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!BOUT 4HE 5NIVERSITY OF 4EXAS AT !USTIN #HARLES ! ANA #ENTER 4HE #HARLES ! ANA #ENTER SUPPORTS TEACHERS EDUCATION LEADERS AND POLICYMAKERS IN STRENGTHENING EDUCATION !S A RESEARCH UNIT OF 4HE 5NIVERSITY OF 4EXAS AT !USTIN S #OLLEGE OF .ATURAL 3CIENCES THE ANA #ENTER MAINTAINS A SPECIAL EMPHASIS ON MATHEMATICS AND SCIENCE EDUCATION 4HE ANA #ENTER S MISSION IS TO STRENGTHEN THE MATHEMATICS AND SCIENCE PREPARATION AND ACHIEVEMENT OF ALL STUDENTS THROUGH SUPPORTING ALIGNMENT OF ALL THE KEY COMPONENTS OF MATHEMATICS AND SCIENCE EDUCATION PREKINDERGARTENn THE STATE STANDARDS ACCOUNTABILITY SYSTEM ASSESSMENT AND TEACHER PREPARATION 7E FOCUS OUR EFFORTS ON PROVIDING RESOURCES TO HELP LOCAL COMMUNITIES MEET THE DEMANDS OF THE EDUCATION SYSTEM BY WORKING WITH LEADERS TEACHERS AND STUDENTS THROUGH OUR )NSTRUCTIONAL 3UPPORT 3YSTEM BY STRENGTHENING MATHEMATICS AND SCIENCE PROFESSIONAL DEVELOPMENT AND BY PUBLISHING AND DISSEMINATING MATHEMATICS AND SCIENCE EDUCATION RESOURCES !BOUT THE DEVELOPMENT OF THIS BOOK 4HE #HARLES ! ANA #ENTER HAS DEVELOPED THIS STANDARDS ALIGNED MATHEMATICS EDUCATION RESOURCE FOR MATHEMATICS TEACHERS 4HE DEVELOPMENT AND PRODUCTION OF THE lRST EDITION OF !LGEBRA )) !SSESSMENTS WAS SUPPORTED IN PART BY THE 4EXAS %DUCATION !GENCY THE .ATIONAL 3CIENCE &OUNDATION UNDER COOPERATIVE AGREEMENT %32 AND THE #HARLES ! ANA #ENTER AT 4HE 5NIVERSITY OF 4EXAS AT !USTIN 4HE DEVELOPMENT AND PRODUCTION OF THIS SECOND EDITION WAS SUPPORTED BY THE #HARLES ! ANA #ENTER !NY OPINIONS lNDINGS CONCLUSIONS OR RECOMMENDATIONS EXPRESSED IN THIS MATERIAL ARE THOSE OF THE AUTHOR S AND DO NOT NECESSARILY REmECT THE VIEWS OF THE 4EXAS %DUCATION !GENCY THE .ATIONAL 3CIENCE &OUNDATION OR 4HE 5NIVERSITY OF 4EXAS AT !USTIN 4HE SECOND EDITION UPDATES THE 4EXAS %SSENTIAL NOWLEDGE AND 3KILLS STATEMENTS AND ALIGNMENT CHARTS TO ALIGN WITH THE STATE S n REVISIONS TO THE -ATHEMATICS 4% 3 4HE ASSESSMENTS THEMSELVES HAVE NOT BEEN UPDATED 4HE SECOND EDITION HAS ALSO BEEN RE EDITED FOR CLARITY AND TO CORRECT SOME MINOR ERRORS 4HE 5NIVERSITY OF 4EXAS AT !USTIN 4HE #HARLES ! ANA #ENTER .ORTH )( 3UITE !USTIN 4EXAS WWW UTDANACENTER ORG PPP
