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DOCUMENT RESUME
ED 357 275 CE 063 744
TITLE Mathematics. Ohio's Competency Analysis Profile.INSTITUTION Ohio State Univ., Columbus. Vocational Instructional
Materials Lab.SPONS AGENCY Ohio State Dept. of Education, Columbus. Div. of
Vocational and Career Education.PUB DATE Aug 92NOTE 127p.; For related documents, see ED 338 827-852, ED
345 048-082, and CE 063 711 and CE 063 743.AVAILABLE FROM Vocational Instructional Materials Lab, Ohio State
University, 1900 Kenny Road, Columbus, OH 43210-1090($1.50).
PUB TYPE Guides Classroom Use Teaching Guides (ForTeacher) (052)
EDRS PRICE MF01/PC06 Plus Postage.DESCRIPTORS Algebra; Competency eased Education; *Correlation;
Data Analysis; Geometry; Mathematical Applications;*Mathematics Skills; Measurement; *MinimumCompetencies; Models; Number Concepts; Numeracy;Probability; Secondary Education; Statewide Planning;*Vocational Education
IDENTIFIERS *Ohio Competency Analysis Profiles
ABSTRACT
This competency analysis profile contains eight listsof mathematics skills that have been identified by employers andverified by math-certified instructors as being core competencies foreight groups of occupational areas. Each list is organized intosubsections dealing with the following: numbers and number relations,measurement, data analysis and probability, algebra, and geometry.The following are among the broad categories of occupations includedin the eight occupational groups: business, marketing, and lawenforcement; agriculture and horticulture; agricultural and automechanics; building trades; allied health occupations; homeeconomics-related, food service, and hospitality occupations;commercial and graphic arts; and technical occupations and machinetrades. Also included in this competency analysis profile arecross-reference charts illustrating the correlation between theidentified competencies and the Ohio Model Competency-BasedMathematics Program. A copy of the Ohio Model Competency-BasedMathematics Program concludes the profile. (MN)
***********************************************************************
Reproductions supplied by EDRS are the best that can be madefrom the original document.
***********************************************************************
OHIO'S COMPETENCY ANALYSIS PROFILE
MATHEMATICS
This OCAP contains eight core mathematics lists thatcorrespond to forty-nine occupational areas, whichhave been divided into eight groups. The corecompetencies have been identified by employers andverified by math-certified instructors. Also includedin this OCAP are cross-reference charts that show the
correlation between these competencies and the Ohio
Model Competency-Based Mathematics Program.U S. DEPARTMENT OF EDUCATION
Once of Educatmeubt Rueetcn and Improvement
EOI CATIONAL RESOURCES INFORMATIONCENTER (ERIC)
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PERMISSION TO REPRODUCE THIS
MATERIAL HAS BEEN GRANTED BY
TO THE EDUCATIONAL RESOURCES
INFORMATION CENTER (ERIC).-
noational Instructional Materials LaboratoryCenter on Education and Training
for Employment
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UNIVERSITY
This OCAP is divided into eight lists that correspondto the following groups of occupational areas.
Group AAccountingAdministrative /Secretarial ServicesBusiness Administration and ManagementBusiness Information SystemsEntertainment MarketingGeneral MaletingLaw EnforcementTravel and Tourism Marketing
Group BAgricultural Business Feed and Grain WorkerAgricultural ProductionAgricultural Products Sales and Service WorkerAnimal Management TechnicianFertilizer /Chemical Sales and Service WorkerFloriculture and Greenhouse WorkerForest Industry WorkerHorticultureNatural Resource.Nursery and Garata Center WorkerResource ConservationTurf and Landscape Worker
Group CAgricultural/Industrial Mechanical
TechnicianAuto Collision TechnicianAuto MechanicsDiesel MechanicsPower Equipment Technology
3
Group DBuilding and Property MaintenanceCarpentryHeating, Ventilation, Air-Conditioning, and
RefrigerationMasonryWelding
Group EDental AssistantDiversified Health OccupationsMedical- kfsrstantNurse AidePractical Nursing
Group FClothing and Interiors, Production and ServicesCosmetologyEarly Childhood Education and CareFood Production, Management, and ServicesHospitality and Facility Care ServicesMeat Processor
Group GCommercial ArtGraphic Communications:
PhotographyGraphic Communications:
Group HDraftingElectrical TradesElectronicsIndustrial MaintenanceMachine Trades
Commercial
Graphic Arts
Ohio Competency Analysis ProfileMathematics
for
Unit 1:Subunit 1.
