District Adopted Materials: Algebra I (Glencoe/McGraw-Hill)

Transcription

1 Grade: High Schl Curse: Algebra District Adpted aterials: Algebra (Glence/cGraw-Hill) Stard : Number Cmputatin The student uses numerical cmputatinal cncepts prcedures in a variety f situatins. Benchmark : Number Sense The student demnstrates number sense fr real numbers algebraic expressins. Benchmark 2: Number Systems Their Prperties The student demnstrates an understing f the real number system; recgnizes, applies, explains their prperties, extends these prperties t algebraic expressins. Benchmark 3: Estimatin The student uses cmputatinal estimatin with real numbers in a variety f situatins. Benchmark 4: Cmputatin The student mdels, perfrms, explains cmputatin with real numbers plynmials in a variety f situatins. Stard 2: Algebra The student uses algebraic cncepts prcedures in a variety f situatins. Benchmark : Patterns The student recgnizes, describes, extends, develps, explains the general rule f a pattern in a variety f situatins. Benchmark 2: Equatins, The student uses variables, symbls, real numbers, algebraic expressins t slve equatins inequalities in variety f situatins. Benchmark 3: Functins The student analyzes functins in a variety f situatins. Benchmark 4: dels The student develps uses mathematical mdels t represent justify mathematical relatinships fund in a variety f situatins invlving tenth grade knwledge skills. Stard 3: Gemetry The student uses gemetric cncepts prcedures in a variety f situatins. Benchmark : Gemetric Figures Their Prperties The student recgnizes gemetric figures cmpares justifies their prperties f gemetric figures in a variety f situatins. Benchmark 2: easurement Estimatin The student estimates, measures uses gemetric frmulas in a variety f situatins. Benchmark 3: Transfrmatinal Gemetry The student recgnizes applies transfrmatins n tw- three-dimensinal figures in a variety f situatins. Benchmark 4: Gemetry Frm An Algebraic Perspective The student uses an algebraic perspective t analyze the gemetry f tw- three-dimensinal figures in a variety f situatins. Stard 4: Data The student uses cncepts prcedures f data analysis in a variety f situatins. Benchmark : Prbability The student applies prbability thery t draw cnclusins, generate cnvincing arguments, make predictins decisins, analyze decisins including the use f cncrete bjects in a variety f situatins. Benchmark 2: Statistics The student cllects, rganizes, displays, explains, interprets numerical (ratinal) nn-numerical data sets in a variety f situatins.

2 ndicatrs The student Blm s Str Sequence HS...K knws, explains, uses equivalent representatins fr real numbers algebraic expressins including integers, fractins, decimals, percents, ratis; ratinal number bases with integer expnents; ratinal numbers written in scientific ntatin; abslute value; time; mney (2.4.Ka) ($), e.g., 4/2 = ( 2); a(-2) b(3) = b3/a2. HS...A generates /r slves real-wrld prblems using equivalent representatins f real numbers algebraic expressins (2.4.Aa) ($), e.g., a math classrm needs 30 bks 5 calculatrs. f B represents the cst f a bk C represents the cst f a calculatr, generate tw different expressins t represent the cst f bks calculatrs fr 9 math classrms HS...K2 cmpares rders real numbers /r algebraic expressins explains the relative magnitude between them (2.4.ka)($). E.g., will ( ) always, smetimes, r never be larger than 5n? The students might respnd with ( ) is greater than 5n if n > ( ) is smaller than 5 if 0 < n < Equivalent epresent Equivalent epresent Cmpare Order Teaching Time HS...A2 determines whether r nt slutins t real-wrld prblems using real numbers algebraic expressins are reasnable (2.4.Aa)($), e.g., in January, a business gave its emplyees a 0% raise. The fllwing year, due t the sluggish ecnmy, the emplyees decided t take a 0% reductin in their salary. s it reasnable t say they are nw making the same wage they made prir t the 0% raise? HS...K3 knws explains what happens t the prduct r qutient when a real number is multiplied r divided by (2.4.Ka): a ratinal number greater than zer less than ne a ratinal number greater than ne a ratinal number less than zer HS..2.K explains illustrates the relatinship between the subsets f the real number system [natural (cunting) numbers, whle numbers, integers, ratinal numbers, irratinal numbers] using mathematical mdels (2.4.Ka), e.g., number lines r Venn diagrams. HS.2.K2 identifies all the subsets f the real number system [natural (cunting) numbers, whle numbers, integers, ratinal numbers, irratinal numbers] t which a given number belngs (2.4.Km) HS.2.K3 names, uses, describes these prperties with the real number system demnstrates their meaning including the use f Knwledge Cmpare Order Numerical ecgnitin Numerical ecgnitin Numerical ecgnitin Number Systems their On-ging

