It STIIMTION REPORT NO . May 74

I

ED 117 571

AUTHORTITLE

It STIIMTIONREPORT NO .PUB DATE '

NOTE

-EDRS.PRICEDESCRIPTORS

IDEtITIFIERS.

DOCUMENT RESUME

CE 006,288/.

Nuschler, Alexandra; And Other3General mathematics: Part 2. Mathematics CurriculumGuide (Career Oriented).Louisiana State Dept. of Education, Baton Rouge.Bull-1281; VT-102-467May 74 1

91p.; For related documents, see CE,(7,0282-291

MP-M83 BC7$4.67 Plus PostageAlgebra; Arithmetic; Behavioral Objectives; *Career'education; *Continuous Progress Plan; *CurriculumGuides; Geometry; Learning Activities; *Mathematics;Mathematics Curriculum; Practical MAhematics;Relevance (Education); *Secondary EducationLouisiana

1 ABSTRACTThe curriculum guide for secondary level,

career-oriented General Mathematics Part 2, correlates performanceobjectives in basic mathematics Idoth career-oriented concepts andactivities. The material-is designed to lead the student in asystematic development that provides for continuous progress.Theguide is in outline format, providing a curriculum outline,performance objectives, and related (career-oriented)oncepts,.objectives, and learning activities. The guide encompasses the,topicheadings of refresher arithmetic and algebra; informal geometry;mathematics-related to shop, construction, n4rsing, homemakihg,sports, and travel; and mathematics fqr electriCians. (PS)

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********************************************************************** 0 Documentsacquired.by ERIC include many informal unpublished/ *

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* reproducibility, are often encouniered and this affects the quality *

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MATHEMATICS CURRICULUM GUIDECAREER ORIENTED

GENERAL MATHEMATICS II

BULLETIN NO. 1281

Louisiana State Department of EdupationLouis J. Michot, Superintendent

k 1974

4.

5 OEPARTMENT OF HEALTH,EOUCATION A WELFARENATIONAL INSTITUTE OF

EOUCATION

THIS DOCUMENT HAS BEEN tREPRO-OUCE0 EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGIN-ATING IT POINTS OP VIEW 014 OPINIONSSTATED op NOT NECESSARILY REPRE-SENT OFFICIAL NATIONAL INSTITUTE OFEOUCATION POSITION OR POLICY

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MATHEMATICS CURRICULUM GUIDE

(CAREER ORIENTED)


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- LOUISIANA STATE DEPARTMENT OF EDUCATION

Louis J. Michot

States Superintendent

May 1974

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ACKNOilLEDGEMENTS

Appreciltion is expressed to the original writing team which tforkedso dilligently in developing the materials and ideas included in thehuideline. .

bits. Alexandra Nuschler, Chairwoman Chalmette High School,Chalmette, Louisiana

Logtowinior HiMonroe, Ilpuisiana

C-.Mrs. Eleanor HJollingsworth

Mrs. Jocelyn Landry

Mr.,John H. Smith , 3/

Cotead-Bayou Blue ElementaryHouma,.Louisianct

Raville High SchoolRayville, Louisiana ,

Mrs. Margaret Thames Mangham Junior High SchoolMangbam, Louisiana

For their consutrctive suggestions and addition in this revisededition, we give specia -'thanks and E\tnowledgement to this year?s team.

Dr. Merlin M. Ohmer, Chairman

Mr. Dale Fredrick

. Dale Hester

-Mr. Joseph Jones

Mrs. Alexandra Nuschler

4

Mrs. Marguerite Sanders

Nicholls State UniversityThibodaux, Louisiana

LaWette-Parish School BoardLafayeete, Louisiana

Nicholls State UniversityThibodaux, Louisiana -

'Mansfield High SchoolMansfield, Louisiana

Chalmette High SchoolChalmette, Louisiana

Sabine Parish School Board'Many, Louisiana

a

Finally, we express our gratitude to Superintendent Louis J. Michot,who has been the spearhead in promoting the concept of career edUcationfor all, and to the Loyisiana Legislature which recognized the need forsuch a program and saw plat funds were made available to carry on thisworthwhile- endeavor.

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PREFACE

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The first working draft of the Mathematics Curriculum Guide'SecondaryLevel was distributed for field testing for the 1973-74 academic year.Feedback indicated that the materials were appropriate for the purposesas stated in the original preface.

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The materials prgsented herein have been changed from the original-,

only In that the mathematical language has been made as Uniform aspossible for clarity and to contort') to the texts adopted by 'the State ofLouisiana.' Additional career learning activities have been introduced.

The format has been revised so that it should he easier to correlatethe curriculum outlines and performance objectives with the related careeroriented concepts and learning activities.

The reade'r who is seeing the materials for the first time can heassured that the career approacg Qf these guidelines in no way weakenthe present program. As in all good educational procedures, materials areincluded so that all levels,may be served. In addition to the ambitiousminimum recommendations the guidelines contain ample materials for thosestudents who need to be challenged.

Mathematics embedded in all of the disciplines and makes a/Solidbase for experiences in career education. This is borne out by the'

' numerous references and career activities from the spectrum of life.

The student is led in a systematic development that is designed toprovide for continuous progress, Dignity of the person was alwaysforemost in devising and revising the guidelines. The goals were setto give maximum development of the individual through all types ofeducational experiences.

Finally, our schools will alWays have a basic curriculum. x Themethods of instruction will be constantly changing, and thecouAselorswill continue to lend their influence in guiding the pupil. The careereducation goals Which-are interwoven with the traditional will help makemore productive citizens of Louisiana's most important assets, itschildren.

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TABLE OF CONTENTS

'Acknowledgements,

Pag e

ii

Preface iii

Refresher Arithmetic 1

Whole Numbers 11

'Number Theory 34

Fra2ctional Numbers

Ratio, Proportion, and Percent a 5

MeasurementMetric and Eitiglish 7

Square Roots 9

Refresher Algebra 11

Introduction 11

,Rational Nlmber System 11

Operations, Grouping and Factoring 13

Equations and Inequalities 15

Informal Geometry 17

Points, Lines, and Planes 17

Angles 17

Constructions 19

Definitions and Relationships 19

Plane Figures 21

Solid Figures 23

Mathematics Rglated to Shop 25

Measurement 25

iv

Automobile

Special Problems

Mathematics Related to,Cons\ruction

,Carpentry

Masonry Estimations

Mathematics for Elec ricians

Resistance

Ohm's Law

/POrwer

Alternating Current

Mathematics Related to Nursing

Numeration

Common Fractions, Decimals and Percents

Ratio and Proportion

Temperature Conversion

Measurement

Using Formulas -

Calculating Dosages

Mathematics. Related to Homemaking

Review

Measurement

Clothing and Textiles

Q.

42.

Page

27

29

31

31

33

37

37

37

39

41

43*

43

43

45

45

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49

51

55

55

55

57

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Food and Nutrition

Home Decorating

Family Budget ss'

. ConsumerlOriented Publications

Mathematics Related to Sports

Baseball

Football

Basketball

Individual Sports--Scoring, Scheduling, andMeasuring

Mathematics Related to Travel)

Latitude and Longitude

Travel by Airplane

Traveling by Car

Traveling by Bus

Tra'veling by Train

Traveling by Ship

International Travel

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'CURRICULUM OUTLINE PERFORMANCEOBJECTIVES'

I. Refresher Arithmetic-

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A. Whole NuMbers(0, 1, 2, 3 )

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1. Addjtion

2. Subtraction

3. Multiplicationa

4. Division,

5. Order of multipleoperations

I. Refresher AVithrnetic

To, demonstrate anunderstanding of wholenumbers and to developproficiency in basicarithmetic operations,the student should beable to:

1. Add a column ofmulti-digit numbers'and check by addingin the reverse order.

2. Compute the differenceof two given multi -digit numbers andcheck by the additionmethod.

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.3. Compute thproduct-of two multi-digitnumbers and chpIck bycasting -out -nines.