AccountingAdministrative /Secretarial Services
Business Administration and ManagementBusiness Information Systems
Entertainment MarketingGeneral MarketingLaw Enforcement
Travel and Tourism Marketing
Numbers and Number Relations1: Group A
Round and/or truncate numbers to designated placevalueCompute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportionsTranslate written and/or verbal statements intomathematical expressionsEstimate answers
Competency 1.1.1:
Competency 1.1.2:
Competency 1.1.3:
Competency 1.1.4:
Competency 1.1.5:
Competency 1.1.6:
Competency 1.1.7:
Competency 1.1.8:
* Advancing** Futuring
1
Mathematics--8/92
Unit 2: MeasurementSubunit 2.1: Group ACompetency 2.1.1: Convert, compare, and compute with common units of
measurement within and/or across measurementsystems
2.1.2: Compute using appropriate units of measurement
2.1.3: Read scale on measurement device(s) to nearest markand make interpolations where appropriate
Competency 2.1.4: Estimate measurements
Competency
Competency
Unit 3: Data Analysis and ProbabilitySubunit 3.1: Group ACompetency
Competency 3.1.2:3.1.1: Interpret and use tables, charts, maps,
Competency 3.1.3:
CompetencyCompetency
Competency
3.1.4:
3.1.5:
3.1.6:
and/or graphsIdentify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphsCollect and organize data into tables, charts, and/orgraphsCompute and interpret mean, median, and/or modeUse elementary notions of probabilityUse problem-solving techniques
Unit 4: AlgebraSubunit 4.1: Group ACompetency 4.1.1: Evaluate and/or simplify algebraic expressions using
simple substitutionsCompetency 4.1.2: Solve linear equations
Competency 4.1.3: Use order of operations to solve problems
Competency 4.1.4: Use formulasCompetency 4.1.5: Compare and compute using scientific notation*
Competency 4.1.6: Use properties of exponents*
* Advancing** Futuring
2
Mathematics--8/92
Unit 5: GeometrySubunit 5.1: Group ACompetency 5.1.1: Find perimeters and areas of geometric figuresCompetency 5.1.2: Find surface areas and volumes of applicable
geometric figuresCompetency 5.1.3: Recognize, classify, and use properties of lines and
anglesCompetency 5.1.4: Recognize, classify, and use properties of two- and
three-dimensional figures (e.g., circles, triangles,rectangles, cylinders)
Competency 5.1.5: Apply Pythagorean theorem*
* Advancing** Futuring
3
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Mathematics--8/92
Ohio Competency Analysis ProfileMathematics
for
Agricultural Business Feed and Grain WorkerAgricultural Production
Agricultural Products Sales and Service WorkerAnimal Management Technician
Fertilizer /Chemical Sales and Service WorkerFloriculture and Greenhouse Worker
Forest Industry WorkerHorticulture
Natural ResourcesNursery and Garden Center Worker
Resource ConservationTurf and Landscape Worker
Unit 1: Numbers and Number RelationsSubunit 1.2: Group B
Round and/or truncate numbers to designated placevalue
Compute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportiorsTranslate written and/or verbal statements intomathematical expressionsEstimate answers
Competency 1.2.1:
Competency 1.2.2:
Competency 1.2.3:
Competency 1.2.4:
Competency 1.2.5:
Competency 1.2.6:
Competency 1.2.7:
Competency 1.2.8:
* Advancing** Futuring
Mathematics--8/92
Unit 2: MeasurementSubunit 2.2: Group BCompetency 2.2.1: Convert, compare, and compute with common units of
measurement within and/or across measurementsystems
Competency 2.2.2: Compute using appropriate units of measurement
Competency 2.2.3: Read scale on measurement device(s) to nearest markand make interpolations where appropriate
Competency 2.2.4: Estimate measurements
Unit 3: Data Analysis and ProbabilitySubunit 3.2: Group BCompetency
Competency
Competency
CompetencyCompetency
Competency
3.2.1: Interpret and use tables, charts, maps, and/or graphs
3.2.2: Identify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphs
3.2.3: Collect and organize data into tables, charts, and/orgraphs
3.2.4: Compute and interpret mean, median, and/or mode
3.2.5: Use elementary notions of probability
3.2.6: Use problem-solving techniques
Unit 4: AlgebraSubunit 4.2: Group BCompetency 4.2.1:
Competency
Competency
Competency
Corn petency
Competency
* Advancing** Futuring
4.2.2:
4.2.3:
4.2.4:
4.2.5:
4.2.6:
Evaluate and/or simplify algebraic expressions usingsimple substitutionsSolve linear equationsUse order of operations to solve problemsUse formdlasUse properties of exponentsDetermine slope, midpoint, and distance
12
Unit 5: GeometrySubunit 5.2: Group BCompetencyCompetency
Competency
Competency
Competency
Competency
* Advancing** Futuring
Mathematics - -8/92
5.2.1: Find perimeters and areas of geometric figures5.2.2: Find surface areas and volumes of applicable