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/UR 4HANKS &IRST %DITION !LGEBRA )) !SSESSMENTS !DVISORY 4EAM "EVERLY !NDERSON #ECILIA !VENDANO 4OMMY "RYAN .ICK #ARTER ,IBBY #HASKIN /SCAR #HAVARRIA ATHI #OOK "ETH 'LASSMAN 'AYE 'LENN "ASIA (ALL 0AM (ARRIS 3USAN (UDSON (ULL (EE *OON IM ,AURIE -ATHIS 3USAN -AY IANE -C'OWAN 0AUL -LAKER "ARBARA -ONTALTO 2ICHARD 0ARR %RIKA 0IERCE 4IM 0OPE IANE 2EED 7ARD 2OBERTS 2OZANNE 2UBIN #INDY 3CHIMEK ICK 3TANLEY 3USAN 4HOMAS "EVERLY 7ELDON 3USAN 7ILLIAMS *EANNE 7OMACK 2EGION 86)) %DUCATION 3ERVICE #ENTER "ROWNSVILLE )NDEPENDENT 3CHOOL ISTRICT "AYLOR 5NIVERSITY )NDEPENDENT #ONSULTANT .ORTHSIDE )NDEPENDENT 3CHOOL ISTRICT 0ASADENA )NDEPENDENT 3CHOOL ISTRICT #HARLES ! ANA #ENTER ,EANDER )NDEPENDENT 3CHOOL ISTRICT 2EGION )) %DUCATION 3ERVICE #ENTER (OUSTON )NDEPENDENT 3CHOOL ISTRICT #ONSULTANT #HARLES ! ANA #ENTER #HARLES ! ANA #ENTER #HARLES ! ANA #ENTER #ONSULTANT #HARLES ! ANA #ENTER 2EGION )6 %DUCATION 3ERVICE #ENTER 4EXAS %DUCATION !GENCY 2ICE 5NIVERSITY #HARLES ! ANA #ENTER (AYS )NDEPENDENT 3CHOOL ISTRICT 9SLETA )NDEPENDENT 3CHOOL ISTRICT 7ICHITA &ALLS )NDEPENDENT 3CHOOL ISTRICT !LIEF )NDEPENDENT 3CHOOL ISTRICT ATY )NDEPENDENT 3CHOOL ISTRICT 5NIVERSITY OF #ALIFORNIA "ERKELEY !LAMO (EIGHTS )NDEPENDENT 3CHOOL ISTRICT 2EGION 8 %DUCATION 3ERVICE #ENTER 5NIVERSITY OF (OUSTON 2EGION ) %DUCATION 3ERVICE #ENTER 7ITH SPECIAL THANKS TO THE TEACHERS AND MATHEMATICS SUPERVISORS WHO REVIEWED AND lELD TESTED THE !LGEBRA )) !SSESSMENTS lRST EDITION !RACELI !VILA 2EGION 88 %DUCATION 3ERVICE #ENTER -ARIA !RACELI #ASTILLO ,ANIER (IGH 3CHOOL ,IBBY #HASKIN .ORTHSIDE )3 4ERY #HAVEZ *OHN *AY (IGH 3CHOOL 2ENEAN #OWAN (ONDO (IGH 3CHOOL 0ATRICIA UNLEVY 0LEASANTON (IGH 3CHOOL ,INDA %VANS (EALTH #AREERS (IGH 3CHOOL 2ENEE &ERGUSON %AST #ENTRAL (IGH 3CHOOL *ESSICA 'ARCIA ,ANIER (IGH 3CHOOL !NN 'REENE 0LEASANTON (IGH 3CHOOL 7ALTER *OHNSON -ARSHAL (IGH 3CHOOL "ARBARA IPLING 2ANDOLPH (IGH 3CHOOL "ONNIE NAPE .ORTHSIDE )3 *ANE -ARRONE (OLMES (IGH 3CHOOL ,ORI -URACH .ORTHEAST )3 "ILL .ORTHUP 7ARREN (IGH 3CHOOL "EN 0ENA 0OTEET (IGH 3CHOOL %RIKA 2OBERTS 2EGION 88 %DUCATION 3ERVICE #ENTER -IKE 3TANLEY / #ONNOR (IGH 3CHOOL 3HERRY 3UMERLIN *UDSON (IGH 3CHOOL AREN 4ALIAFERRO -ADISON (IGH 3CHOOL .ORMA 4ORRES -ARTINEZ 2EGION 88 %DUCATION 3ERVICE #ENTER ONNA 4ROTT (ONDO (IGH 3CHOOL "RENDA 6ANEK *UDSON (IGH 3CHOOL ,U!NN 7EYNAND .ORTHEAST )3 -ERCILLE 7ISAKOWSKY !LAMO (EIGHTS (IGH 3CHOOL *UDY 7RIGHT ,ANIER (IGH 3CHOOL *OHN :UKOWSKI #LARK (IGH 3CHOOL ]PP