4. Compute the quotientof multi-digitnumbers, and check

.by the multiplicationprocess.

5. Apply the correctorder to anexpression.involving multipleoperations

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RELATED CAREER ORIENTEDCONCEPTS AND OBJECTIVES

RELATED CAREER ORIENTEDLEARNING ACTIVITIES

. Career Concept

Careers require differentlevels of competence incomputation.

.

Performance Objectives

A. An airplane pilot useswhole numbers todetermine the averageflying speed and theflight time for a

. given trip.

A prix eA al of a schoolused who nuipbers tocompute the totalenrollment.

A. An airplane pilot flew anairplane 2,175 miles fromPortland, Oregon,*to Atlanta,Georgia in 6 hours. 'Computethe average flying speed. At

A the same rate, hoW long willit take .to fly from Los Angelesto Indianapolis, a distance of1, 810 miles ?

In the Franklin High .Schoolthere are 5 classes with 32pupils on roll, 13 classeswith 30 pupils, and 12 classeswith 28 students. Find thetotal enrollment of the school.

CUIIRICuLU,M OUTLINE PERFORMANCE0 JECTIVE

Bo Number theory

,

1. Definitions

a Naturalnumher

b.: Factorc. Even'd. Odde. C omrpon

factor,af. Greatest

common factorPrime numberComposite .

numberi. Multiple

h.

J. Commonmultiple .

k. Least commonmultiple

1. Primefactorization

2. Fundamentaltlbrem ofArithrn(atic (uniquePrime Factori-zation Theory)

C. Fractional numbers

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B. To demonstrate an under--standing_of basic numberthe.ory,. the student shouldbe able to:

C.

1. Dianne and giveexamples ofa. 'Natural number

b. Factorz. EVend. Odde. Common

factorf. Greatest common.

factor (G. C. F. )

2.

g. Prime numberh. Composite

number s'i. Multiple of a

numberCommonMultiple

k. Least common\- multiple (L. C. M. )

1. Prin-Te factorization

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Express a number as aproduc f its primefactors.

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To demOnstrate-an under-standing of and proficiency)in)he use of fractional LI'numbers, the studentshould be able to:



7B. A mathmatician

applies the. concept ofprime numbers andcoi:rnposite numbers tothe explanation of theFundamental Theoremof Arithmetic.

1'1

C. A ship captain usesfractional numbers tocompute the number ofnautical miles a shipwill travel at a givenrate of speed in agiv'en time.

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B. The fundamental theorem ofarithmetic states that everycompostte number can beexpressed as a product of,primes. Express each of thefollowing numbers as a productof prime: 24k. 18, 32.

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C. A ship steams at 14 1/2 knots. Atthat rate how many nautical milesdoes it gb in 6 1/4 hours ?1 nautical m. p. h. )

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(1 knot =

CURRICULUM ,PUT.LINE PERFORMANCEOBJECTIVES

t.

1. Commonfractions'

Z. DecimaLfractions

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3. Comparing, fractional numbers

4. Scientificnotation

D. Ratio, Proportion,and Percent

1. Definitions

a. Lowest terms

b. Problemsolving

Z. Percenta. Conversion

, 1,4

1. Add, subtract,multiply, arid dividecommon fractions.

a. Add; subtract,multiply, and dividedecimal fractions.

Compare twO givenfractional numbers.

4. Express'a givennumber in 4sientificnotation.

,1D. To demonstrate an under- ,

standing of ratio, proportionand percent, the studentshould be able to:

1. Define ratio, pro-portion, means terms,extreme termsa. Express a ratio

in lowest terms.b. Compute the

missing term ina proportionwhen three termsare given.

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Define percenta. Convert a common

fraction to adecimal fraction'and to a percent;a decimal fractionto a commonfraction and toa percent; apercent to acommon fractionand to a decimal.

RELATE CAREER ORIENTEDCONCEPTS AND OBJECTIVES

RELATED CAREER ORIENTEDLEARVING ACTIVITIES

A professionalAtypist uses proportionto determine the timesnecessary to type amanuscript.

A real estate agentuses percent tocompute the commis-sion on the sale of ahouse, and the amountof money the sellerwill receive.

D. Donna, aRprofessional typist,can type 8 pages of manuscriptin 52 minutes. She agreed totype an article of 20 pages.How long will. it take her totype the article ?

4 real estate agent sold a housefor $13, 500 and was paid acommission of 5%. What was theamount of his commission? Howmuch did the seller of the houseieceive?

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CURRICULUM" OUTLINE PERFORMANCE,OBJECTIVES

Problem,.solying

E. Measurement:-- tricand English

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Definitions. a. Approximate

numberb. Precision.c. Greatest

possible errord. Accuracy

(number ofsignificantdigits)

e. Relative errorf. Percent error

2. Calculations

3. Least precisemeasurement

4. Precision versusaccuracy

7

a

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Use proportionsto solve Problemsof the type:(1) What is 40%

of 50? ,

(2) What percentof 90 is 60?

(3) 50 is 20% of' what number?

E. To demonstrate an under-c?standinof measurement,

the, student should be ableto: s*

c.

la Define:a. Approxi

numberb.' Precisionc.. .Greatest possible

errord. Accuracy

(number ofsignificant digits)

e. Relative errorPercefit error

2. Comptite the precision,greatest possible error,the relative error, andpercent error of ameasurement.

,3. . Determine which ofci eve r a 1 given measure-ments is least precise.

4. Determine which oftwo measurements iSmore precise and whichis more accurate.

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E. An auto parts manu-facturer uses the-concept of tolerance'in

A manufacturing parts.

A watch repairmanmeasures a Watch to .determine the sizeof.aAcrystal needed.

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E. If the..tolerance is i 1/32",what iq the maximuMA.ndminimum alkowablertength fora part if the dimension is, givenat 5 5/16"?

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What is tFie relative error ofa measu ement'of a 1 1/4"watch cr, stal, if the' measureis repor ed`p the nearest1/4 Inch

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CURRICULUM. OUTLINE PERFORMANCEOBJECTIVES

F. Square Roots

1. Table

2. Algorithm

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5F. To demonstrate a working

knowledge of square .roots,the student should beable to:

1. Determine the squareroot of a given numberby using tables.

2. Determine the squareroot of a given numberby using the squareroot algorithm.

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F. A sheet metal tech-nician applies squareroot in computing theradius of stretch-outof the top part of acone-shaped cover.

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F. Compute the radius of thestieteihout of a cone 3 feetin diameter with an altitudeof'2 feet. (fhe radius ofstretchout is equal to theslant height of the coneand can be computed ninthe fOrmula H =

(a = altitude, d = diameter)

1

CURRICULUM OUTLINE PERFORMANCEOBJECTIVES

II. Refresher Algebra

A. Introduction

1:

1. Identification ofsymbols

2. Definitions,. .

B. Rational numbersystem

1. Closureproperties

2. Commutative"property`

II. Refresher Algebra

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A. To demonstrate an under-standing of algebraicsymbols and terms, thestudent should be ableto:

1. Identify: = , >, <,'+ -, X, ,

2. Define or illustrate:positive number,,negative number,equation, inequality,

*las oluee value,variable, coefficient,exponent, constant,term, like terms,monomial, binomial,tr nomial, polynomial.

To demonstrate an under-standing of the rationalnumber system, thestudent should be able toexpress, recognize, andus e:

1. The closure propertyfor:a. Additionb. Multiplication

2.

KThe commutativeproperty for:a. Additionb. Multiplication


RELATED CAREER ORIENTEDLEARNING ACTIVITIES°

II. Career Concept

Career° require differentlevels of competence incomputation.


