwed t brrw a calculatr during the class perid ONLY in exchange fr the student s ID badge. Students withut a calculatr wh d nt have their ID will be encuraged t find a friend t share. Nte: If yur child has a TI-89, TI-92 Casi-300, r any ther mdel f calculatr that has symblic slutin capabilities, please be aware that such calculatrs are nt allwed n Accelerated Algebra 2 tests. Yur student may brrw a TI-84 frm the teacher fr the test perid. Students wh d nt have adequate internet capabilities at hme will be able t use Glence cmputers and/r chrme-bks befre and after schl in the Glence Library daily, during Learning Lab (3:30-4:30 pm T, W, Th), r in rm 112 every day during first lunch. Students may als chse t use the cmputers at the public library. This curse is ffered with ptinal dual credit fr Math 95 thrugh PCC. Details, requirements and deadlines will be discussed in class. Curse Schedule (details f standards fllw belw) Curse Objectives: Students will learn t mdel, graph and slve linear, quadratic, radical, ratinal and expnential equatins using symblic, numeric and graphical methds. Students will learn the graphical prperties f the fllwing families f functins: quadratic, plynmial, radical, ratinal, expnential, lgarithmic and trignmetric. Students will be intrduced t functins, inverses, dmain and range, alng with standard ntatin fr each. Students will learn cmpund and cnditinal prbability, and unit circle trignmetry. See a cmplete list f standards belw. Make-up Wrk Plicy: Make-up wrk is frm students with excused absences, wh are allwed ne mre day than the number f days absent t cmplete and submit any assigned make-up wrk. Students in need f a make-up test will be allwed the same grace perid. On time make-up wrk receives full credit. Late Wrk Plicy: The majrity f learning takes place nt in the classrm, but during hmewrk practice. Students wh d their hmewrk prmptly have better success as well as better retentin f cncepts. Students withut cmpleted hmewrk d nt receive much-needed feedback n their effrts. Oregn Department f Educatin defines nine essential skills fr graduatin. Essential Skill number 9 is Demnstrate persnal management and teamwrk skills which includes the bullet pint, Plan, rganize and cmplete assigned tasks accurately and n time. Because hmewrk is required practice, I d nt accept late wrk. Re-take tests Retake tests are by teacher discretin nly and are reserved fr students wh have nt yet met required prficiencies. Habitual retakes will be discuraged. Students wishing t retake a test will develp a detailed, individualized plan with the teacher fr learning the missing prficiencies, fllw thrugh in a time-specified manner, and cmplete a student-reflectin n what is learned by these activities. PCC recgnizes grades ONLY frm the first attempt at each test.
Cheating: Cheating / plagiarism in nt tlerated and will be subject t disciplinary actin. Classrm Cnduct: All students need t cme t class with calculatr and supplies. Graph paper is required fr hmewrk. If fr any reasn, a student cmes withut a calculatr, (s)he may brrw ne frm the teacher fr the perid in exchange fr a student identificatin card. All students are expected t participate in all classrm investigatins, discussin and practice prblems. We fllw the student-parent handbk regarding dress cde, electrnic devices and tardy plicy. COURSE STANDARDS QUARTER 1 Linear Equatins, Inequalities and Functins A.CED.1: Create equatins and inequalities in ne variable and use them t slve prblems. Include equatins A.CED.4: Rearrange frmulas t highlight a quantity f interest, using the same reasning as in slving equatins. Fr example, rearrange Ohm s law V = IR t highlight resistance R. F.IF.6: Calculate and interpret the average rate f change f a functin (presented symblically r as a table) ver a specified interval. Estimate the rate f change frm a graph. F.IF.7: Graph functins expressed symblically and shw key features f the graph, by hand in simple