4% 3 AND 4! 3 2ESOURCES 4HE MATHEMATICS 4EXAS %SSENTIAL NOWLEDGE AND 3KILLS 4% 3 WERE DEVELOPED BY THE STATE OF 4EXAS TO CLARIFY WHAT ALL STUDENTS SHOULD KNOW AND BE ABLE TO DO IN MATHEMATICS IN KINDERGARTEN THROUGH GRADE ISTRICTS ARE REQUIRED TO PROVIDE INSTRUCTION THAT IS ALIGNED WITH THE MATHEMATICS 4% 3 WHICH WERE ORIGINALLY ADOPTED BY THE 3TATE "OARD OF %DUCATION IN AND IMPLEMENTED STATEWIDE IN 2EVISIONS TO THE -ATHEMATICS 4% 3 WERE ADOPTED IN n AND IMPLEMENTED STARTING IN &ALL 4HE MATHEMATICS 4% 3 ALSO FORM THE OBJECTIVES AND STUDENT EXPECTATIONS FOR THE MATHEMATICS PORTION OF THE 4EXAS !SSESSMENT OF NOWLEDGE AND 3KILLS 4! 3 4HE MATHEMATICS 4% 3 CAN BE DOWNLOADED IN PRINTABLE FORMAT FREE OF CHARGE FROM THE ANA #ENTER S -ATHEMATICS 4% 3 4OOLKIT WEBSITE WWW MATHTEKSTOOLKIT ORG 0ERFECT BOUND AND SPIRAL BOUND VERSIONS OF THE MATHEMATICS AND SCIENCE 4% 3 BOOKLETS ARE AVAILABLE FOR A FEE TO COVER THE COSTS OF PRODUCTION FROM THE #HARLES ! ANA #ENTER AT 4HE 5NIVERSITY OF 4EXAS AT !USTIN WWW UTDANACENTER ORG 2ESOURCES FOR IMPLEMENTING THE MATHEMATICS 4% 3 ARE AVAILABLE THROUGH THE #HARLES ! ANA #ENTER REGIONAL EDUCATION SERVICE CENTERS AND THE 4EXAS %DUCATION !GENCY /NLINE RESOURCES CAN BE FOUND AT IN THE ANA #ENTER S -ATHEMATICS 4% 3 4OOLKIT AT WWW MATHTEKSTOOLKIT ORG 4HE FOLLOWING PRODUCTS AND SERVICES ARE ALSO AVAILABLE FROM THE ANA #ENTER AT WWW UTDANACENTER ORG CATALOG % 2EVISED -ATHEMATICS 4% 3 BOOKLETS AND -ATHEMATICS 4% 3 CHARTS FOR n AND n % -ATHEMATICS 3TANDARDS IN THE #LASSROOM 2ESOURCES FOR 'RADES n AND n % -IDDLE 3CHOOL -ATHEMATICS !SSESSMENTS 0ROPORTIONAL 2EASONING % 'EOMETRY !SSESSMENTS % !LGEBRA ) !SSESSMENTS % 0ROFESSIONAL DEVELOPMENT FOR MATHEMATICS AND SCIENCE TEACHERS s 0ROFESSIONAL DEVELOPMENT MODULES FOR EDUCATORS INCLUDING ADMINISTRATORS TEACHERS AND OTHER LEADERS ]PPP
#/.4%.43 )NTRODUCTION XI !LGEBRA )) 3OLUTION 'UIDE XIV !SSESSMENT !LIGNMENT TO 4% 3 AND 4! 3 XV 4% 3 AND 4! 3 !LIGNMENT TO !SSESSMENT XVII #HAPTER &OUNDATIONS OF &UNCTIONS (IT THE 7ALL 7ALK THE 9O 9O 0IZZA 7ARS #ATCH )T #HAPTER 4RANSFORMATIONS ATA ILEMMA 3LIP 3LIDING !WAY 4RANSFORMATION 4WO 3TEP )NVESTIGATING THE %FFECT OF A H AND K ON Y A X %XPONENTIAL &UNCTION 0ARAMETERS ,OGARITHMIC &UNCTION 0ARAMETERS H K #HAPTER ,INEAR 3YSTEMS ! ,INEAR 0ROGRAMMING 0ROBLEM 0ARKING AT THE -ALL 4HE -ILD AND 7ILD !MUSEMENT 0ARK 7EATHER 7OES #HAPTER 1UADRATIC &UNCTIONS "ASKETBALL 4HROW &IXED 0ERIMETER 2ECTANGLES -OTION 5NDER 'RAVITY 0ARABOLIC 0ATHS 4RIANGLE 3OLUTIONS 3PINNING 3QUARE 4ORRICELLI S ,AW OING 7HAT -ATHEMATICIANS O &IXED !REA 2ECTANGLES #OMPARING 6OLUMES P
