G r a d e 1 2 E s s e n t i a l M a t h e m a t i c s ( 4 0 S )

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1 G r a d e 1 2 E s s e t i a l M a t h e m a t i c s ( 4 0 S ) Grade 12 Essetial Mathematics (40S) is iteded for studets whose post-secodary plaig does ot iclude a focus o mathematics ad sciece-related fields. Grade 12 Essetial Mathematics (40S) is a oe-credit course cosistig of two half-credits each emphasizig cosumer applicatios, problem solvig, decisio makig, ad spatial sese. Studets are expected to work both idividually ad i small groups o mathematical cocepts ad skills ecoutered i everyday life i a techological society. Assessmet of Grade 12 Essetial Mathematics should be a balace of assessmet for learig, assessmet as learig, ad assessmet of learig. Assessmet tools used i Grade 12 Essetial Mathematics should be varied ad may iclude observatio, homework, learig coversatios or iterviews, summative uit essays, demostratios, presetatios, performace tasks, learig logs, projects, ivestigatios, reflective jourals, portfolios, quizzes, tests, ad examiatios. A appropriately prepared portfolio requires a cosistet effort throughout the school term ad a commitmet to completig quality work o a daily basis. The followig tables list the uits of study for each halfcourse alog with a estimated umber of hours for each uit. The time for each uit icludes istructioal ad assessmet time. Grade 12 Essetial Mathematics (45S) Half Course V Grade 12 Essetial Mathematics (45S) Half Course VI Uit Suggested Hours Uit Suggested Hours Aalysis of Games ad Numbers 7 Aalysis of Games ad Numbers 7 Vehicle Fiace 17 Home Fiace 12 Statistics 7 Geometry ad Trigoometry 10 Precisio Measuremet 12 Busiess Fiace 15 Career Life 12 Probability 11 Total 55 Total 55 Geeral ad Specific Learig Outcomes 169

3 Geeral ad Specific Learig Outcomes with Achievemet Idicators by Course Grade 12 Essetial Mathematics Half Course V [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E5.A.1. Strad: Aalysis of Games ad Numbers Specific Learig Outcomes It is expected that studets will: Aalyze puzzles ad games that ivolve logical reasoig, usig problem-solvig strategies. [C, CN, PS, R] It is iteded that this learig outcome be itegrated throughout the course by usig puzzles ad games such as Sudoku, Mastermid, Nim, ad logic puzzles. Geeral Learig Outcome: Develop critical thikig skills. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Determie, explai, ad verify a strategy to solve a puzzle or to wi a game such as guess ad check look for a patter make a systematic list draw or model elimiate possibilities simplify the origial problem work backward develop alterative approaches Idetify ad correct errors i a solutio to a puzzle or i a strategy for wiig a game. Create a variatio o a puzzle or a game, ad describe a strategy for solvig the puzzle or wiig the game. Geeral ad Specific Learig Outcomes 171

4 Grade 12 Essetial Mathematics Half Course V [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E5.V.1. Strad: Vehicle Fiace Specific Learig Outcomes It is expected that studets will: Solve problems that ivolve the acquisitio, operatio, ad maiteace of a vehicle, whe buyig leasig leasig to buy [C, CN, PS, R, T] Geeral Learig Outcome: Develop a uderstadig of owig ad operatig a vehicle. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Describe ad explai various optios for buyig, leasig, or leasig to buy a vehicle. Determie costs associated with buyig, leasig, or leasig to buy a ew or used vehicle. Solve, with or without techology, problems that ivolve the purchase, lease, or lease to purchase of a vehicle. Determie costs associated with operatig a vehicle icludig regular maiteace, repairs, fuel cosumptio, or depreciatio. Determie the costs of isurig a vehicle for various uses. Justify a decisio related to buyig, leasig, or leasig to buy a vehicle, based o factors such as persoal fiaces, iteded use, maiteace, warraties, mileage, isurace, or safety cosideratios. 172 Grades 9 to 12 Mathematics: Maitoba Curriculum Framework of Outcomes (2014)