cases and using technlgy fr mre cmplicated cases. c. Graph plynmial functins, identifying zers when suitable factrizatins are available, and shwing end behavir. F.BF.3: Identify the effect n the graph f replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) fr specific values f k (bth psitive and negative); find the value f k given the graphs. Experiment with cases and illustrate an explanatin f the effects n the graph using technlgy. Include recgnizing even and dd functins frm their graphs and algebraic expressins fr them. S.IC.1: Understand statistics as a prcess fr making inferences abut ppulatin parameters based n a randm sample frm that ppulatin. Systems f Linear Equatins and Inequalities A.REI.11: Explain why the x-crdinates f the pints where the graphs f the equatins y = f(x) and y = g(x) intersect are the slutins f the equatin f(x) = g(x); find the slutins apprximately, e.g., using technlgy t graph the functins, make tables f values, r find successive apprximatins. Include cases where f(x) and/r g(x) are linear, plynmial, ratinal, abslute value, expnential, and lgarithmic functins. A.CED.2: Create equatins in tw r mre variables t represent relatinships between quantities; graph equatins n crdinate axes with labels and scales. A.CED.3: Represent cnstraints by equatins r inequalities, and by systems f equatins and/r inequalities, and interpret slutins as viable r nn-viable ptins in a mdeling cntext. Fr example, represent inequalities describing nutritinal and cst cnstraints n cmbinatins f different fds.
Quadratic Functins F.IF.4: Fr a functin that mdels a relatinship between tw quantities, interpret key features f graphs and tables in terms f the quantities, and sketch graphs shwing key features given a verbal descriptin f the relatinship. Key features include: intercepts; intervals where the functin is increasing, decreasing, psitive, r negative; relative maximums and minimums; symmetries; end behavir; and peridicity. F.IF.8: Write a functin defined by an expressin in different but equivalent frms t reveal and explain different prperties f the functin. F.BF.3: Identify the effect n the graph f replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) fr specific values f k (bth psitive and negative); find the value f k given the graphs. Experiment with cases and illustrate an explanatin f the effects n the graph using technlgy. Include recgnizing even and dd functins frm their graphs and algebraic expressins fr them. N.CN.1: Knw there is a cmplex number i such that i2 = 1, and every cmplex number has the frm a + bi with a and b real. N.CN.2: Use the relatin i2 = 1 and the cmmutative, assciative, and distributive prperties t add, subtract, and multiply cmplex numbers. N.CN.7: Slve quadratic equatins with real cefficients that have cmplex slutins. QUARTER 2 Quadratic Functins, cntinued frm Quarter 1 F.IF.4: Fr a functin that mdels a relatinship between tw quantities, interpret key features f graphs and tables in terms f the quantities, and sketch graphs shwing key features given a verbal descriptin f the relatinship. Key features include: intercepts; intervals where the functin is increasing, decreasing, psitive, r negative; relative maximums and minimums; symmetries; end behavir; and peridicity. F.IF.8: Write a functin defined by an expressin in different but equivalent frms t reveal and explain different prperties f the functin. interpret P(1+r) n as the prduct f P and a factr nt depending n P. F.BF.3: Identify the effect n the graph f replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) fr specific values f k (bth psitive and negative); find the value f k given the graphs. Experiment with cases and illustrate an explanatin f the effects n the graph using technlgy. Include recgnizing even and dd functins frm their graphs and algebraic expressins fr them. N.CN.1: Knw there is a cmplex number i such that i2 = 1, and every cmplex number has the frm a + bi with a and b real.