A. A football player gainsor loses yardage onconsecutive plays.These results may be'represented by positiveand negative numbers.

B. People in all walks oflife use proaperties ofnumbers in solvingproblems.

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A.

B.

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On four plays the followingyardage was made: 15, -2, 6,-8. What was his total gain?

A housewife went to the marketto buy food for a family picnic.She bought 4 pounds ofhamburger meat for $1. 2i) perpound, and 4 pioundo of weniersfor 74 c per pound. Use thedistributive property torepresent the cost of the food,'then determine the total cost.

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CURRICULUM OUTLINE PERFORMANCEOBJECTIVES /--T

3. As sociativeproperties

4. Identity properties

5. Inverse properties

6. Distributiveproperty '

C. Operations, groupinand factoring

1. Addition

2. Subtraction

3. Multiplication

,4. Division('

3. The associative_property for:a. Additionb. Multiplication

4. The identity propertyfor:a. Additionb. Multiplication

5. The inverseproperty for:a. Additionb. Multiplication

6. The distributiveproperty for ,

multiplication overaddition

To demonstrate a basicskill in algebra, thestudent should be able to:

1. Add:a. Signed numbers"

-1 b. Other poly-nomials

2. Subtract:a. Signed numbersb. Other

polynomials

3. Multiply:a. Signed numbersb. A polynomial

by a monomial

4. Divide:a. Signed numbersb. A polynomial by

a monomial

RELATED CAREER ORIIMTEDCONCEPTS AND OBJEC"kIVES

RELATED CAREE ORIENTEDLEARNING ACTIVITIES

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C. A meteorologist appliesthe concept of additiveinverse in computingthe difference betweentemperatures above andbelow zero.

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C.

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If the temperature ate New Orleansis 48 degrees and the temperatureat Minneapolis is -13 degrees,,how many degrees warmer is itin New Orleans than atM eapolis ?

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CURRICULUM OUTLINE PERFORMANCE. OBJECTIVES

5. , Grouping

t)

6. Factoring

II

D. Equations andinequalities

1. Trans lation

2. Evaluation

3. Solving opensentences

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5. Remove symbols ofgrouping and combinerlike terms.

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6. Faetor aicbraicexpreoRion byremoving thegreatest commoenmonomial factor. -

To demonstrate an under-0. standing of equations and

inequalities, the studentshould be able to: "

1. Translate:a. An English

expression intoan algebraicexpression

b. An Englishstatement intoan algebraicsentence

c. An algebraicsentence intowords.

2. Evaluate an expressiong. , 6L - 2W, if

L= 8, and W = 3.)

3. Solve:a. An equation in

one variableb. An equation for

a specified variablec. A formula for a

specified variablewhen values aregiven for all othervariables'

d. An inequality

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D. An appliance dealermay use an equation todetermine the sellingprice of an appliance.

D. The Cost of a television set is$175 and the profit is 30% ofthe selling price, what is theselling price of the televisionSet? What the profit?Let x = selling priceCost + Profit = Selling price$175.+ . 30x = x, $175 F . 70x

= $250Profit, . 30x = $75. GO

a

URRICULUM OUTLINE PERFORMANCEOBJECTIVE

III. Informal Geornetry

A. Points, lines, andplanes

1. Identification

2. Linesa. Positions of

lines

. Intersecting

c. Paralleld. Perpendicular

e. Transversal

B. Angle s

1. Definitions

2. Measuring angles

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'3. Classifyingangles

III. Basic Geometry Review,

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A. To demonstrat an under-tstanding of inforgeornifft., the stshoutig14-1;ie

aldent

0:

1. Identify points,lines, and planes.

2. Define or identifyVertical line,horizontal lines,oblique lines

b. Intersectinglines

c. Parallel linesd. Perpendicular

linese. Transversal

B. To demonstrate an understanding of angles, thestudent should be able to:

1. Define, identify, andsketch: an angle, a rightangle, an acute angle,and obtuse angle, and astraight angle.

2. Determine the measure ofan angle by using aprotractor.

3. Classify angles from theirmeasures {e. g. , if m(A) =90°, m(B) = 65°, m(C) =120°, and m(D) = 180°1



III. Career Concept

Every ca'reer re uires someepecial prep n.


A. The ground crew for a.football field usesparp.11e1 andperpendicular linesin laying out the fiefor a ga

B. A navigator of anairplane uses anglesin constructing ascale drawing to showthe position of a plahegiven the necessarydata

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ft

A. Construct a diagram of afootball field given the'scale of the drawing andthe dimensions of the field.

B. Make a scale drawing showingthe position of an airplaneat the end of 3 hours whenflying'on a course of 60°,with a ground speed"of 250 m. p. h.


C. Constructions

1. Angle

2. Congruent triangles

3. Regular polygOns

4. Bisecting a linesegment

5. Bisecting an angle

6. Perpendicularlines

7. Parallel lines

D. Defintions andrelationships

1. Angle sum of apolygon

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then IA is a- rightangle, LB is anacute angle, LC,ioan obtuse angle, and

D is a straight angle.

C. Todemonstrate a basicunderstanding of fundamentalconstruction by using acompass and straight edge,the student should be able to:

1. Copy a given angle.

2.. Construct congruenttriangles.

.3. Construct a regularpolygon of 3 sides,4 sides, 6 sides.

4. Bisect a line segment.

5. Bisect an angle.

6. Construct a perpe dicularto a given line:a. At a point not on

the line.b. From a point n

on the line.

7. Construct a line p. rallelto a given line.

D. To demonstrate a under-standing of ang relationships,the student should be able to:

1. Determine the sum of themeasures of the angles of:a. A triangleb. A quadrilateralc. A pentagon'



A craftsman uses basicconbtructions in layingout geometric shapes.

D. A machinist uses anglerelationship in hiswork.

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C. A piece of round stock is 3" indiameter. Construct thelargest square that can bemachined at one end.

D. What angle does side B of aregular hexagonal bar makewith the surface plate as shown'in the diagram?

CURRICULUM OUTLINE4

PERFORMANCEOBJECTIVES

2. Special angle pairs

E. Plane figures

I. Definitions

2. Perimeter andcircumference

2. Define and sketch:a, Complementary

anglesb. Supplementary

anglesc. VeTtical anglesd. Corresponding

anglesassociate&with parallel lines.

e. Alternate interiorangles

f. Alternate exteriorangles

E. To demonstrate a basicunderstanding of planefigures, the student shouldbe able to:

1. Define, sketch, andidentify:a. Right triangle ,b. Equilateral

trianglec. Isosceles triangled.. 'Scalene trianglee. Quadrilateralf, Parallelogramg. Rectangleh. Squarei. Trapezoidj. Rhombusk. Circle1.c;. Pentagon

2. Determine the perimeteror circumference, of eachfigure listed above whenthe dimensions aregiven.

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RELIATE13 CAREER ORIENTEDCONCEPTS AND OBJECTIVES


E. A forest rangercomputes the area of acircle in determiningthe area of the forestthat he can observefrom a firetower.

E. If a forest ranger can see fromhis tower for a distance of24 miles in all directions, howmany square miles can hewatch?

CURRICULUM OUTLINE. PERFORM4NCEOBJECTIVES

3. Xrea

F. Solid figures

1. Terminologya. Polyhedreil.b. Cylinderc. Prismd. Conee. Pyramidf. Sphere

2. Lateral and totalarea

3. Volume

23 °

3. Compute the area of:a. A triangleb. A parallelogramc. A rectangled. A squaree. A trapezoidf. A circle

F. To demonstrate a basicunderstanding of solidfigures, the studentshould be able to:

1. Identify;a. A polyhedronb. A cylinderc. A prismd. A conee. A pyramidf. A sphere

2. Determine the lateral',area and the total area

of:a. A cylinderb. A prism

6 c. A coned. A pyramid

' e. A sphere

3. Comp to the volumeof:a. A linaerb. A smc. Ad. A amide. A re



F. An automotivetechnician uses thebasic principle@ ofarea.

F. 'A mechanic relines a truckbody with flat stock. Thefloor measures 12' x 8', thesides are 12' x 4', and thefront measures 8' x 4'. Whatis the total area covered?