3 cncrete bjects (2.4.Ka) ($): cmmutative (a + b = b + a ab = ba), assciative [a + (b + c) = (a + b) + c a(bc) = (ab)c], distributive [a (b + c) = ab + ac], substitutin prperties (if a = 2, then 3a = 3 x 2 = 6); identity prperties fr additin multiplicatin inverse prperties f additin multiplicatin (additive identity: a + 0 = a, multiplicative identity: a = a, additive inverse: = 0, multiplicative inverse: 8 x /8 = ); symmetric prperty f equality (if a = b, then b = a); additin multiplicatin prperties f equality (if a = b, then a + c = b + c if a = b, then ac = bc) inequalities (if a > b, then a + c > b + c if a > b, c > 0 then ac > bc); zer prduct prperty (if ab = 0, then a = 0 /r b = 0) HS..2.A generates /r slves real-wrld prblems with real numbers using the cncepts f these prperties t explain reasning (2.4.Aa) ($): cmmutative, assciative, distributive, substitutin prperties, e.g., the chrus is spnsring a trip t an amusement park. They need t purchase 5 adult tickets at $6 each 5 student tickets at $4 each. Hw much mney will the chrus need fr tickets? Slve this prblem tw ways. identity inverse prperties f additin multiplicatin, e.g., the purchase price (P) f a series EE Savings Bnd is fund by the frmula ½ F = P where F is the face value f the bnd. Use the frmula t find the face value f a savings bnd purchased fr $500. symmetric prperty f equality, e.g., Sam tk a $5 check t the bank received a $0 bill a $5 bill. Later Sam tk a $0 bill a $5 bill t the bank received a check fr $5. $ additin multiplicatin prperties f equality, e.g., the ttal price fr the purchase f three shirts in $624 including tax. f the tax is $3.89, what is the cst f ne shirt, if all shirts cst the same? additin multiplicatin prperties f equality, e.g., the ttal price fr the purchase f three shirts is $624 including tax. f the tax is $3.89, what is the cst f ne shirt? T = 3s + t $624 = 3s + $ $3.89 $624 - $3.89 = 3s Prperties

4 $58.65 = 3s $58.65 = 3s = 3s 3 $95 = s zer prduct prperty, e.g., Jenny was thinking f tw numbers. Jenny said that the prduct f the tw numbers was 0. What culd yu deduct frm this statement? Explain yur reasning. HS..2.A2 analyzes evaluates the advantages disadvantages f using integers, whle numbers, fractins (including mixed numbers), decimals r irratinal numbers their ratinal apprximatins in slving a given real-wrld prblem (2.4.Aa) ($), e.g., a stre sells CDs fr $2.99 each. Knwing that the sales tax is 7%, arie estimates the cst f a CD plus tax t be $4.30. She selects nine CDs. The clerk tells arie her bill is $57.8. Hw can arie explain t the clerk she has been vercharged? HS.2.K4 uses describes these prperties with the real number system (2.3.Ka) ($): transitive prperty (if a = b b = c, then a = c), reflexive prperty (a = a). HS..3.K estimates real number quantities using varius cmputatinal methds including mental math, paper pencil, cncrete bjects, /r apprpriate technlgy (2.4.Ka) ($) HS..3.A adjusts riginal ratinal number estimate f a real-wrld prblem based n additinal infrmatin (a frame f reference) (2.4.Aa) ($), e.g., estimate hw lng it takes t walk frm here t there; time hw lng it takes t take five steps adjust yur estimate. HS..3.K2 uses varius estimatin strategies explains hw they were used t estimate real number quantities algebraic expressins (2.4.Ka) ($) HS..2.A2 estimates t check whether r nt the result f a real-wrld prblem using real numbers /r algebraic expressins is reasnable makes predictins based n the infrmatin (2.4.Aa) ($), e.g., if yu have a $4,000 debt n a credit card the minimum f $30 is paid per mnth, is it reasnable t pay ff the debt in 0 years? HS..3.K3 knws explains why a decimal representatin f an irratinal number is an apprximate value(2.4.ka). HS..3.A3 determines if a real-wrld prblem calls fr an exact r apprximate answer perfrms the apprpriate cmputatin using varius cmputatinal strategies including mental math, paper pencil, cncrete bjects, /r apprpriate technlgy (2.4.Aa) ($), Number Systems their Prperties Cmprehensin Estimatin Estimatin Equivalent epresent On-ging On-ging