#HAPTER 3QUARE 2OOT &UNCTIONS ) #AN 3EE &OREVER ) 7AS 'OING (OW &AST 4IC 4OC #HAPTER %XPONENTIAL AND ,OGARITHMIC &UNCTIONS ESERT "IGHORN 3HEEP #OMPARING AN %XPONENTIAL &UNCTION AND )TS )NVERSE 3AVING -ONEY -AKING -ONEY ! 'RADUATION 0RESENT #HAPTER 2ATIONAL &UNCTIONS 0AINTINGS ON A 7ALL 3ALINE 3OLUTION 0IZZA 7ARS 0ART 9OU RE 4OAST UDE 7HAT S -Y %QUATION #HAPTER #ONICS #ONTEMPLATING #OMETS ,OST IN 3PACE ALOTONIC APER
)NTRODUCTION 4HE IMPORTANCE OF MATHEMATICS ASSESSMENT 4HE ANA #ENTER DEVELOPED !LGEBRA )) !SSESSMENTS AS A RESOURCE FOR TEACHERS TO USE TO PROVIDE ONGOING ASSESSMENT INTEGRATED WITH !LGEBRA )) MATHEMATICS INSTRUCTION 4HE .ATIONAL #OUNCIL OF 4EACHERS OF -ATHEMATICS LISTS AS ONE OF ITS SIX PRINCIPLES FOR SCHOOL MATHEMATICS THAT h!SSESSMENT SHOULD SUPPORT THE LEARNING OF IMPORTANT MATHEMATICS AND FURNISH USEFUL INFORMATION TO BOTH TEACHERS AND STUDENTS v &URTHER .#4- IDENTIlED THE FOLLOWING SIX STANDARDS TO GUIDE CLASSROOM ASSESSMENT 4HE -ATHEMATICS 3TANDARD 4HE ,EARNING 3TANDARD 4HE %QUITY 3TANDARD 4HE /PENNESS 3TANDARD 4HE )NFERENCES 3TANDARD 4HE #OHERENCE 3TANDARD !SSESSMENT SHOULD REmECT THE MATHEMATICS THAT ALL STUDENTS NEED TO KNOW AND BE ABLE TO DO !SSESSMENT SHOULD ENHANCE MATHEMATICS LEARNING !SSESSMENT SHOULD PROMOTE EQUITY !SSESSMENT SHOULD BE AN OPEN PROCESS !SSESSMENT SHOULD PROMOTE VALID INFERENCES ABOUT MATHEMATICS LEARNING !SSESSMENT SHOULD BE A COHERENT PROCESS 7HAT ARE THE !LGEBRA )) !SSESSMENTS 4EACHERS CAN USE THESE !LGEBRA )) !SSESSMENTS TO PROVIDE ONGOING ASSESSMENT INTEGRATED WITH !LGEBRA )) INSTRUCTION 4HE PERFORMANCE TASKS WHICH EMBODY WHAT ALL STUDENTS NEED TO KNOW AND BE ABLE TO DO IN A HIGH SCHOOL !LGEBRA )) COURSE MAY BE USED FOR FORMATIVE SUMMATIVE OR ONGOING ASSESSMENT 4HE TASKS ARE DESIGNED TO DIAGNOSE STUDENTS UNDER STANDING OF CONCEPTS AND THEIR PROCEDURAL KNOWLEDGE RATHER THAN SIMPLY DETERMINE WHETHER THEY REACHED THE hRIGHTv OR hWRONGv ANSWERS 4EACHERS SHOULD ASSESS FREQUENTLY TO MONITOR INDIVIDUAL PERFORMANCE AND GUIDE INSTRUCTION 4HE PURPOSE OF THESE ASSESSMENTS IS TO % CLARIFY FOR TEACHERS STUDENTS AND PARENTS WHAT IS BEING TAUGHT AND LEARNED IN !LGEBRA )) % HELP TEACHERS GAIN EVIDENCE OF STUDENT INSIGHT AND MISCONCEPTIONS TO USE AS A BASIS FOR INSTRUCTIONAL DECISIONS AND s PROVIDE TEACHERS WITH QUESTIONING STRATEGIES TO GUIDE INSTRUCTION AND ENHANCE STUDENT LEARNING .ATIONAL #OUNCIL OF 4EACHERS OF -ATHEMATICS 0RINCIPLES AND 3TANDARDS FOR 3CHOOL -ATHEMATICS 2ESTON 6! .ATIONAL #OUNCIL OF 4EACHERS OF -ATHEMATICS 3UMMARY AVAILABLE AT STANDARDS NCTM ORG .ATIONAL #OUNCIL OF 4EACHERS OF -ATHEMATICS !SSESSMENT 3TANDARDS FOR 3CHOOL -ATHEMATICS 2ESTON 6! .ATIONAL #OUNCIL OF 4EACHERS OF -ATHEMATICS PAGES AND P