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CURRICULUM OUTLINEP


IV. Mathematics Related toShop

A. MeaSurement

.'

Linearrn 1.1

devicesa

2. Speedometer andodometer

3. Feeler gauge

4. Tolerance

5. Missing dimensions

6. Area

7. Angle

IV. Mathematics Related to Shop

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34

A. To develop a basic'understanding of measure-ment pertaining to thechop and industry, thestudent should be ableto:

Use and read linearmeasuring devicesboth metric andnon-metric.a. Steel ruleb. Caliperc. Micrometerd. . Gauge

2. Distinguish betweenan odometer and aspeedometer, andread each.

3. Use a feeler gauge tomeasure the gap on aspark plug.

4. Calculate the tolelanceof a given manufacturedpart.

5. Compute, the lAgth of themissing dimension in anirregular figure.

6. Compute the area of anirregular figure.

7. Measure an angleusing a protractor..

4



IV. Career Concept

Careers are interrelated.


A. 'A painter computs,stie area of a cylinderto determine theamount and cost ofthe paint needed topaint the structure.

4

A. A gasoline storage tank 7'in diameter and.1.8' long isto be painted with two coats ofpaint. Each gallon of painthas a maximum coverage of400 sq. ft. for two coats. Ifpaint of this quality sells for$6. 79 per gallon, what will bethe cost of the paint requiredto do the job? (Consider afractional part of a gallOn asa whole gallon. )

1


8. Estimation

9. Scale drawing

10. Temperaturea. Reading

b, Conversion

' B. Automobile

1. Brake horsepower

2. SAE Horespower

3. Displacement

4. Rear axle ratio

5. Work

6. Power

7. Mechanicalefficiency

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36

8, Estimate ameasurement.

9. Draw a figure toa specific scale.

10. Read a thermometera. Fahrenheit and

Celsiusb. Convert a

Fahrenheitreading to aCelsius reading;a Celsius readingto a Fahrenheitreading.

B. To demonstrate a basicunderstanding of mathe-matics _related to anautomobile, each studentshould be able to:

1. Compute the brakehorsepower of anengine.

2. Compute the SAEhorsepower of anengine.

3. Compute the displacementof an. engine.

4. Compute rear axle ratio.

5. Apply the formula forwork.

6. Apply the formula forpower.

0

7. Compute the mechanicalefficiency of an engine.



B. An automobilemechanic computesthe horsepower ofan engine.

28

B. Find the horsepower developedby an engine having a pistondiameter (d) of 4", a strokelength (L) of 5", a meaneffective pressure (P) of42 lb. per square inch, andturning at the rate of 275 rpm(N). In the formula (A)represents the area of thepiston and is equal to 0. 7854d2.

Formula

PXLXAXNh. p. =33,000


C. Special problems

1 Odometer

2. Using a micro-meter

3. Balance

4. Sundial

5. Pulleys

6. Gears%-

Cutting speed

8. Rim speed

9. Screw pitch

29

38

C. Toextend the above conceptsand skills, the studentshould be able to:

p

1. Construct a model ofan odometer.

--2 Use a micrometer tomeasure severalpieces of wire.

3. Build a balancL

4. Construct a sundial.

5. Solve a problemdealing with pulleys.

6. Compute the rpm of adriven geir'when thegear ratio and the rpmof the pinion is specified.,

Compute the cuttingspeed of a jointersaw.

8. Compute the rim speedof a revolving object.

9. Compute the pitchof a screw.


RELATED.CAREER'ORI VTEDLEARNING ACTIVITIES

C. . A machinist computesthe pitch of a screw.

A race car designercomputes the brakehorsepower of anautomobile engine.

U

C. Compute the pitch of severalscrews and make a chartshowing the variousopitches.

Compute the brake horsepowerof an engine using a prony brakewith an arm 4 ft. long. Theengine speed is 1200 rpm, andthe (load is 120 lbs.

6

Collect data from newspaperson the horsepower of various'race cars.

..

CURRICULUM OUTLINE PERFORMANCEOBJECTIVES,

V. Mathematics, Related toConi,truction

1. Lumbermeasurement

2. Estimation of-board feet

3. Coiriputationa. Cost of lumber

b. Unit stress.

c. Number ofshingles

d. Steps for stairs

e. Pitch of a roof

V. Mathematics Related toConCatruction

31

A. To develop an under-standing of rnatIvmaticorelated to carpentry, thestudent should be able to:

1. Measure and computethe number of boardfeet in a pi oflumber.

fE

2. Estimate tho nu er ofboard feet of'lum ernecessary tc floor a.structure toispecificationsif 1" thick flooringused. j

3. Define corninitatioa. Corrkputeithe,

-of 1 mber. V.`"

b. Compute unfri4ra,sesof variOus:4ptG oftbuil4ing

c. Compute the .numberof shingles neededto cover a roOf ifthe shingles arelaid 5" troy he weather.

d. Comput the nurii berof otepd,necessary fora rise of Stairs, ifeach riser must be

inches.Compute the pitchof a roof.

e.


RELATED CAREER ORIENTEDLEARNIN6 ACTIVITIES

V. Career Concept

Careers are interrelated.


A carpenter compute'sthe number of board fefeetqn a given amountof lumber.

A contractor computesthe total cost ofbeilding a house giventhe specifiedinformation.

32

A. Using the formula for board feet,compute the number of board feetin the following pieces of lumber:120 pieces of 2" X 4" X fit. Whatis the price of this lumber if itsells for $126 per M?

A carpenter intends to buildthree small houses in a lowcost subdivision through asubcontract. Using the table,determine the total cost ofmaterials and labor forbuilding each of the three houses.

Subcontract CostsTWO

BedroomRanch(1000

sq. ft.)

TwoBedroomProvincial(1050 sq.ft.)

ThreeBedroomColonial(1350

sq. ft.?

Lumber and Trim lI$3620 $3756 $4100

Carpenjry Labor $1050 I $115Q $1600

Insulation $ 300 $ 315 $ 395

Cabinets $ 327 $ 375- $ 450

Hardwood, Flooring $ 200 $ 765 $ 370'

Total Cost

41


f. Cost of paint

g. Number ofnails

h. Length ofrafters

i. Number ofstuds

4. Estimation ofcost of a building

B. Masonry estimations

1. Quantities ofcement, sand, andgravel

33

f. Estimate theamou.rit and thecost of paintnecessary topaint a house,interior andexterior.

g. Estimate thenumber of nailsneeded for aspecified job:

h. Compute thelength of raftersfor a building. ,

i. Compute thenumber of out-side studs neededfor a wall giventhe spacing anddimensions ofthe wall.

4. Estimate the cost ofbuilding materialsneeded to build ahouse to givenspecifications.

B. To develop a basic under-standing of mathematicsrelated to masonry, eachstudent shoiild be able to:

1. Estimate the quantitiesof cement, sand, andgravel needed for aconcrete wall, giventhe specifications ofthe wall and the ratioof the mixture.



,r A

B. A brick wriasoncomputes the amountand price of concretethat will be neededto construct adriveway.

A cement finisherdetermines the costof cement for aconcrete slab fora new house.

34

43

B. How many cubic yards ofconcrete are-required for asidewalk 9 ft. wide, 24 ft.long, and 6 inches thick? 'Howmuch will it cost at $24.50per cubic yard?

'Given the diagram below, computethe amount and sptice of readymix cement for the slab which isto be 10" thick, if the priceis $24.50 per cubic yard?