5 e.g., d yu need an exact r an apprximate answer in calculating the area f the walls t determine the number f rlls f wallpaper needed t paper a rm? What wuld yu d if yu were wallpapering 2 rms? HS..3.K4 knws explains between which tw cnsecutive integers an irratinal number lies (2.4.Ka). HS..3.A4 explains the impact f estimatin n the result f a realwrld prblem (underestimate, verestimate, range f estimates) (2.4.Aa) ($), e.g., if the weight f 25 pieces f paper was measured as grams, what wuld the weight f 2,000 pieces f paper equal t the nearest gram? f the student were t estimate the weight f ne piece f paper as abut 20 grams then multiply this by 2,000 rather than multiply the weight f 25 pieces f paper by 80; the answer wuld differ by abut 2,400 grams. n general, multiplying r dividing by a runded number will cause greater discrepancies than runding after multiplying r dividing. HS..4.K cmputes with efficiency accuracy using varius cmputatinal methds including mental math, paper pencil, cncrete bjects, apprpriate technlgy. HS..4.K2 perfrms explains these cmputatinal prcedures (2.4.Ka): N additin, subtractin, multiplicatin, divisin using the rder f peratins multiplicatin r divisin t find ($): a percent f a number, e.g., what is 0% f 0? percent f increase decrease, e.g., a cllege raises its tuitin frm $,320 per year t $,425 per year. What percent is the change in tuitin? percent ne number is f anther number, e.g., 89 is what percent f 82? a number when a percent f the number is given, e.g., 80 is 32% f what number? manipulatin f variable quantities within an equatin r inequality (2.4.Kd), e.g., 5x 3y = 20 culd be written as 5x 20 = 3y r 5x(2x + 3) = 8 culd be written as 8/(5x) = 2x + 3; simplificatin f radical expressins (withut ratinalizing denminatrs) including square rts f perfect square mnmials cube rts f perfect cubic mnmials; simplificatin r evaluatin f real numbers algebraic mnmial expressins raised t a whle number pwer Synthesis Numerical ecgnitin Numerical ecgnitin Numerical ecgnitin On-ging 8

6 algebraic binmial expressins squared r cubed; simplificatin f prducts qutients f real number algebraic mnmial expressins using the prperties f expnents; matrix additin ($), e.g., when cmputing (with ne peratin) a building s expenses (data) mnthly, a matrix is created t include each f the different expenses; then at the end f the year, each type f expense fr the building is ttaled; scalar-matrix multiplicatin ($), e.g., if a matrix is created with everyne s salary in it, everyne gets a 0% raise in pay; t find the new salary, the matrix wuld be multiplied by.. HS.4.A numbers algebraic expressins using cmputatinal prcedures (additin, subtractin, multiplicatin, divisin, rts, pwers excluding lgarithms), mathematical cncepts with ($): applicatins frm business, chemistry, physics that invlve additin, subtractin, multiplicatin, divisin, squares, square rts when the frmulae are given as part f the prblem variables are defined (2.4.Aa) ($), e.g., given F =ma, where F = frce in newtns, m = mass in kilgrams, a =acceleratin in meters per secnd squared. Find the acceleratin if a frce f 20 newtns is applied t a mass f 3 kilgrams. vlume surface area given the measurement frmulas f rectangular slids cylinders (2.4.Af), e.g., a sil has a diameter f 8 feet a height f 20 feet. Hw many cubic feet f grain can it stre? prbabilities (2.4.Ah), e.g., if the prbability f getting a defective light bulb is 2%, yu buy 50 light bulbs, hw many wuld yu expect t be defective? applicatin f percents (2.4.Aa), e.g., given the frmula, A = P(+r )^nt, A = amunt, P= principal, r = annual interest, n =number f cmpunding perids per year, t = number f years. f $,000 is placed in a savings accunt with a 6% annual interest rate is cmpunded semiannually, hw much mney will be in the accunt at the end f 2 years? simple expnential grwth decay (excluding lgarithms) ecnmics (2.4.Aa) ($), e.g., a ppulatin f cells dubles every 20 years. f there are 20 cells t start with, hw lng will it take fr there t be mre than 50 cells? Cmputatin 4