geometric figures5.2.3: Recognize, classify, and use properties of lines and
angles5.2.4: Recognize, classify, and use properties of two- and
three-dimensional figures (e.g., circles, triangles,rectangles, cylinders)
5.2.5: Apply problem solving to geometric figures5.2.6: Apply Pythagorean theorem*
13
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Mathematics--8/92
Ohio Competency Analysis ProfileMathematics
for
Agricultural /Industrial Mechanical TechnicianAuto Collision Technician
Auto MechanicsDiesel Mechanics
Power Equipment Technology
Unit 1: Numbers and Number RelationsSubunit 1.3: Group C
Round and/or truncate numbers to designated placevalueCompute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportionsTranslate written and/or verbal statements intomathematical expressionsEstimate answers
Competency 1.3.1:
Competency 1.3.2:
Competency 1.3.3:
Competency 1.3.4:
Competency 1.3.5:
Competency 1.3.6:
Competency 1.3.7:
Competency 1.3.8:
* Advancing** Futuring
21
Mathematics--8/92
Unit 2: MeasurementSubunit 2.3: Group CCompetency 2.3.1:
Competency 2.3.2:Competency 2.3.3:
Competency 2.3.4:
Convert, compare, and compute with common units ofmeasurement within and/or across measurementsystemsCompute using appropriate units of measurementRead scale on measurement device(s) to nearest markand make interpolations where appropriateEstimate measurements
Unit 3: Data Analysis and ProbabilitySubunit 3.3: Group CCompetency
Competency
Competency
Competency
CompetencyCompetency
3.3.1: Interpret and use tables, charts, maps, and/or graphs3.3.2: Identify patterns, note trends, and/or draw
conclusions from tables, charts, maps, and/or graphs3.3.3: Collect and organize data into tables, charts, and/or
graphs3.3.4: Compute and interpret mean, median, and/or mode
3.3.5: Use elementary notions of probability3.3.6: Use problem-solving techniques
Unit 4; AlgebraSubunit 4.3: Group CCompetency 4.3.1: Evaluate and/or simplify algebraic expressions using
Competency 4.3.2:
Competency 4.3.3:
Competency 4.3.4:
Competency 4.3.5:
Competency 4.3.6:
* Advancing** Futuring
simple substitutionsSolve linear equationsUse order of operations to solve problemsUse formulasDetermine slope, midpoint, and distance*
Graph linear functions*
22
3:;
1
Unit 5: GeometrySubunit 5.3: Group CCompetency 5.3.1:
Competency 5.3.2:
Competency 5.3.3:
Competency 5.3.4:
Competency 5.3.5:
Competency 5.3.6:
* Advancing** Futuring
Mathematics--8/92
Find perimeters and areas of geometric figuresFind surface areas and volumes of applicablegeometric figuresRecognize, classify, and use properties of lines andanglesRecognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)Apply Pythagorean theorem*Describe and apply properties of similar and /orcongruent figures*
23
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Mathematics - -8/92
Ohio Competency Analysis ProfileMathematics
for
Heating,
Building and Property MaintenanceCarpentry
Ventilation, Air-Conditioning, and RefrigerationMasonryWelding
Unit 1: Numbers and Number RelationsSubunit 1.4: Group DCompetency 1.4.1: Round and/or truncate numbers to designated place
value
1.4.2: Compute and solve problems involving integers,fractions, decimals, and percentages using order ofoperations
1.4.3: Compare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)
1.4.4: Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbers
1.4.5: Set up, solve, and apply ratios and proportions1.4.6: Solve problems and make applications involving
integers, fractions, decimals, percentages, ratios, andproportions
1.4.7: Translate written and/or verbal statements intomathematical expressions
1.4.8: Estimate answers
Competency
Competency
Competency
Competency
Competency
Competency
Competency
* Advancing** Futuring
31
45
Mathematics--8/92
Unit 2: MeasurementSubunit 2.4: Group DCompetency 2.4.1:
Competency 2.4.2:Competency 2.4.3:
Competency 2.4.4:
Convert, compare, and compute with common units ofmeasurement within and/or across measurementsystemsCompute using appropriate units of measurementRead scale on measurement device(s) to nearest markand make interpolations where appropriateEstimate measurements
Unit 3: Data Analysis and ProbabilitySubunit 3.4: Group DCompetency 3.4.1: Interpret and use tables, charts, maps, and/or graphs
Competency 3.4.2: Identify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphs
Competency 3.4.3: Collect and organize data into tables, charts, and/orgraphs
Competency 3.4.4: Compute and interpret mean, median, and/or mode
Competency 3.4.5: Use elementary notions of probabilityCompetency 3.4.6: Use problem-solving techniques
Unit 4: AlgebraSubunit 4.4: Group DCompetency 4.4.1: Evaluate and/or simplify algebraic expressions using