2. Cost. of cement

3. Nurnbei of bricks

4. Cost of bricks fora building

Y35

44

2. Estimate the cost ofcement for a sidewalk.

3. Estimate the numberof bricks needed for abuilding.

4. Estimate the cost ofbricking a building.

O

RELATED CAREER ORIENTEDCONCEPTS AND 0 JECTIVES

RELATED CA EER ORIENTEDLEARNING ACTIVITIES

4

12-0"

12.-O"

36

45

161,- 0" -1 321 -0"


VI. Mathematics forElectricians

A. Resistance

Wire

2. Resistors inseries

3. Resistors inparallel

B. Ohm's Law

P. Current

2. Voltage

3. Resistance

VI. Mathematics for Electricians

37.

46

A. To demonstrate anunderstanding of mathe-matics related toresistance, a studentshould be able to:

1. Compute the resistanceof a wire, given the

. total length and theresistance per unity.length.

2. Compute the totalresistance of a seriesof resistors.

3. Corgpute the totalresiStance of a given

f resistors in-paral el.

B. To demonstrate an under-standing of Ohm's Law, thestudent should be able to:

1. 'Compute current,given the resistanceand voltage.

Compute voltage, giventhe' resistance and current.

3. Compute resistance,given the resistance andcurrent.



VI. Career Concept

In our highly mechanizedworld, careers that helpkeep machines andappliances operationefficiently are veryimportant.


A. An electriciancomputes theresistance of wireused in electricalcircuits.

B. Radio repairmencompute the totalvoltage (E) for ac cuit.

38

4 l

A. What is the resistance, R,of 300' of copper wire witha cross sectional area of10, 380 circular mils ?Use: R = K+ L where R =

resistance, K = resistivity ofcopper (10.4 ohm circular mil),L = length in feet, d = diameterin mils.

B. Find thctotal voltage (E) forthe circuit shown bel

+ (EL - Ed

A


4. Series circuit

C. Pow'er

1. Wattage

2. Cost

3. Horsepower

4. Meters

39.

46

4. Compute the totalresistance, the linevoltage, and thecurrent through eachpart when given aseries of resistors,the voltage acrosseach one, and thecurrent.

5; Compute the linedrop of a powerline given t heresistance and thecurrent.

C. To demonstrate a know-ledge of mathematicsrelated to power, thestudent should be able to: \1. Compute the power

(wattage) in a d-ccircuit, given thevoltage and current.

2. Compute the cost ofelectricity given therate per kilowatthour, wattage, andtime.

3. Convert kilowatts tohorsepower.

4. Read electric metersand determine the costfor electricity usedbetween two successiveMeter readings.

RELATED CAREER ORIENTEDCONCEPTS AND 0 JECTIVES

RELATED CAREE ORIENTEDLEARNING ACTIVITIES

C. An electriciancomputes the amountof curr nt anelectrica pliancerequires and theresistance of theappliance.

C. How many amperes of currentwill a 550-watt electric ironrequire if the iron is used on a110-volt circuit? Compute theresistance of the iron.

CURRICULUM OU-TLINE PERFORMANCEOBJECTIVES

a

o D. Alternating current

1. Frequency

2. Power

a

41

D. To demonstrate a basicunderstanding of mathematicsrelated' to alternatingcurrent, the student shouldbe able to:

1. Compute the frequencyof an alternating currentgiven the number ofpoles and the revolutionsper minute of thealterrkator.

2. Compute the power inan a-c circuit whenthe effective value ofthe current, the voltageand the power factoris known.

,

RELATED CAREER ORIENTEDCONCEPTS ANQ OBJECTIVES \


D. An electriciancomputes the,frequency of analternating currentproduced by acommercial a -cgenerator.

D. What is the frequency inhertz (H) of the currentfurnished by an alternatorhaving 4 poles and runningat a speed of 1800 revolutionsper minute?Use:

f = P X 60

0

where f = frequency in hertz,P = number of pairs of poles,and N = revolutions perminute.

CURRICULUM OUTLINE PERFORMANCE0 JECTIVES

_VII. Mathematics Related toNuising

A.

B.

Numeration

1. Conversion-Arabic numeralsto Romannumerals

2. Conversion-Roman numeralsto Arabic numerals

Common fractions,decimals? and percents

1. Decimal notation

2. Conversion ofcommon fractionsto decimals

3. Conversion of ,decimals tocommon fractions

4. Basic operationson commonfractions

VII. Mathematics Related to Nursing

43

A. To demonotra.te a workingknowledge of the Arabicand the Roman system ofnumeration, the studentshould be able to:

1. Convert Arabicnumerals toRoman numerals.

2. Convert Romannumerals toArabic numerals.

B. To demonstrate competencyin working with commonfractions and percents, thestudent should be able to:

1. Read and write decimalscorrectly.

2. Convert a given commonfrac,tion to its decimalequivalent.

3. Convert a given decimalto its decimal equivalent.

4. Perform the basicoperations of reduction,addition, subtraction,multiplication anddivision of commonfractions.

RELATE CAREE 0 ENTEDCONCEPTS AND 0 JECTIVES

RELATED CAREE ORIENTEDLEA ',NINO ACTIVITIES

VII: Career Concept

Every occupationcontributes to society.


A. A registered nurseinterprets thesymbols us ecD byphysicians to prescribemedications.

B. An office nurseprepares a specifiedsolution from stocksolutions.

o

A.

B.

44

5u

Request a nurse to visit theclass and discuss how shemust be able to interpretsythbolo in order to followdoctors orders concerningpatients. Use sampleprescript ono to illustrate.

To calculate the amount ofsolute needed to make asolution of a given strengthnurses may use the following:.

,Strength desired x Quantity 'desired=Strength on handAmount of solute. How manygrams of sodium bicarbonateare needed to prepare 500 mlbfa 1% solution?Solution:1% x 51)40 ml = 5.100%5 /grams of 100 percent puresodium bicarbonate are needed.

as

6


5. Basic operationson decimals

6. Conversion topercent

7. Calculation ofpercentage

C. Ratio and proportion

D. Temperatureconversion

1. Celsius toFahrenheit

45

5 4

h C.

5. Perform the basicoperations "of addition,subtraction,multiplication; _ an4:division of decimalfractions.

6. Convert commonfractions and decimalfractions to percentsand vice versa.

Calctilate the percentageof ,a given quantity.

To demonstrate a basicunderstanding'of ratio andproportion, the student

'should be able to:

1. Convert a commonfraction, a decimal,and a per tent to aratio, such as 3/4 ='3:4.

2. Set up a proportionand solve for the'unknown term.

D. To demonstrate a basic-understanding of temperatureconversion, the studentshould be able to:

1. Convert a Celsius toa Fahrenheit measureby using the followingformula: F = 9/5C +32.

...RELATED CAREER ORIENTED .CONCEPTS AND OBJECTIVES


A private duty nursema 14 s conversionsfro.rs on onesyringe to scales ondifferent syringes.'

D. A practical nursedconverts a Celsiustemperature to aFahrenheittemperature.

A doctor's orders states thatthe nurse must give U30 of aU40 solution of insulin toa diabetic patient. She doesnot have a U40 syringe, butshe does have a U80 syringe.How does, she determine thedesired/amount using a U80zyringe.Solution:U30:U40 = X:U8040x = 2400x .= 60 units of U40 solution tobe given in a U80 syringe.