7 r f the radiatin level is nw 400 it decays by ½ r its half-life is 8 hurs, hw lng will it take fr the radiatin level t be belw an acceptable f level 5? HS..4.K3 finds prime factrs, greatest cmmn factr, multiples, the least cmmn multiple f algebraic expressins (2.4.Kb) HS 2..K identifies, states, cntinues the fllwing patterns using varius frmats including numeric (list r table), algebraic (symblic ntatin), visual (picture, table, r graph), verbal (ral descriptin), kinesthetic (actin), written arithmetic gemetric sequences using real numbers /r expnents (2.4.Ka); e.g., radiactive half-lives; patterns using gemetric figures (2.4.Kh); algebraic patterns including cnsecutive number patterns r equatins f functins, e.g., n, n +, n + 2,... r f(n) = 2n (2.4.Kc,e); Knwledge Cmputatin Cncepts Number Cncepts special patterns (2.4.Ka), e.g., Pascal s triangle the Fibnacci sequence HS.2..A recgnizes the same general pattern presented in different representatins [numeric (list r table), visual (picture, table, r graph), written] (2.4.Ai) ($). HS.2..K2 generates explains a pattern (2.4.Kh) Cmprehensin Number Cncepts HS.2..K3 classify sequences as arithmetic, gemetric, r neither Number Cncepts HS.2..A2 slves real-wrld prblems with arithmetic r gemetric sequences by using the explicit equatin f the sequence (2.4.Kc) ($), e.g., an arithmetic sequence: A brick wall is 3 feet high the wners want t build it higher. f the builders can lay 2 feet every hur, hw lng will it take t raise it t a height f 20 feet? r a gemetric sequence: A savings prgram can duble yur mney every 2 years. f yu place $00 in the prgram, hw many years will it take t have ver $,000? HS.2..K4 defines (2.4.Ka): a recursive r explicit frmula fr arithmetic sequences finds any particular term, a recursive r explicit frmula fr gemetric sequences finds any particular term HS.2.2.K knws explains the use f variables as parameters fr a specific variable situatin (2.4.Kf), e.g., the m b in y = mx + b r Equatins, Patterns 2 2

8 the h, k, r in (x h) 2 + (y k) 2 = r 2 HS.2.2.A represents real-wrld prblems using variables, symbls, expressins, equatins, inequalities, simple systems f linear equatins (2.4.Ac-e) ($). HS.2.2.K2 manipulates variable quantities within an equatin r inequality (2.4.Ke), e.g., 5x 3y = 20 culd be written as 5x 20 = 3y r 5x(2x + 3) = 8 culd be written as 8/(5x) = 2x + 3 HS.2.2.K3 slves (2.4.Kd) ($): N linear equatins inequalities bth analytically graphically; quadratic equatins with integer slutins (may be slved by trial errr, graphing, quadratic frmula, r factring); N systems f linear equatins with tw unknwns using integer cefficients cnstants; radical equatins with n mre than ne inverse peratin arund the radical expressin; equatins where the slutin t a ratinal equatin can be simplified as a linear equatin with a nnzer denminatr, e.g., 3 = 5. (x + 2) (x 3) equatins inequalities with abslute value quantities cntaining ne variable with a special emphasis n using a number line the cncept f abslute value. expnential equatins with the same base withut the aid f a calculatr r cmputer, e.g., 3x + 2 = 35. HS.2.2.A2 represents /r slves real-wrld prblems with (2.4.Ac) ($): N linear equatins inequalities bth analytically graphically, e.g., tickets fr a schl play are $5 fr adults $3 fr students. Yu need t sell at least $65 in tickets. Give an inequality a graph that represents this situatin three pssible slutins. quadratic equatins with integer slutins (may be slved by trial errr, graphing, quadratic frmula, r factring), e.g., a fence is t be built nt an existing fence. The three sides will be built with 2,000 meters f fencing. T maximize the rectangular area, what shuld be the dimensins f the fence? systems f linear equatins with tw unknwns, e.g., when cmparing tw cellular telephne plans, Plan A csts $0 per mnth $.0 per minute Plan B csts $2 per mnth $.07 per minute. The prblem is represented by Plan A =.0x + 0 Plan B =.07x + 2 where x is the Synthesis Equatins, Equatins, Equatins,, On-ging 2 0