simple substitutionsCompetency 4.4.2: Solve linear equations
Competency 4.4.3: Use order of operations to solve problemsCompetency 4.4.4: Use formulas
* Advancing** Futuring
32
Unit 5: GeometrySubunit 5.4: Group DCompetency 5.4.1:Competency 5.4.2:
Competency
Competency
Competency
Competency
* Advancing** Futuring
Mathematics- -8/92
Find perimeters and areas of geometric figuresFind surface areas and volumes of applicablegeometric figures
5.4.3: Recognize, classify, and use properties of linesangles
5.4.4: Recognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)
5.4.5: Apply problem solving to geometric figures
5.4.6: Apply Pythagorean theorem
and
33
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Mathematics--8/92
Ohio Competency Analysis ProfileMathematics
for
Dental AssistantDiversified Health Occupations
Medical AssistantNurse Aide
Practical Nursing
Unit 1: Numbers and Number RelationsSubunit 1.5: Group ECompetency 1.5.1:
Competency 1.5.2:
Competency 1.5.3:
Competency 1.5.4:
Competency 1.5.5:
Competency 1.5.6:
Competency 1.5.7:
Competency 1.5.8:
Competency 1.5.9:
Competency 1.5.10:
* Advancing** Futuring
Round and/or truncate numbers to designated placevalueCompute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios,and proportionsTranslate written and/or verbal statements intomathematical expressionsEstimate answersConvert between Arabic and Roman numeralsSet up problems involving rational numbers
41
Mathematics--8/92
Unit 2: MeasurementSubunit 2.5: Group ECompetency 2.5.1:
Competency 2.5.2:Competency
Convert, compare, and compute with common units ofmeasurement within and/or ac..oss measurementsystemsCompute using appropriate units of measurement
2.5.3: Read scale on measurement device(s) to nearest mark
Competency 2.5.4:
and make interpolations where appropriateEstimate measurements
Unit 3: Data Analysis and ProbabilitySubunit 3.5: Group ECompetency 3.5.1:Competency 3.5.2:
Competency 3.5.3:
CompetencyCompetencyCompetency
3.5.4:
3.5.5:
3.5.6:
Interpret and use tables, charts, maps, and/or graphsIdentify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphsCollect and organize data into tables, charts, and/orgraphsCompute and interpret mean, median, and /or mode
Use elementary notions of probabilityUse problem-solving techniques
Unit 4: AlgebraSubunit 4.5: Group ECompetency 4.5.1: Evaluate andlor simplify algebraic expressions using
simple substitutions4.5.2: Solve linear equations
4.5.3: Use order of operations to solve problems
4.5.4: Use formulas
Competency
Competency
Competency
* Advancing** Futuring
42
Unit 5: GeometrySubunit 5.5: Group ECompetency 5.5.1:
Competency 5.5.2:
Competency 5.5.3:
Competency 5.5.4:
* Advancing** Futuring
Mathematics--8/92
Find perimeters and areas of geometric figuresFind surface areas and volumes of applicablegeometric figuresRecognize, classify, and use properties of lines andanglesRecognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)
43
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8-81
for
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Pro
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cod
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8-81
for
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Com
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Pro
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cod
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CROSS-REFERENCE CHARTGROUP E
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8-81
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8-81
for
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Pro
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cod
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8-81
for
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pete
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mat
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Pro
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cod
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Mathematics--8/92
Ohio Competency Analysis ProfileMathematics
for
Clothing and Interiors, Production and ServicesCosmetology
Early Childhood Education and CareFood Production, Management, and Services
Hospitality and Facility Care ServicesMeat Processor
Unit 1: Numbers and Number RelationsSubunit 1.6: Group FCompetency 1.6.1:
Competency 1.6.2:
Competency 1.6.3:
Competency 1.6.4:
Competency 1.6.5:
Competency 1.6.6:
Competency 1.6.7:
Competency 1.6.8:
* Advancing** Futuring
Round and/or truncate numbers to designated placevalue
Compute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportionsTranslate written and/or verbal statements intomathematical expressionsEstimate answers
t'l e",.)