D. Convert 46°,C to Fahrenheit.

a


2. Fahrenheitto Celsius

E. Measurement,

1. Apothecaries'systema. Symbols.

(1) Weight(2) Volume

(liquid)b. Abbreviations

and symbols

2; Metric system

3. Household system

4. Conversion

47-56

2. Convert a Fahrenheitto a Celsius measureby using the followingformula:C 5/9 (F - 32).

E. To develop a basicunderstanding of measure-ment, the student shouldbe able to:

1. Use the apothecaries'system by:a. Identifying the

symbols used forweight and volume,(Z, M, 0)

b. Identifying theabbreviation usedfor eight and

2. Identify the symbols forweights and volumesused in the metricsystem.

3. Identify the abbreviationsfor weights and volumesused in the householdsystem.

4. Convert given weightsand volumes (liquid)from the apothecaries'system to the othertwo systems and viceversa.

ti



E. A nurse converts adoctor's ordersconcerning a dose ofmedicine fromapothecaries' measureto household measure.

E. Convert Z tt to teaspoonfuls.0


F. Using formulas

1. Calculatingchildren's dosesa. Young's Rule

- b. Fri-enirl's Law

c. Clark's Rule

2. Problems insolutions

49

56

To develop a basic competencyin calculating dosages, the

student should be ablet,,to:

1. Calculate children'sdoses by using:a. Young's Rule

child's dose=age of child Xage of child + 12average adultdosage.

b. Fried's Law(dosage for infantsunder one year ofage). It may beused for olderchildren.infant's dosageage in months'

150adult dosage.

c. Clark's Rule(Narcotic andsomeantibioticd othermedicines areadministered to achild according tohis weight. )

ya child's dose =child's weight in pounds

150adult 'dosage

2. Solve solution problemsby:a. Calculating the

amount of puredrug needed tomake -a certainsolution.(1) Formula A

amount of solute

x

strength desiredstrength on handquantity desired

RELATED CAREER ORIENTEDCONCEPTS AND,0 JECTIVES


F. A pediatric nursecalculates a childdosage of medicine-from the known adultdosage.

50

F. A doctor &eated a 4 year oldchild and ordered the followingmedicine: hykinone and cortisone'acetate. Compute the child'sdosage if the adult dosage is2mg. of hykinone, and 150 mg.of cortisone acetate.

CURRICULUM OUTLINE, PERFORMANCEOBJECTIVES

. Calculating dosages

1. Oral medications

2. Insulin

3'2.' Hypodermicinjection

V \

-

51

GO

(a) Formula B usingproportions

amountamount of desired solute21-eLT,th of desired solutionstrength on hand

b. `Calculating the amountof stock solutionneeded to make aspecified dilutesolution.

c. Calculating theamounts of solventand solute in asolution of a. givenpercentage.

G. To develop a basic under-standing in the, methods ofcalculating dosa.ges, the fr

student should be"table to:

1. Calculate the amountof oral medication tobe given from a stocksolution.

2. Calculate insulindosages accordingto a syringe calibratedin units.

3. Calculate dosage for aninjection in terms of thestrength of the drug onhand.

R WED CAREER ORIENTEDC NCEPTS AND OBJECTIVES

RELATED CAREER ,ORIENTEDLEARNING ACTIVITIES

G. An Armed Forcesnurse calculatesdosages fromstock bottles.

I

A private duty nurse, calculates dosages for

hypodermic injections.

G. How much of a given stocksolution should be given toa patient when a doctorprescribes . 75 g terrarnycinsuspensicn per dose ? Thestock solution label reads5 ml = 250mg.

One of the duties of a privatenurse is to give hypodermicinjections. Many times themedicine is not in liquid form

. /-and must be put---thto solution.The accuracy of the solutionis very important to the healthof the patient. No more than2 ml should be used for asubcutaneous injection and nomore than 5m1 for anintramuscular injection.

.

CURRICULUM OUTLINE PERFORMANCE0 JECTIVES .

53

Ca



1

54

Calculate the following dosagesfor hypodermic injections. Give(a) the number of tablets to bedissolved; (b) the amount ofsterile water to be used as solvent,and (c) the amount of solution tobe given to the patient.1. The dose ordered is . 12 mg.

s. c. (subcutaneous). Thetablets on hand are . 6 mg.a. b. - c.

Z. The dose ordered is 15 mg.I. M. (intramuscular). Thetablets onhand are 25mg.a. b. c.

3. The dose ordered in 10 mg.I. M. The tablets on hand are. 03 g. Convert to milligramsbefore calculating.Part of tablet to be used =amount desiredamount on handInvert the fractiwi whichexpresses the part of thetablet to be used and use itin the following formula: ,

Iriveked fraction x numberof tablets x number of ml toto given patient* = numberof ml of solvent.CSelect the number of ml to begiven the patient by choosinga number divisible by thedenominator of the invertedfraction, and which is no morethan should be given by themethod of injection to be used.

O

CURRICULUM OUTLINECL


VIII. Mathematics Related toHomemaking

A. Review'

1. Ratio

2. Proportion

fl

3. Applice.tion

B. Measurement

I. Linear

VIII. Mathematics Related toHoinerAaking

55

64

A. To demonstrate a basAcunderstanding of ratioand proportion, thestudent should be 0.

able to:

1. Define and identifyratio. Reduce agiVen ratio tosimplest form.

2. Define and identifypropOrtion. Findthe this sing term ofa proportion whenthree of the termsare given.

3. Apply proportion toproblem solving.

B. To demonstrate a basicunderstanding of measure-ment, the student shouldbe able to:

I. Convert from a givenlinear measure to aspecified linearmeasure in the samesystem. (e. g. , convert42 inches tcrfeet)

. RELATED CAREER ORIENTEDCONCEPTS AND OBJECTIVES,


VIII. Career Concept

Careers are opportunitiesfor accornodating differencesin human development.


A. A landscape designeruses a workingk/iowledge of proportionin drawing plans for aspecified project.

B. A sales lady in afabric store estimatesthe amount -of fabricneeded for agarment.

56

Draw a plan of your schoolgrounds. Design an attractiveplan for landscaping thesegrounds over a three yearperiod.

B. Invite a representative from alocal fabric store to bring

ti

samples of material and disctisshow need and price shouldaffect the selection of materialfor a garment.

CURRICULUM OUTLINE

111


2. Liquid

3. Weight

4. Conversion-Metric to English

C. Clothing and textiles

1. Pattern'adfustment

2. Estimating fabric

3. Size of pattern

4. Size of clothing

5. Comparativebuying

C-

57

2. Convert from a givenliquid measure to aspecified liquidmeasure in the samesystem.

3. Convert from a givenweight measure to aspecified weightmeasure in the samesystem.

4. Convert metricmeasures to Englishmeasures and Englishmeasures to metricmeasures.

C. To demonstrate a workingknowledge of the mathe-matics related to clothingand textiles, the studentshould be able to:

1. Make necessarypattern adjustments.

2. Estimate the amountof fabric required ina width other thanthat specified.

3. Determine patternsize .from givenbody measurement.

4. Determine clothingsize from given bodymeasurement andweight.

5. Compare pricesbefore purchasing.


RELA.TED'CAREER ORIB,ONTEDLE RNING ACTIVITIES

C. A children's clothingsales lady sellsclothing and keeps an

merchandiseof

on hand.She also advisescustomers of theappropriateness ofsizes and fabrics forgiven age groups.

C. Interview .a sales person todiscuss the following:1. The best season of the

year to purchase clothingat a savings.

2. The average rate ofdiscount of end-of-seasOnsales.

3. The most common sizesold.

4. Quality versus price.5, Labeling.

CURRICULUM, OUT LINE PERFORMANCEOBJECTIVES

D. Food and nutritiori

LA'1. Increasing or

decreasing recipes

2. Estimating foodneeds

3; Counting calories

'4. Comparativebuying

E. Home decorating

1. Measuringwindows

2. Scale drawing forhouse plan

3. Comparativebuying

59

Go

D. To derncinotrate a basicknowledge of the mathe-matics related to foodand nutritional needs,the student should beable to:

1. Increase or decrease arecipe as specified.

2. Estimate the amountof food needed tofeed.a specifiednumber of persona.

3. Plan a balanced mealwith a specifiedcaloric value.

4. Compare 'priceswhen shopping for

`food to determinethe best buy.