9 number f minutes. radical equatins with n mre than ne inverse peratin arund the radical expressin, e.g., a square rug with an area f 200 square feet is 4 feet shrter than a rm. What is the length f the rm? a ratinal equatin where the slutin can be simplified as a linear equatin with a nnzer denminatr, e.g., Jhn is 2 feet taller than Fred. Jhn s shadw is 6 feet in length Fred s shadw is 4 feet in length. Hw tall is Fred? HS.2.2.A3 explains the mathematical reasning that was used t slve a real wrld prblem using equatins inequalities analyzes the advantages disadvantages f varius strategies that may have been used t slve the prblem (2.4.Ac). HS.2.3.K evaluates analyzes functins using varius methds including mental math, paper pencil, cncrete bjects, graphing utilities r ther apprpriate technlgy (2.4.Ka,d-f) HS.2.3.A translates between the numerical, graphical, symblic representatins f functins (2.4.Ac-e) ($). HS.2.3.K2 matches equatins graphs f cnstant linear functins quadratic functins limited t y = ax 2 + c (2.4.Kd,f) HS.2.3.A2 interprets the meaning f the x- y- intercepts, slpe, /r pints n ff the line n a graph in the cntext f a real-wrld situatin (2.4.Ae) ($), e.g., the graph belw represents a tank full f water being emptied. What des the y-intercept represent? What des the x-intercept represent? What is the rate at which it is emptying? What des the pint (2, 25) represent in this situatin? What des the pint (2,30) represent in this situatin? HS.2.3.K3 determines whether a graph, list f rdered pairs, table f values, r rule represents a functin (2.4.Ke-f) HS.2.3.K4 determines x- y-intercepts maximum minimum values f the prtin f the graph that is shwn n a crdinate plane (2.4.Kf) HS.2.3.K5 identifies dmain range f: relatinships given the graph r table (2.4.Ke-f) linear, cnstant, quadratic functins given the equatin(s) (2.4.Kd) Evaluatin Synthesis Cmprehensin Knwledge elatins Functins elatins Functins Equatins,, Equatins, Equatins,, Equatins,, Pints; elatins Functins 2

10 HS.2.3.K6 recgnizes hw changes in the cnstant /r slpe within a linear functin changes the appearance f a graph (2.4.Kf)($) Equatins,, HS.2.3.K7 uses functin ntatin elatins Functins HS.2.3.K8 evaluates functin(s) given a specific dmain ($) elatins Functins HS.2.3.K9 describes the difference between independent dependent variables identifies independent dependent variables ($) HS.2.3.A3 analyzes (2.4.Ac-e): the effects f parameter changes (scale changes r restricted dmains) n the appearance f a functin s graph, hw changes in the cnstants /r slpe within a linear functin affects the appearance f a graph, hw changes in the cnstants /r cefficients within a quadratic functin in the frm f y = ax 2 + c affects the appearance f a graph. HS.2.4.K knws, explains, uses mathematical mdels t represent explain mathematical cncepts, prcedures, relatinships. athematical mdels include: prcess mdels (cncrete bjects, pictures, diagrams, number lines, hundred charts, measurement tls, multiplicatin arrays, divisin sets, r crdinate grids) t mdel cmputatinal prcedures, algebraic relatinships, mathematical relatinships t slve equatins ((..K-3,.2.K,.2.K3-4,.3.K-4,.4.K,.4.K2a-b, 2..Ka, 2..Kd, 2..K2, 2.2.K4, 2.3.K, 3.2.K-3, 3.2.K6, 3.3.K-4, 4.2.K3-4) ($); factr trees t mdel least cmmn multiple, greatest cmmn factr, prime factrizatin (.4.K3) algebraic expressins t mdel relatinships between tw successive numbers in a sequence r ther numerical patterns (2..Kc) equatins inequalities t mdel numerical gemetric relatinships (.4.K2c, 2.2.K3, 2.3.K-2, 3.2.K7) ($) functin tables t mdel numerical algebraic relatinships (2..Kc, 2.2.K2, 2.3.K, 2.3.K3, 2.3.K5) ($) crdinate planes t mdel relatinships between rdered Cmprehensin elatins Functins elatins Functins dels 2