51
Mathematics--8/92
Unit 2: MeasurementSubunit 2.6: Group FCompetency 2.6.1: Convert, compare, and compute with common units of
measurement within and/or across measurementsystems
Competency 2.6.2: Compute using appropriate units of measurement
Competency 2.6.3: Read scale on measurement device(s) to nearest markand make interpolations where appropriate
Competency 2.6.4: Estimate measurements
Unit 3: Data Analysis and ProbabilitySubunit 3.6: Group FCompetency 3.6.1: Interpret and use tables, charts, maps, and/or graphs
Competency 3.6.2: Identify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphs
Competency 3.6.3: Collect and organize data into tables, charts, and/orgraphs
Competency 3.6.4: Compute and interpret mean, median, and/or mode
Competency 3.6.5: Use elementary notions of probability
Competency 3.6.6: Use problem-solving techniques
Unit 4: AlgebraSubunit 4.6: Group FCompetency 4.6.1: Evaluate and/or simplify algebraic expressions using
simple substitutionsCompetency 4.6.2: Solve linear equations
Competency 4.6.3: Use order of operations to solve problems
Competency 4.6.4: Use formulas
*Advancing 52** Futuring
Unit 5: GeometrySubunit 5.6: Group FCompetency 5.6.1:
Competency 5.6.2:
Competency 5.6.3:
Competency 5.6.4:
* Advancing** Futuring
Mathematics--8/92
Find perimeters and areas of geometric figuresFind surface areas and volumes of applicablegeometric figuresRecognize, classify, and use properties of lines andanglesRecognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)
53
CROSS-REFERENCE CHARTGROUP F
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8-81
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mat
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Mathematics--8/92
Ohio Competency Analysis ProfileMathematics
for
Commercial ArtGraphic Communications: Commercial Photography
Graphic Communications: Graphic Arts
Unit 1: Numbers and Number RelationsSubunit 1.7: Group GCompetency
Competency
Competency
Competency
Competency
Competency
Competency
Competency
1.7.1: Round and/or truncate numbers to designated placevalue
1.7.2: Compute and solve problems involving integers,fractions, decimals, and percentages using order ofoperations
1.7.3: Compare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)
1.7.4: Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbers
1.7.5: Set up, solve, and apply ratios and proportions
1.7.6: Solve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportions
1.7.7: Translate written and/or verbal statements intomathematical expressions
1.7.8: Estimate answers
Unit 2: MeasurementSubunit 2.7: Group GCompetency 2.7.1: Convert, compare, and compute with common units of
measurement within and/or across measurementsystems
2.7.2: Compute using appropriate units of measurement
2.7.3: Read scale on measurement device(s) to nearest markand make interpolations where appropriate
Competency 2.7.4: Estimate measurements
Competency
Competency
* Advancing** Futuring
60
Mathematics--8/92
Unit 3: Data Analysis and ProbabilitySubunit 3.7: Group GCompetency 3.7.1: Interpret and use tables, charts, maps, and/or graphsCompetency 3.7.2: Identify patterns, note trends, and/or draw
conclusions from tables, charts, maps, and/or graphsCompetency 3.7.3: Collect and organize data into tables, charts, and/or
graphsCompetency 3.7.4: Compute and interpret mean, median, and/or modeCompetency 3.7.5: Use elementary notions of probabilityCompetency 3.7.6: Use problem-solving techniques
Unit 4: AlgebraSubunit 4.7: Group GCompetency 4.7.1: Evaluate and/or simplify algebraic expressions using
simple substitutionsCompetency 4.7.2: Solve linear equationsCompetency 4.7.3: Use order of operations to solve problemsCompetency 4.7.4: Use formulas
Unit 5: Geometry6ubunit 5.7: Group G
5.7.1:
5.7.2:
Competency
Competency
Competency 5.7.3:
Competency 5.7.4:
Competency 5.7.5:
* Advancing** Futuring
Find perimeters and areas of geometric figuresFind surface areas and volumes of applicablegeometric figuresRecognize, classify, and use properties of linesanglesRecognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)Describe and apply properties of similar andcongruent figures
and
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CROSS-REFERENCE CHARTGROUP G
Com
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Mathematics- -8/92
Ohio Competency AnalysisMathematics
for
DraftingElectrical Trades
ElectronicsIndustrial Maintenance
Machine Trades