5 Grade 12 Essetial Mathematics Half Course V [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E5.S.1. 12E5.S.2. Strad: Statistics Specific Learig Outcomes It is expected that studets will: Solve problems that ivolve measures of cetral tedecy, icludig mea media mode weighted mea trimmed mea [C, CN, PS, R] Aalyze ad describe percetiles. [C, CN, PS, R] Geeral Learig Outcome: Develop statistical reasoig. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Explai, usig examples, the advatages ad disadvatages of each measure of cetral tedecy. Determie the mea, media, ad mode for a set of data. Idetify ad correct errors i a calculatio of a measure of cetral tedecy. Idetify the outlier(s) i a set of data. Explai the effect of outliers o mea, media, ad mode. Determie the trimmed mea for a set of data, ad justify the removal of the outliers. Explai, usig examples such as course marks, why some data i a set would be give a greater weightig i determiig the mea. Determie the weighted mea of a set of data, ad justify the differet weightigs. Explai, usig examples from prit or other media, how measures of cetral tedecy ad outliers are used to provide differet iterpretatios of data. Solve a cotextual problem that ivolves measures of cetral tedecy. Explai, usig examples, percetile raks i a cotext. Explai decisios based o a give percetile rak. Explai, usig examples, the differece betwee percet ad percetile rak. Explai the relatioship betwee media ad percetile. Solve a cotextual problem that ivolves percetiles. Determie the percetile rak of a give score usig a formula. Geeral ad Specific Learig Outcomes 173

6 Grade 12 Essetial Mathematics Half Course V [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E5.P.1. Strad: Precisio Measuremet Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of the limitatios of measurig istrumets, icludig precisio accuracy ucertaity tolerace [C, PS, R, T, V] Geeral Learig Outcome: Develop spatial sese relatig to the limitatios of measurig istrumets. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Explai why, i a give cotext, a certai degree of precisio is required. Explai why, i a give cotext, a certai degree of accuracy is required. Explai, usig examples, the differece betwee precisio ad accuracy. Compare the degree of accuracy of two istrumets used to measure the same attribute. Relate the degree of accuracy to the ucertaity of a give measure. Aalyze precisio ad accuracy i a cotextual problem. Determie maximum ad miimum values, usig a degree of tolerace i cotext. Describe, usig examples, the limitatios of measurig istrumets such as tape measure, micrometer, or Verier caliper, used i a specific trade or idustry. Solve a problem that ivolves precisio, accuracy, or tolerace. 174 Grades 9 to 12 Mathematics: Maitoba Curriculum Framework of Outcomes (2014)

7 Grade 12 Essetial Mathematics Half Course V [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E5.C.1 Strad: Career Life Specific Learig Outcomes It is expected that studets will: Create a pla for the future, icludig possible career choices ad their requiremets. [C, CN, PS, R] Geeral Learig Outcome: Develop a pla for the future. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Describe factors importat i selectig careers, icludig job descriptio, educatioal requiremets ad costs, aptitude, values, salary/wage levels, employmet opportuities, opportuities for advacemet, ad work/life balace. Prepare a mothly budget for the preparatory period for a chose career. Prepare a mothly budget for the lifestyle achievable for a chose career. Aalyze the lifestyle oe specific career could etail i terms of mothly budget, lifestyle appropriate to the career, ad ay egative factors of the job. Prepare a resumé for your career choice. Geeral ad Specific Learig Outcomes 175

8 Grade 12 Essetial Mathematics Half Course VI [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E6.A.1. Strad: Aalysis of Games ad Numbers Specific Learig Outcomes It is expected that studets will: Aalyze puzzles ad games that ivolve logical reasoig, usig problem-solvig strategies. [C, CN, PS, R] It is iteded that this learig outcome be itegrated throughout the course by usig puzzles ad games such as Sudoku, Mastermid, Nim, ad logic puzzles. Geeral Learig Outcome: Develop critical-thikig skills. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Determie, explai, ad verify a strategy to solve a puzzle or to wi a game such as guess ad check look for a patter make a systematic list draw or model elimiate possibilities simplify the origial problem work backward develop alterative approaches Idetify ad correct errors i a solutio to a puzzle or i a strategy for wiig a game. Create a variatio o a puzzle or a game, ad describe a strategy for solvig the puzzle or wiig the game. 176 Grades 9 to 12 Mathematics: Maitoba Curriculum Framework of Outcomes (2014)