11 pairs equatins inequalities linear quadratic functins (2.2.K, 2.3.K-6, 3.4.K-8) ($) cnstructins t mdel gemetric therems prperties (3..K2, 3..K6) tw- three-dimensinal gemetric mdels (gebards, dt paper, crdinate plane, nets, r slids) real-wrld bjects t mdel perimeter, area, vlume, surface area, prperties f tw- three-dimensinal figures, ismetric views f three-dimensinal figures (2..Kb, 3..K-8, Pascal s Triangle t mdel binmial expansin prbability (3.2.K, 3.2.K4-5, 3.3.K-4) scale drawings t mdel large small real-wrld bjects gemetric mdels (spinners, targets, r number cubes), prcess mdels (cncrete bjects, pictures, diagrams, r cins), tree diagrams t mdel prbability (4..K-3) frequency tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single duble stem-leaf plts, scatter plts, bx--whisker plts, histgrams, matrices t rganize display data (4.2.K, 4.2.K5-6) ($) Venn diagrams t srt data shw relatinships (.2.K2) HS.2.4.A The student recgnizes that varius mathematical mdels can be used t represent the same prblem situatin. athematical mdels include: prcess mdels (cncrete bjects, pictures, diagrams, flwcharts, number lines, hundred charts, measurement tls, multiplicatin arrays, divisin sets, r crdinate grids) t mdel cmputatinal prcedures, algebraic relatinships, mathematical relatinships, prblem situatins t slve equatins (..K,.2.A-2,.3.A-4,.4.Aa,.4Ad-e, 3..A-3, 3.2.A-3, 3.3.A2, 3.3.A4, 3.4.A2, 4.2.Aa-b) ($); algebraic expressins t mdel relatinships between tw successive numbers in a sequence r ther numerical patterns; equatins inequalities t mdel numerical gemetric relatinships (2..A2, 2.2.A-3, 2.3.A) ($); functin tables t mdel numerical algebraic relatinships (2.3.A, 2.3.A3, 3.4.A2) ($); crdinate planes t mdel relatinships between rdered pairs equatins inequalities linear quadratic

12 functins (2.2.A, 2.3.A-3, 3.4.A-2, 3.4.A4) ($); tw- three-dimensinal gemetric mdels (gebards, dt paper, crdinate plane, nets, r slids) real-wrld bjects t mdel perimeter, area, vlume, surface area, prperties f tw- three-dimensinal figures ismetric views f three-dimensinal figures (3.3.A, 4.2.Ac); scale drawings t mdel large small real-wrld bjects (3.3.A3, 3.4.A3); gemetric mdels (spinners, targets, r number cubes), prcess mdels (cins, pictures, r diagrams), tree diagrams t mdel prbability (.4.Ac, 4.2.A, 4.2.A3); HS.2.4.A2 uses mathematical mdeling prcess t analyzes make inferences abut real wrld situatins HS.3..K5-Ab 3.2.Ad uses the Pythagrean Therem t (2.4.Kh): determine if a triangle is a right triangle find a missing side f a right triangle slve related real wrld prblems HS.3.3.K4 states. recgnizes, applies frmulas fr (2.4.Kh) ($) perimeter area f squares, rectangles triangles HS3.3.K7 knw, explains, uses ratis prprtins t describe rates f change(2.4.kd)($),e.g., miles per galln, meters per secnd, calries per unce, r rise ver run HS.3.3.K, A2, A4 describes, perfrms single multiple transfrmatins -refectin, rtatin, translatin, reductin (cntractin/shrinking), enlargement (magnificatin/grwing)] n tw three-dimensinal figures(withut r the cncrete figure) including explaining sketches crdinate systems (2.4.Ka). HS.3.3.A analyzes the impact f transfrmatins n the perimeter area f circles, rectangles, triangles vlume f rectangular prisms cylinders (2.4.Af), e.g., reducing by a factr f ½ multiplies an area by a factr f ¼ multiplies the vlume by a factr f /8, whereas, rtating a gemetric figure des nt change perimeter r area. HS.3.4.K2 determines f a given pint lies n the graph f a given line r parabla withut graphing justifies the answer(2.4.ka) HS.3.4.K3 calculates the slpe f a line frm a list f rdered pairs n the line explains hw the graph f the line is related t its slpe (2.4.Kf) Equatins,, Perimeter, Area, Vlume Equatins,, Transfrmatins Tessellatin Transfrmatins Tessellatin Number Lines Crdinate Number Lines Crdinate 5