Unit 1: Numbers and Number RelationsSubunit 1.8: Group HCompetency 1.8.1:
Competency 1.8.2:
Competency 1.8.3:
Competency 1.8.4:
Competency 1.8.5:
Competency 1.8.6:
Competency 1.8.7:
Competency 1.8.8:
Competency 1.8.9:
* Advancing** Futuring
Profile
Round and/or truncate numbers to designated placevalue
Compute and solve problems involving integers,fractions, decimals, and percentages using order ofoperationsCompare, order, and determine equivalence of realnumbers (e.g., fractions, decimals, percentages)Estimate, apply, and solve problems involvingfractions, decimals, percentages, and real numbersSet up, solve, and apply ratios and proportionsSolve problems and make applications involvingintegers, fractions, decimals, percentages, ratios, andproportionsTranslate written and/or verbal statements intomathematical expressionsEstimate answersCompare, compute, and solve problems involvingbinary, octal, decimal, and hexadecimal numberingsystems (Electronics Only)
'PO
69
Mathematics-8/92
Unit 2: MeasurementSubunit 2.8: Group HCompetency 2.8.1: Convert, compare, and compute with common units of
measurement within and/or across measurementsystems
2.8.2: Compute using appropriate units of measurement
2.8.3: Read scale on measurement device(s) to nearest markand make interpolations where appropriate
Competency 2.8.4: Estimate measurements
Competency
Competency
Unit 3: Data Analysis and ProbabilitySubunit 3.8: Group HCompetency 3.8.1:Competency 3.8.2:
Competency 3.8.3:
Competency
Competency
Competency
3.8.4:
3.8.5:
3.8.6:
Interpret and use tables, charts, maps, and/or graphsIdentify patterns, note trends, and/or drawconclusions from tables, charts, maps, and/or graphsCollect and organize data into tables, charts, and/orgraphsCompute and interpret mean, median, and/or mode
Use elementary notions of probabilityUse problem-solving techniques
Unit 4: AlgebraSubunit 4.8: Group HCompetency 4.8.1: Evaluate and/or simplify algebraic expressions using
simple substitutions
Competency 4.8.2: Solve linear equations
Competency 4.8.3: Use order of operations to solve problems
Competency 4.8.4: Use formulas
Competency 4.8.5: Compare and compute using scientific notation
Competency 4.8.6: Use properties of exponents
Competency 4.8.7: Select and use appropriate problem-solvingtechniques
Competency 4.8.8: Determine slope, midpoint, and distance (NotElectronics)
Competency 4.8.9: Graph functions
Competency 4.8.10: Use Boolean algebra (Electronics Only)
* Advancing 70** Futuring
Unit 5:Subunit 5.CompetencyCompetency
Mathematics--8/92
Geometry8: Group H
5.8.1: Find perimeters and areas of geometric figures5.8.2:
Competency 5.8.3:
Competency 5.8.4:
Competency 5.8.5:Competency 5.8.6:
Find surface areas and volumes of applicablegeometric figuresRecognize, classify, and use properties of lines andanglesRecognize, classify, and use properties of two- andthree-dimensional figures (e.g., circles, triangles,rectangles, cylinders)Apply Pythagorean theoremDescribe and apply properties of similar andcongruent figures (Not Electronics)
Unit 6: TrigonometryCompetency 6.0.1:
Competency 6.0.2:
Competency 6.0.3:
* Advancing** Futuring
Identify basic functions of sine, cosine, and tangentCompute and solve problems using basictrigonometric functionsGraph basic functions using polar and/or Cartesiancoordinate systems
71
CROSS-REFERENCE CHARTGROUP H
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81 fo
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12
Mathematics-8/92
Ohio Model Competency-Based Mathematics ProgramPSS=Problem-Solving StrategiesNR=Numbers and Number RelationsM=MeasurementE=F..stimation and Mental ComputationD=Data Analysis and ProbabilityA=AlgebraG=GeometryP=Patterns, Relations, and Functions
Problem-Solving Strategies
Numbers and Number RelationsNR1 Compare, order, and determine equivalence of real numbersNR2 Estimate answers, compute, and solve problems involving real numbersNR3 Compare and contrast real number system, rational number system, and whole
number systemNR4 Extend understanding to complex number system and develop facility with its
operation
MeasurementM1 Estimate and use measurementsM2 Understand need for measurement and probability that any measurement is accurate
to some designated specificationM3 Understand and apply measurements related to power and workM4 Understand and apply measurement concepts of distance-rate-time problems and