E. To demonstrate a basicundertnding of themathexpat5cs related tohome ilkoorating, thestude0 Should be able to:

easure a windowFturately to determine

rthe correct yardagenecessary for draperies.

Draw a floor plan toscale.

3. Determine the bestbuy for specified piecesof furniture, wheninformation concerningquality and prices aregiven.

RELATED CAREER ORIENTEDCONCEPTS, AND OBJECTIVES


D. A caterer plans,prepares, and servesfood for groupentertainment. Sheuses mathematics toestimate the foodrequirement, and topurchase it atreasonable prices.

D. Plan a weddizig reception for200 guests. A budget of $500foi food is allowed. Decideon a menu, determine thefood costs and the overhead, .

allowing a reasonable profit.

E. An interior decoratorplans and furnishesinteriors of homes andinstitutional buildings.He selects and plansarrangement of ,

furniture, draperies,.floor coverings, andaccessories.

-

60

Estimate what it would cost toredecorate your living room.Consult a catalog to determineapproximate prices of furniture,draperies, lamps, otheraccessories, and wall paint orpaper.


F. Family budget

1. Planning

2. Maintainingrecords

-

G. Consumer orientedpublications

F. To demonstrate a bleicunderstanding of familybudgeting the studentshould be able to:

1. Plan a budget fora specified incomeproviding funds fornecessary expendituresand for a avingo.

2. Set up and maintainrecords of expenditureand balances withinbudgeted amounts.

G. To demonstrate an under-standing of comparativeshopping,,.the student shouldbe aware of the availabilityof several publicationswhich present to theconsumer the results ofunbiased comparativetests of similar productsmanufactured by differentcompanies.



F. A family budgets itsdisposable income tomeet current livingexpenses and to savefor the future.

G. A homemakerplans carefully forthe bes.t buys.

F. Plan a budget for a family thathas a disposable income of$685 per month, if the incomeis budgeted as follows:Food 18%Household Operation 6. 5%Clothing 6%Shelter 25%Transportation 18%Personal Advancement 15%Savings 11.5 %,

62

71

Mrs. Smith has the followinglist of groceries to buy:4 lbs chuck ,roast (Store, A, 87c lb. ,

Store 13, 93' lb. )nShorte ing, 3 lbs (Store A, $1. 3,5

for 3 lb, Store B; $1. 27 for3 lbs. )

Sugar, 10 lbs./ (Store A, $1. 73Store B, $1. 69)

Apples, 5 lbs. (Store A, lb.`Store B, 39c lb. )

If the items at each store are ofequal quality, at which store willshe get the best bargain if she

k plan to buy all four items at onestore?

CURRICOLUKOUTLINE PERFORMANCEOBJECTIVES

IX. Mathematics Related toSports

A. Bas eball

1. Batting averageand field average

2. Earned runaverage

.Won-losspercentage

4. Games behind

5. Bases accumulated

6. Sluggingpercentage

7. Box score

8. Scaleconstruction

IX. Mathematics Related to Sports

63 .

7 g

A. To demonstrate a basicunderstanding of mathe-matics as related tobaseball, the studritshould be able to:'

1. CompUte the battingand fielding averagesof a baseball player.

2. Compute the ERA(earned run average)of a pitcher.

3. Compute a team'swon-loss percentage.

Calculate the numberof games a giventeam is behind theleader in a particularleague.

11&""="0-

5. Compute the totalnumber of basesaccumulated by aplayer.

6. Compute the sluggingpercehfage of a batter.

7. Complete a boxscore of a baseballgame.

A. Draw a baseballfield to scale.

P

RELAXED CAREER ORIENTEDCONCEPTS., AND OBJECTIVES


IX. Carigkr.-Concept

'Individuals may be suitedfor several different careers.

Perf rmance Objectives

A. A professional baseballplayer computes battingfielding, and pitchingpercentages.

A. Use the information below tocompute the batting, fielding,and pitching percentages for abaseball team.

BattingAB R H Pct.

Bevanski 9F 17 , 38Riley ci6 19 32Wardman 88 13 29

FieldingPO A E ,Pct.

Hatton 108 ,,16 1

Chaptharl- 60 87 3

Rociseaun 51 43 2

PitchingWon Lost Pct.

17 3

15 6

12

DrewsofiShieldPhillips

Do similar computations for thelocal baseball team.

0


9. Team's leagueprogress

10. Pitcher's fastball

11. Percent ofgames won

12. Percentagepoint

B. Football

1. Passcompletion rate

. Interception rate

3. Touchdown passrate

4. NFL quarterbackrate

5. Net yardage

6. Numbering system

65

74

0

9. Illustrate a' team'sprogress in a leagueby means of a graph.

10. 'Compute the speed ofa pitcher's fastballfrom the elapsedtime.

11. Relate a team'srecord to thepercent of gameswon (e. g. , a recordof 507 really meansthat the, team won50. 7% of its games).""

12. Explain the truemeaning of the teenr'percentage. point. "

B. To demonstrate a basicunderstanding of mathe-mptics as related tofootball, the studentshould be able to:

1. Compute percent ofpass completions.

2. Compute percent ofinterceptions.

3. Compute percent oftouchdown passes.

. Compute the NFLpercentage for aquarterback.

5. Compute the netyardage in a givenfootball game.

6, Devise a system fornumbering football plays.


RELATED CAREER ORIENTEDLEARNING ACTIVrTIES

4

L

000

B. The coach of afootball team computesthe average weight ofhis linemen, backfieldand entire team.

A statistician for afootball leaguecomputes thepercentage of gameswon.

B.,

66

76

A

The weights of the seven linemenon the State College football teamstarting with left end are 170,195, 185, 188, 174, 215, and 182pounds, respectively. The weightof the backfield men are 168,182, 175, and 179 pounds. Whatis the average weight per manof the line? In the backfield? Ofthe entire team?

Using the information below,compute the percent of wins forteams in this league.

Won Lost Pct.South 10 1

East 8West 4 4North 3 6


7. Weight average

C. Basketball

1. Field goal rate

2. Free throw rate

3. Shot frequencychart

4. Single eliminationtournament

D. Individual sports--scoring, scheduling,and measuring

1. Bowling

2. Handicap

67

7. Compute the averageweight of:a. A team's lineb. A team's backfield

C. To demonstrate a liasicundexotanding of mathe-matics as related tobasketball, each studentshould be able to:

1. Compute the precentof field goals of abasketball player.

2. Compute the percentof free throws of abasketball player,

3. Prepare a shotfrequency chart.

4.' Devise brackets fora single eliminationtournament for eightteams and for sixteenteams,

D. To demonstrate an under-standing of mathematicsrelated to individualsports, each student should.be able to:

1. Compute the score of aplayer in a bowlinggame.

2. Compute the handicapfor a team in a bowlingleague.

10.



C. A statistician forthe school basketball-team computes thetotal points scoredand the averagepoints per game foreach` player.

/

D. A track coach computesthe time for a milerelay team based onthe time of eachrunner.

C. Using the info\rrnation below,find the total points scoredby each player and his averageper game.

Basketball - -Find the total points scoredand average per game to thenearest tenth for each player:

AverageField Foul Total Points

Games Goals Goals Points Per gameFarley 18 136 74Burns 17 129 80Monroe 15 123 87Smith 16 119 68Wood 18 108 59Jones 12 95 47

D.

68

Don, Joe, Fred, ancl,,arsterare members of the mile relayteam. Each boy runs one-fourthof a mile in a mile relay. Intheir last race, the boys wereclocked in 53. 4 seconds, 52. 8seconds, 53. 6 seconds and 51.7seconds respectively. What wasthe time it took the team to runone mile? (Give your answer inseconds, then change this answerto minutes and seconds. )


3.. League schedule

k

4,, Track measure.measurement

5. Qolfing

6. Wrestling

7. Auto racing

69

'3. Devise a schedule fora six-team bowlingleague and a schedulefoil an eight team/league.