13 HS.3.4.K4 finds explains the relatinship between the slpes f parallel perpendicular lines (2.4.Kf), e.g., the equatin f a line 2x + 3y = 2. The slpe f this line is. 2/3 What is the slpe f a line perpendicular t this line? HS.3.4.K5 uses slve real wrld prblems, using the Pythagrean Therem t find distance (may use the distance frmula) (2.4.Kf). HS.3.4.K6 recgnizes the equatin f a line transfrms the equatin int slpe-intercept frm in rder t identify the slpe y- intercept uses this infrmatin t graph the line (2.4.Kf). HS.3.4.K7 recgnizes the equatin y = ax 2 + c as a parabla; represents identifies characteristics f the parabla including pens upward r pens dwnward, steepness (wide/narrw), the vertex, maximum minimum values, line f symmetry; sketches the graph f the parabla (2.4.Kf). HS.3.4.A represents, generates, /r slves real-wrld prblems that invlve distance tw-dimensinal gemetric figures including parablas in the frm ax 2 + c (2.4.Ae), e.g., cmpare the heights f 2 different bjects whse paths are represented h(t) = 3t² + h 2 (t) = ½t² + 4 (where h represents the height in feet t represents elapsed time in secnds) after 5 secnds. HS.3.4.A2 translates between the written, numeric, algebraic, gemetric representatins f a real-wrld prblem (2.4.Aa-e) ($), e.g., given a situatin, write a functin rule, make a T-table f the algebraic relatinship, graph the rdered pairs. HS.3.4.A3 recgnizes explains the effects f scale changes n the appearance f the graph f an equatin invlving a line r parabla (2.4.Ag). HS.3.4.A4 analyzes hw changes in the cnstants /r leading cefficients within the equatin f a line r parabla affects the appearance f the graph f the equatin (2.4.Ae). HS.3.4.K8 explains the relatinship between the slutin(s) t systems f equatins systems f inequalities in tw unknwns their crrespnding graphs (2.4.Kf), e.g., fr equatins, the lines intersect in either ne pint, n pints, r infinite pints; fr inequalities, all pints in duble-shaded areas are slutins fr bth inequalities. HS.4..K3 explains the relatinship between prbability dds cmputes ne given the ther (2.4.Ka,k) Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate Number Lines Crdinate 2 Prbability 6

14 HS.4.2.K A rganizes, displays, reads quantitative (numerical) qualitative (nn-numerical) data in a clear, rganized, accurate manner including a title, labels, categries, ratinal number intervals using these data displays (2.4.Kl): HS.4.2.A uses data analysis in real-wrld prblems with ratinal number data sets t cmpare cntrast tw sets f data, t make accurate inferences predictins, t analyze decisins, t develp cnvincing arguments frm these data displays: frequency tables line plts; bar, line, circle graphs; Venn diagrams r ther pictrial displays; charts tables; stem--leaf plts (single duble); scatter plts; bx--whiskers plts; histgrams HS.4.2.K4 A5a,b explains analyzes the effects f utliers n the measures f central tendency (mean, median, mde) range interquartile range f a real number data set (2.4.Ka) Data Statistics HS.4.2.K5- A6 apprximates a line f best fit given a scatter plt makes predictins using the graph r the equatin f that line (2.4.Kk). Statistics