acceleration problemsM5 Use real experiments to investigate elasticity, heat, sound, electricity, magnetism,
light, acceleration, velocity, energy, and gravityM6 Use real-world problem situations involving mass and weightM7 Use real-world problem situations involving simple harmonic motionM8 Establish ratios with and without common unitsM9 Construct and interpret maps, tables, charts, and graphs as they relate to real-world
mathematicsM10 Understand and solve rate-change problemsMl l Understand and solve right triangle relationships as they relate to measurement,
specifically to Pythagorean theoremM12 Graph and interpret ordered pairsM13 Compute total sales from a variety of itemsM14 Comprehend and compute rates of growth or decayM15 Comprehend, compute, and interpret real problems involving annuitiesM16 Develop an ability to identify real problems and provide possible solutionsM17 Express and apply different types of measurement scalesM18 Determine area and volume
78
Mathematics--8/92
Estimation and Mental ComputationEl Use estimation to eliminate choices in multiple-choice testsE2 Use estimation to determine reasonableness of problem situations in a wide variety
of applicationsE3 Estimate shape of graphs of various functions and algebraic expressionsE4 Use mental computation when computer and calculator are inappropriate
Data Analysis and ProbabilityDl Organize data into tables, charts, and graphsD2 Understand and apply measures of central tendency, variability, and correlationD3 Use curve fitting to predict from dataD4 Use experimental or theoretical probability, as appropriate, to represent and solve
problems involving uncertaintyD5 Use computer simulations and random number generators to estimate probabilitiesD6 Test hypotheses using appropriate statisticsD7 Read, interpret, and use tables, charts, and graphs to identify patterns, note trends,
draw conclusions, and make predictionsD8 Determine probabilities of events involving unbiased objectsD9 Use sampling and recognize its role in statistical claimsD10 Design a statistical experiment to study problem, conduct experiment, and interpret
and communicate outcomesDll Describe normal curve in general terms and use its propertiesD12 Create and interpret discrete probability distributionsD13 Understand concept of random variableD14 Apply concept of random variable to generate and interpret probability distributions,
including binomial, uniform, normal, and chi square
AlgebraAl Describe problem situations by using and relating numerical, symbolic, and
graphical representationsA2 Use language and notation of functions in symbolic and graphing settingsA3 Recognize and use equivalent zeros of a function, roots and the solution of an
equation in terms of graphical and symbolic representationsA4 Describe and use logic of equivalence in working with equations, inequalities, and
functionsA5 Develop graphical techniques of solution for problem situations involving functionsA6 Explore and describe characterizing features of functionsA7 Make arguments and proofs in algebraic settingsA8 Factor differerv..e of two squaresA9 Determine slot midpoint, and distanceA10 Explore and combine rational functionsAl 1 Explore factoring techniquesAl2 Solve quadratic equations by factoring and formulaA13 Set up and solve linear equationsA14 Solve systems of linear equations with two variablesA15 Describe geometric situations and phenomena using variables, equations, and
functionsA16 Describe measures of central tendency, mean, median, mode, and variance
algebraically and waphicallyA17 Represent inequalities on number line and in coordinate plane
79 1 ?4`-;
Mathematics--8/92
A18 Use coordinate arguments in making geometric proofsA19 Symbolize transformations of figures and graphsA20 Explore geometric basis for functions of trigonometryA21 Graph linear functionsA22 Develop and use vectors to represent direction and magnitude including operations
A23 Use polar and parametric equations to describe, graph, and solve problem situationsA24 Represent sequences and series as functions both algebraically and graphically
A25 Explore recursive functions and procedures using spreadsheets, other computerutilities, and appropriate notions
A26 Describe and solve algebraic situations with matricesA27 Describe and use inverse relationship between functions including exponential and
logarithmicA28 Analyze and describe errors and error sources that can be made when using