7HAT S NEW 4HE lRST EDITION OF !LGEBRA )) !SSESSMENTS WAS PUBLISHED IN )N THIS SECOND EDITION WE HAVE INCLUDED THE REVISED SECONDARY MATHEMATICS 4EXAS %SSENTIAL NOWLEDGE AND 3KILLS AND UPDATED THE 4% 3 ALIGNMENT CHARTS (OW DO THE ASSESSMENTS SUPPORT 4% 3 BASED INSTRUCTION %ACH PERFORMANCE TASK IN THE ASSESSMENTS BOOK % IS ALIGNED WITH THE REVISED !LGEBRA )) 4% 3 STUDENT EXPECTATIONS % IS ALIGNED WITH THE GRADE EXIT LEVEL 4EXAS !SSESSMENT OF NOWLEDGE AND 3KILLS 4! 3 OBJECTIVES AND % IS ALIGNED WITH A ANA #ENTER 4%84%!-3 INSTITUTE 0RACTICE "ASED 0ROFESSIONAL EVELOPMENT !LGEBRA )) !SSESSMENTS (OW ARE THE ASSESSMENTS STRUCTURED 4EACHERS MAY USE THESE ASSESSMENTS FORMATIVELY OR SUMMATIVELY FOR INDIVIDUAL STUDENTS OR GROUPS OF STUDENTS %ACH ASSESSMENT s INCLUDES A PERFORMANCE TASK s IS ALIGNED WITH THE !LGEBRA )) MATHEMATICS 4% 3 KNOWLEDGE AND SKILLS AS WELL AS STUDENT EXPECTATIONS s IS ALIGNED WITH THE 4! 3 OBJECTIVES s INCLUDES hSCAFFOLDINGv QUESTIONS THAT THE TEACHER MAY USE TO HELP THE STUDENT ANALYZE THE PROBLEM s PROVIDES A SAMPLE SOLUTION AND s INCLUDES EXTENSION QUESTIONS TO BRING OUT ADDITIONAL MATHEMATICAL CONCEPTS IN A SUMMATIVE DISCUSSION OF SOLUTIONS TO THE PROBLEM 4HE SAMPLE SOLUTION IS ONLY ONE WAY THAT A PERFORMANCE TASK MAY BE APPROACHED AND IS NOT NECESSARILY THE hBESTv SOLUTION &OR MANY OF THE TASKS THERE ARE OTHER APPROACHES THAT WILL ALSO PROVIDE A CORRECT ANALYSIS OF THE TASK 4HE AUTHORS HAVE ATTEMPTED TO ILLUSTRATE A VARIETY OF MATHEMATICAL APPROACHES IN THE VARIOUS SAMPLE SOLUTIONS 3EVERAL OF THE ASSESSMENTS ALSO INCLUDE SAMPLES OF ANONYMOUS STUDENT WORK !LGEBRA )) !SSESSMENTS PRESENTS PERFORMANCE TASKS BASED ON THE lVE STRANDS IN THE !LGEBRA )) 4% 3 WE HAVE SUBDIVIDED THE TASKS INTO EIGHT CATEGORIES PP &OUNDATIONS OF &UNCTIONS 4RANSFORMATIONS ,INEAR 3YSTEMS 1UADRATIC &UNCTIONS 3QUARE 2OOT &UNCTIONS %XPONENTIAL AND ,OGARITHMIC &UNCTIONS 2ATIONAL &UNCTIONS #ONICS
7HAT IS THE SOLUTION GUIDE 4HE SOLUTION GUIDE IS A ONE PAGE PROBLEM SOLVING CHECKLIST IN THE FRONT OF THE BOOK THAT TEACHERS MAY USE TO TRACK WHAT IS NECESSARY FOR A STUDENT TO GIVE A COMPLETE SOLUTION FOR A PERFORMANCE TASK BECAUSE STUDENTS NEED TO KNOW WHAT CRITERIA THEY ARE EXPECTED TO MEET IN THEIR SOLUTIONS 7HEN ASSIGNING THE PERFORMANCE TASK THE TEACHER CAN GIVE STUDENTS