N.CN.2: Use the relatin i2 = 1 and the cmmutative, assciative, and distributive prperties t add, subtract, and multiply cmplex numbers. N.CN.7: Slve quadratic equatins with real cefficients that have cmplex slutins. N.CN.8: (+) Extend plynmial identities t the cmplex numbers. Fr example, rewrite x2 + 4 as (x + 2i)(x 2i). Plynmial Functins F.IF.8: Write a functin defined by an expressin in different but equivalent frms t reveal and explain different prperties f the functin. A.APR.1: Understand that plynmials frm a system analgus t the integers, namely, they are clsed under the peratins f additin, subtractin, and multiplicatin; add, subtract, and multiply plynmials. A.APR.2: Knw and apply the Remainder Therem: Fr a plynmial p(x) and a number a, the remainder n divisin by x a is p(a), s p(a) = 0 if and nly if (x a) is a factr f p(x). A.APR.3: Identify zers f plynmials when suitable factrizatins are available, and use the zers t cnstruct a rugh graph f the functin defined by the plynmial. A.APR.6: Rewrite simple ratinal expressins in different frms; write a(x)/b(x) in the frm q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are plynmials with the degree f r(x) less than the degree f b(x), using inspectin, lng divisin, r, fr the mre cmplicated examples, a cmputer algebra system. F.BF.1: Write a functin that describes a relatinship between tw quantities.* b. Cmbine standard functin types using arithmetic peratins. Fr example, build a functin that mdels the temperature f a cling bdy by adding a cnstant functin t a decaying expnential, and relate these functins t the mdel. N.CN.9: (+) Knw the Fundamental Therem f Algebra; shw that it is true fr quadratic plynmials. F.IF.7: Graph functins expressed symblically and shw key features f the graph, by hand in simple cases and using technlgy fr mre cmplicated cases. c. Graph plynmial functins, identifying zers when suitable factrizatins are available, and shwing end behavir. F.IF.4: Fr a functin that mdels a relatinship between tw quantities, interpret key features f graphs and tables in terms f the quantities, and sketch graphs shwing key features given a verbal descriptin f the relatinship. Key features include: intercepts; intervals where the functin is increasing, decreasing, psitive, r negative; relative maximums and minimums; symmetries; end behavir; and peridicity. F.IF.9: Cmpare prperties f tw functins each represented in a different way (algebraically, graphically, numerically in tables, r by verbal descriptins). Fr example, given a graph f ne quadratic functin and an algebraic expressin fr anther, say which has the larger maximum. Statistics (Inferences and Cnclusins frm Data) S.IC.1: Understand statistics as a prcess fr making inferences abut ppulatin parameters based n a randm sample frm that ppulatin. S.IC.2: Decide if a specified mdel is cnsistent with results frm a given data-generating prcess, e.g., using simulatin. Fr example, a mdel says a spinning cin falls heads up with prbability 0.5. Wuld a result f 5 tails in a rw cause yu t questin the mdel? S.IC.3: Recgnize the purpses f and differences amng sample surveys, experiments, and bservatinal studies; explain hw randmizatin relates t each. S.IC.4: Use data frm a sample survey t estimate a ppulatin mean r prprtin; develp a margin f errr thrugh the use f simulatin mdels fr randm sampling. S.IC.5: Use data frm a randmized experiment t cmpare tw treatments; use simulatins t decide if differences between parameters are significant.