9 Grade 12 Essetial Mathematics Half Course VI [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E6.H.1. Strad: Home Fiace Specific Learig Outcomes It is expected that studets will: Solve problems ivolvig the purchase ad maiteace of a house. [C, CN, ME, R, T] Geeral Learig Outcome: Develop a uderstadig of housig costs. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Solve a problem ivolvig mortgages. Describe the costs ivolved i purchasig a home, such as closig costs, lad trasfer tax, lawyer s fees, house isurace, ad movig expeses. Solve a problem ivolvig home isurace optios. Discuss the differece betwee prevetative maiteace ad emergecy repair costs. Compare the beefits of owig ad retig a house. Discuss eergy efficiecy optios ad the immediate ad log-term impact o your housig costs. Discuss the daily costs ivolved with home maiteace. Determie the property tax for a house. Determie the ecoomic feasibility of a home purchase usig the Gross Debt Service Ratio. Geeral ad Specific Learig Outcomes 177

10 Grade 12 Essetial Mathematics Half Course VI [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E6.G.1. 12E6.G.2. Strad: Geometry ad Trigoometry Specific Learig Outcomes It is expected that studets will: Solve problems by usig the sie law ad cosie law, excludig the ambiguous case. [CN, PS, V] Solve problems that ivolve triagles quadrilaterals regular polygos [C, CN, PS, V] Geeral Learig Outcome: Develop spatial sese ivolvig polygos. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Idetify ad describe the use of the sie law or cosie law i costructio, idustrial, commercial, or artistic applicatios. Solve a problem, usig the sie law or cosie law, whe a diagram is give. Describe ad illustrate properties of triagles, icludig isosceles or equilateral. Describe ad illustrate properties of quadrilaterals i terms of agle measures, side legths, diagoals, or agles of itersectio. Describe ad illustrate properties of regular polygos. Explai, usig examples, why a give property does or does ot apply to certai polygos. Idetify ad explai a applicatio of the properties of polygos i costructio, idustrial, commercial, domestic, or artistic cotexts. Solve a cotextual problem that ivolves the applicatio of the properties of polygos. 178 Grades 9 to 12 Mathematics: Maitoba Curriculum Framework of Outcomes (2014)

11 Grade 12 Essetial Mathematics Half Course VI [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E6.B.1. 12E6.B.2. Strad: Busiess Fiace Specific Learig Outcomes It is expected that studets will: Critique the viability of small busiess optios by cosiderig expeses sales profit or loss [C, CN, R] Demostrate a awareess of the govermet taxatio forms ad procedures ivolved i owig a busiess. [C, CN] Geeral Learig Outcome: Develop a uderstadig of busiess fiace. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Idetify expeses i operatig a small busiess, such as a hot-dog stad or a law maiteace compay. Idetify feasible small busiess optios for a give commuity. Geerate optios that might improve the profitability of a small busiess. Determie the break-eve poit for a small busiess. Explai factors, such as seasoal variatios ad hours of operatio, that might affect the profitability of a small busiess. Idetify receipts eeded to be retaied for icome tax forms. Idetify appropriate deductios that ca be claimed uder busiess expeses but ot uder persoal expeses. Idetify the major sectios of the T-1 Geeral Icome Tax Form ad related schedules. Geeral ad Specific Learig Outcomes 179

12 Grade 12 Essetial Mathematics Half Course VI [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 12E6.P.1. Strad: Probability Specific Learig Outcomes It is expected that studets will: Aalyze ad iterpret problems that ivolve probability. [C, CN, PS, R] Geeral Learig Outcome: Develop critical thikig skills related to ucertaity. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific learig outcome. Describe ad explai the applicatios of probability, such as medicatio, warraties, isurace, lotteries, weather predictio, 100-year flood, failure of a desig, failure of a product, vehicle recalls, or approximatio of area. Determie the probability of a evet based o a data set. Express a give probability as a fractio, decimal, percet, or i a statemet. Determie the expected gai or loss of a situatio. Explai the differece betwee odds ad probability. Determie the probability of a evet, give the odds for or agaist. Explai, usig examples, how decisios may be based o a combiatio of theoretical probability calculatios, experimetal results, ad subjective judgmets. Solve a cotextual problem that ivolves a probability. 180 Grades 9 to 12 Mathematics: Maitoba Curriculum Framework of Outcomes (2014)

Consortium: North Carolina Community Colleges

Consortium: North Carolina Community Colleges Associatio of Research Libraries / Texas A&M Uiversity www.libqual.org Cotributors Collee Cook Texas A&M Uiversity Fred Heath Uiversity of Texas BruceThompso Texas A&M Uiversity Martha Kyrillidou Associatio