COPIES OF A SOLUTION GUIDE CUSTOMIZED WITH MARKS INDICATING WHICH OF THE CRITERIA SHOULD BE CONSIDERED IN THE PERFORMANCE TASK ANALYSIS &OR MOST PERFORMANCE TASKS ALL THE CRITERIA WILL BE IMPORTANT BUT INITIALLY THE TEACHER MAY WANT TO FOCUS ON ONLY TWO OR THREE CRITERIA /N THE PAGE BEFORE A STUDENT WORK SAMPLE WE PROVIDE COMMENTS ON SOME OF THE SOLUTION CRITERIA THAT ARE EVIDENT FROM THE STUDENT S SOLUTION 4HE PROFESSIONAL DEVELOPMENT EXPERIENCE DESCRIBED BELOW WILL HELP THE TEACHER USE THE SOLUTION GUIDE IN THE CLASSROOM AND WILL ALSO HELP GUIDE THE TEACHER TO USE OTHER ASSESSMENT EVALUATION TOOLS 7HERE CAN ) GET A COPY OF !LGEBRA )) !SSESSMENTS SECOND EDITION !LGEBRA )) !SSESSMENTS SECOND EDITION IS AVAILABLE FOR PURCHASE IN BOOK OR # 2/FORMAT BY VISITING OUR ONLINE CATALOG AT WWW UTDANACENTER ORG CATALOG 4HE SECOND EDITION OF !LGEBRA )) !SSESSMENTS OR A PORTION THEREOF IS ALSO AVAILABLE FREE OF CHARGE FROM THE ANA #ENTER S MATHEMATICS TOOLKIT AT WWW MATHTEKSTOOLKIT ORG )S PROFESSIONAL DEVELOPMENT AVAILABLE TO SUPPORT THE !LGEBRA )) !SSESSMENTS 9ES 4HE ANA #ENTER HAS DEVELOPED A THREE DAY 4%84%!-3 INSTITUTE THAT FOCUSES ON THE IMPLEMENTATION OF THE ASSESSMENTS 4%84%!-3 0RACTICE "ASED 0ROFESSIONAL EVELOPMENT !LGEBRA )) !SSESSMENTS 0ARTICIPANTS IN THESE INSTITUTES WILL % EXPERIENCE SELECTED ASSESSMENTS % ANALYZE STUDENT WORK TO EVALUATE STUDENT UNDERSTANDING % CONSIDER METHODS FOR EVALUATING STUDENT WORK % VIEW A VIDEO OF STUDENTS WORKING ON THE ASSESSMENTS % DEVELOP STRATEGIES FOR CLASSROOM IMPLEMENTATION AND % CONSIDER HOW THE ASSESSMENTS SUPPORT THE 4! 3 #ONTACT YOUR LOCAL SCHOOL DISTRICT OR REGIONAL SERVICE CENTER TO lND OUT WHEN THESE INSTITUTES ARE OFFERED PPP
P] 4HE TEACHER WILL MARK THE CRITERIA TO BE CONSIDERED IN THE SOLUTION OF THIS PARTICULAR PROBLEM #RITERIA 5SES APPROPRIATE TOOLS 5SES CORRECT TERMINOLOGY AND NOTATION 3TATES A CLEAR AND ACCURATE SOLUTION USING CORRECT UNITS #OMMUNICATES A CLEAR DETAILED AND ORGANIZED SOLUTION STRATEGY )NTERPRETS THE REASONABLENESS OF ANSWERS IN THE CONTEXT OF THE PROBLEM EMONSTRATES ALGEBRA CONCEPTS PROCESSES AND SKILLS 5SES MULTIPLE REPRESENTATIONS SUCH AS TABLES GRAPHS SYMBOLS VERBAL DESCRIPTIONS CONCRETE MODELS AND MAKES CONNECTIONS AMONG THEM )NTERPRETS FUNCTIONAL RELATIONSHIPS CORRECTLY ElNES VARIABLES APPROPRIATELY USING CORRECT UNITS ESCRIBES FUNCTIONAL RELATIONSHIPS !LGEBRA )) 3OLUTION 'UIDE #HECK IF SOLUTION SATISlES THIS CRITERIA