S.IC.6: Evaluate reprts based n data. S.MD.6: (+) Use prbabilities t make fair decisins (e.g., drawing by lts, using a randm number generatr). S.MD.7: (+) Analyze decisins and strategies using prbability cncepts (e.g., prduct testing, medical testing, pulling a hckey galie at the end f a game). S.ID.4: Use the mean and standard deviatin f a data set t fit it t a nrmal distributin and t estimate ppulatin percentages. Recgnize that there are data sets fr which such a prcedure is nt apprpriate. Use calculatrs, spreadsheets, and tables t estimate areas under the nrmal curve. A.APR.5: (+) Knw and apply the Binmial Therem fr the expansin f (x + y)n in pwers f x and y fr a psitive integer n, where x and y are any numbers, with cefficients determined fr example by Pascal s Triangle. QUARTER 3 Pwers, Rts and Radicals F.BF.4: Find inverse functins. a. Slve an equatin f the frm f(x) = c fr a simple functin f that has an inverse and write an expressin fr the inverse. Fr example, f(x) = 2 x3 r f(x) = (x+1)/(x-1) fr x 1. F.IF.5: Relate the dmain f a functin t its graph and, where applicable, t the quantitative relatinship it describes. Fr example, if the functin h(n) gives the number f persn-hurs it takes t assemble n engines in a factry, then the psitive integers wuld be an apprpriate dmain fr the functin. A.REI.2: Slve simple ratinal and radical equatins in ne variable, and give examples shwing hw extraneus slutins may arise. Expnential and Lgarithmic Functins F.IF.5: Relate the dmain f a functin t its graph and, where applicable, t the quantitative relatinship it describes. Fr example, if the functin h(n) gives the number f persn-hurs it takes t assemble n engines in a factry, then the psitive integers wuld be an apprpriate dmain fr the functin. F.IF.7: Graph functins expressed symblically and shw key features f the graph, by hand in simple cases and using technlgy fr mre cmplicated cases. b. Graph square rt, cube rt, and piecewise-defined functins, including step functins and abslute value functins. e. Graph expnential and lgarithmic functins, shwing intercepts and end behavir, and trignmetric functins, shwing perid, midline, and amplitude. A.SSE.4: Derive the frmula fr the sum f a finite gemetric series (when the cmmn rati is nt 1), and use the frmula t slve prblems. Fr example, calculate mrtgage payments. QUARTER 4
Ratinal Functins interpret P(1+r) n as the prduct f P and a factr nt depending n P. F.IF.5: Relate the dmain f a functin t its graph and, where applicable, t the quantitative relatinship it describes. Fr example, if the functin h(n) gives the number f persn-hurs it takes t assemble n engines in a factry, then the psitive integers wuld be an apprpriate dmain fr the functin. A.APR.7: (+) Understand that ratinal expressins frm a system analgus t the ratinal numbers, clsed under additin, subtractin, multiplicatin, and divisin by a nnzer ratinal expressin; add, subtract, multiply, and divide ratinal expressins. A.REI.2: Slve simple ratinal and radical equatins in ne variable, and give examples shwing hw extraneus slutins may arise. A.APR.4: Prve plynmial identities and use them t describe numerical relatinships. Fr example, the plynmial identity (x2 + y2)2 = (x2 y2)2 + (2xy)2 can be used t generate Pythagrean triples. A.REI.11: Explain why the x-crdinates f the pints where the graphs f the equatins y = f(x) and y = g(x) intersect are the slutins f the equatin f(x) = g(x); find the slutins apprximately, e.g., using technlgy t graph the functins, make tables f values, r find successive apprximatins. Include cases where f(x) and/r g(x) are linear, plynmial, ratinal, abslute value, expnential, and lgarithmic functins. Trignmetry F.TF.1: Understand radian measure f an angle as the length f the arc n the unit circle subtended by the angle. F.TF.2: Explain hw the unit circle in the crdinate plane enables the extensin f trignmetric functins t all real numbers, interpreted as radian measures f angles traversed cunterclckwise arund the unit circle. F.TF.5: Chse trignmetric functins t mdel peridic phenmena with specified amplitude, frequency, and midline. F.TF.8: Prve the Pythagrean identity sin 2 (θ) + cs 2 (θ) = 1 and use it t find sin (θ), cs (θ), r tan (θ), given sin (θ), cs (θ), r tan (θ), and the quadrant f the angle. ESSENTIAL SKILLS Successful cmpletin f this curse indicates that a student has demnstrated the Essential Skills that are checked belw. Read and interpret a variety f texts at different levels f difficulty (2012) Write clearly and accurately (2013) Listen actively, speak clearly, and present publicly Apply mathematical reasning in a variety f settings (2014) Use technlgy t learn, live, and wrk Think critically and analytically Demnstrate civic and cmmunity engagement Demnstrate glbal literacy Demnstrate persnal management and teamwrk skills