computers and calculators to solve problemsA29 Decide whether problem situation is best solved using computer, calculator, paper
and pencil, or mental arithmetic/estimation techniquesA30 Explore relationships between complex numbers and vectorsA31 Make arguments concerning limits, convergence and divergence in context
involving sequences, series, and other types of functionsA32 Represent transformations in plane with matricesA33 Contrast and compare algebras of rational, real, and complex numbers with
characteristics of a matrix algebra systemA34 Construct polynomial approximations of a function over specified intervals of
convergenceA35 Examine complex numbers as zeros of functionsA36 Translate verbal statements into symbolic languageA37 Simplify algebraic expressionsA38 Use laws and exponents (including scientific notation)A39 Expand and extend idea of vectors and linear algebra to higher dimensional
situationsA40 Use the idea of independent basis elements for a vector space and associated
fundamental concepts of finite dimensional linear algebraA41 Develop and communicate arguments about limit situationsA42 Use matrices to describe and apply transformationsA43 Develop and use polar and parametric equations to represent problem situations
A44 Explore proofs by mathematical induction
GeometryG1 Create and interpret drawings of three-dimensional objectsG2 Represent problem situations with geometric models and apply properties of figures
G3 Apply Pythagorean theoremG4 Demonstrate understanding of angles and parallel and perpendicular lines05 Explore inductive and deductive reasoning through applications to various subject
areasG6 Translate between synthetic and coordinate representationsG7 Identify congruent and similar figures using transformations with computer
programsG8 Deduce properties of figures using transformations and coordinatesG9 Use deductive reasoningG10 Explore compass and straightedge constructions in context of geometric theorems
G11 Demonstrate understanding of and ability to use proofG12 Use variety of proof techniques (e.g., synthetic, transformational, and coordinate)
80
Mathematics - -8/92
G13 Use variety of proof formats, including T-proof (i.e., two-column) and paragraphproof
G14 Explore different proof strategies015 Investigate different proofs of theoremsG16 Develop understanding of an axiomatic systemG17 Apply transformations and coordinates in problem solvingG18 Represent problem situations with geometric models and apply properties of figuresG19 Deduce properties of figures using vectorsG20 Analyze properties of Euclidian transformations and relate translations to vectorsG21 Apply vectors in problem solvingG22 Develop further understanding of axiomatic systems by investigating and
comparing various geometries
Patterns, Relations, and FunctionsP1 Model real-world phenomena with polynomial and exponential functionsP2 Explore relationship between zeros and intercepts of functionsP3 Translate among tables, algebraic expressions, and graphs of functionsP4 Use-graphing calculator or computer to generate graph of a functionP5 Explore relationship between a linear function and its inverseP6 Describe and use characteristics of polynomial functions in problem-solving
situationsP7 Explore conic sections and graph using graphing calculator or computerP8 Apply trigonometric functions to problem situations involving trianglesP9 Discover relationships between algebraic description, kind, and properties of conicP10 Explore periodic real-world phenomena using sine and cosine functionsP11 Analyze effects of parameter changes on graphsP12 Use graphing calculator or computer to graph functionsP13 Develop an understanding of rational and transcendental functionsP14 Understand connections between trigonometric and circular functionsP15 Use circular functions to model periodic real-world functionsP16 Solve trigonometric equations and verify trigonometric identitiesP17 Understand connections between trigonometric, exponential, and logarithmic
functions and polar coordinates, complex numbers, and seriesP18 Model real-world phenomena with a variety of functionsP19 Graph using polar coordinatesP20 Explore graphs in three dimensionsP21 Explore functions of several variablesP22 Explore recursive functions using spreadsheets and/or programming languages
i 7i;
81
Distributed by
Vocational Instructional Materials LaboratoryThe Ohio State University
1900 Kenny RoadColumbus, Ohio 43210-1090
127