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Introduction A description logic (DL) knowledge base (KB) consists of a terminological box (TBox), storing conceptual knowledge, and an assertion box (ABox), storing data. Typical applica-tions of KBs involve answering queries over incomplete data sources (ABoxes) augmented by ontologies (TBoxes) that provide additional information about the domain of interest as well as a convenient .
Loughborough College Local Offer Des Gentleman Learner Services Manager des.gentleman@loucoll.ac.uk . 2 Regulation 3 Special Educational Needs and Disability (Information) Regulations (2014) School/College Name: Loughborough College Address: Radmoor Road, Loughborough, Leicestershire Telephone Number: 01509 618375 Principal and CEO: Jo Maher Executive Lead Learner Services: Heather Clarke .
Sanjeev Agarwal, Guide to Indian Capital Market, Bharat Law House, 2009 5. Imaad A Moosa, Foreign Direct Investment: Theory Evidence and Practice, Palgrave MacMillan, 2010. 6. Niti Bhasin, FDI In India, New Century Publication, 2008. 6 Paper – VII L4 RTDA2 C5 Subject: Corporate Taxation Paper Code: CRL 114 Unit-I: Income Tax 1. Type of Companies – (a) Indian Company (b) Domestic Company (c .
2.3 Gresham’s Law 2.4 Money and near money 2.5 Role of money in Capitalist, Socialist and mixed Economy 3. Money Supply and Banks (14) 3.1 Narrow and broad definition of money 3.2 Alternative measures of money supply in India and their components 3.3 Concept of High Powered Money 3.4 Definition of Bank – Functions of bank 3.5 Multiple credit creation by bank and limitations to it. 4 .
85% of chemistry students graduated with upper-second or first-class honours in 2019. School of Chemistry bristol.ac.uk/chemistry Full time work Full time education Part time work or education Travel Unemployed Other 86% of our 2017 graduates were in work or education six months after graduation Destinations of Leavers from Higher Education Survey 2017, response rate 90%. School of Chemistry .
constant evolution, including in the post-Cold War era; now China wants to drive a new set of changes. While China under Xi Jinping expresses a sense of confidence, even hubris, about its capacity .
Bond Mathematics & Valuation Below is some legalese on the use of this document. If you’d like to avoid a headache, it basically asks you to use some common sense. We have put some effort into this, and we want to keep the credit, so don’t remove our nam e.