Convert English,units used in trackto the correspondingmetric units.

5. Determine the ironwith leaser pitchof two given numberedgolfing irons.Total the score of agolf game (usingthe terms --birdie,eagle, bogie, andpar).

6. Total the score ofa collegerestling

7. Compute the brakingtime of a givenautomobile in agiven race.

RELATED CARER ORIENTEDCONCEPTS AND 0 JECTIVES


An athletic directorof a universitydetermines thewinning team at ,atrack meet, thewinning team at awrestling match,and the. winning teamof a cross countryrace.

70

Find the winning team ineach of the followingmeets or events:

TrackFLA the total points scored, byeach team if 5 points are givenfor each 1st place, 3 points foreach 2nd pla-ce, and 1 point foreach 3replace.

Total1 2 3 Points

Team A 5 3 4=Team B 4 3 3=Team C 2 6 1=Team D 3 1 5=Team E 1 2.2=

O

WrestlingFind the total points scored by eachteam if 5 points are given for a fall,3 points fora decision, and 2 pointsfor. a draw.

FallDecisionDrawTotal points

Team X22

Team Y1

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1

Cross -countryFind the scores of Team A, B, C, D,and E by adding the numberscorresponding to the order in whichthe first 5 members of each teamfinished. The team with the lowest'score (or smallest sum) is thewinner. Which team won if therunners placed as follows: 1. B2. A 3. D 4. E,5. C 6. A 7. D 8. D9. E 10. B 11. A 12. C 13. C 14. A15 C 16. B 17. D 18.1E1 19. E 20. E21. E 22. C 23. A 24., E 25. B 26. D27. C 28. A 29. D 30. E 31. B 32. A.Score: AB C DE Winner: Team


X. Mathematics Related toTravel

A. Latitude and Longitude

1. Definition

a. Equatorb. Parallel of

latitudec. Great circled. prime

'meridiane. International

date linef. Nautical mile

2. Geographic location

3. Distance

4. Time zones

X. Mathematics Related to Travel

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A. To demonstrate anunderstanding of globalcoordinate relationships,the student should beable to:

I. Explain and define thefollowing terms:a. Equatorb. Parallel of

latitude.c. Great circled. Prime meridian

e. Inter nationaldate' line

f. Nautical mile

2. Locate a place on theWorld globe given thelatitude and longitude.

3. Determine the distancebetween two geographiclocations given thelatitude and longitudeof each.

4.. Determine the differencein time given a specifiedtime in two differenttime zones.



X. Career Concept

A person's relationshipswith other people, with hisemployer, and with society,affect his own career aswell as the careers ofothers.


A. A ticket agent computesthe flight time of anairplane trip thatinvolves the crossingof one or more timezones.

A.

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lof

Flight 24/208 left Los Angeles,California at 9:30 A. M.. (PDT)and arrived in Pittsburgh, Pa;at 5:48 P. M. (EDT). Howmany'hours did it take to flyfrom Los Ange les- toPittsburgh? At the time ofarrival in Pittsburgh, whattime is it in Los Angles ?

I''CURRICULUM OUTLINE PERFORMANCE,OBJECTIVES

5. Twenty-four hourclock

Travel by airplane

1. Classes of travel

2. Reading a flightschedule

3. Computing faresa. Basicb. Family planc. Youth

4. Flight insurance

5. Baggage andpersonal effectsinsurance

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5. Convert a 24-hour clockreading to a 12-hourclock reading (e. g. ,2030 hours is 8:30 p. rn. )

B. To demonstrate an under-standing of travel by air,the student should be ableto:

1. Explain the three basictypes of service availableincluding:a. First class (F)b. Coach (Y)

2. Read a flight schedule todetermine for a specifiedflighta. The time of

departureb. The time of

arrival.The connectionsin route

d. The actual hoursin flight regardlessof difference intime zones

3. Compute faies using:a. Basic planb. Family planc. youth plan

4. Determine the amountof flight insurancedesired and thepremium for the policy.

5. Determine the amountof insurance desired onbaggage and personaleffects; compute thepremium.

A

tti

FiHJ0

0

IP



B.

-4.

0

A passenger whotravels by air readsfare tables andflight schedules.

B. Plan a trip from New Orleansto Chicago and use a fare tableand flight schedule to determine'the following:1. Tiine'of arrival at the

destiriation on a specifiedflight.Numbi and identity ofenroute" stops. Time ofarrival and time of

'departure each -itop.

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CURRICULUM, OUT LINE 'PERFORMANCEOBJECTIVES

6. Comparison ofservices

41-C. Traveling by car

1. Car ownership

a. Pa,yments

b. Insurance

c. Operating costs

d. . Depreciation'

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6.. Compare the routes; timeschedules, and fares ofcompetitive lines todetermine the mostconvenient and economicalairline.

C. To demonstrate a basicknowledge 13f travel bycar, the student shouldbe able to:

1. Determine the expensesinvolved in car owner=ship by:'a. Computing the

monthly paymentsafter making adown payment

;b. Computing frominsurance charts ,thefollowing types ofcoverage on acar: prorPertydamage, bodilyinjury, collision,',and comprehensive'insurance'

c. Computing the 'operating costs ,

to include gasoline', _

oil, repairs; etc.

d. Compute the annualdepreciation, and theaverage annualdepreciation for 'aspecified number ofyears.



C. An automobile ownercomputes the operatingcost of his automobilefor a.designatedperiod of time.

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C. Mr. Deville kept an accountof the expenses of his carfor one year. Based on thefollowing data, how much ishis operating cost?

800 gallons of t asoline,,$. 55 per gallon (average);oil filter (every second oilchange), $3. 40 each; .2 pintsdifferential lube, $. 40 perpint; 1 quart transmissionfluid, $1. 00 per quart; 1 canrust inhibitor (radiator);$1. 50 per can; 1 power steeringbelt, $2. 50 each; 12 changesof enging oil (see note)$. 65 per quart; 6 grease jobs,$2. 50 each; miscellaneousrepair charges, $29. 40 total;estimated tire wear $36. 00total (Depreciation notconsidered).Note: 5 quarts with filter change;

4 quarts without filter change.


4

2. Reading a roadmap

3. Determine averagespeed

4. Traveling costs

5. Renting a car

D. Traveling by bus

1. Reading aschedule

2. Computing care

3. Comparison ofcost

2. Read a road map todetermine:a. Which highways to

travel to get fromcity a to city b.

. The distance betweentwo given towns,using the scale inthe legend__

3. Determine the averagespeed maintained on

trip, given the dis-tance and time.

4. Compute the cost ofa trip when a creditcard is used to payfor the trip.

5. Compute the cost ofrenting a car for aspecified length oftime.

D. To demonstrate a basicunderstanding of travelingby bus, the student shouldbe able to:

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1. Interpret a busschedule.

2. Determine fare for aspecified trip.

3. Compare the cost and/orthe advantages of travelby public bus with thoseof travel by privateautomobile.


RELATED CAREEN ORIENTEDLEARNING ACTIVITIES

D. A tourist comparesthe time and cost oftravel by bus withtravel by plane todetermine the mode oftravel he will use on.his vacation.

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D. A factory worker in Baton Rougehas a three week's vacation. Heplans to spend his time inSeattle, Washington. Discus sthe advantages and disadvantagesof (1) making the trip by air and(2) making the trip by bus.(consider time and cost)

CURI{ICULUM OUTLINE PERFORMANCEOBJECTIVES

E. Traveling by,train

1. Reading schedule

2,. Computing basicfare

3. Comparison ofcost

F. Traveling by ship

1., Modes of travela. Cruitheb. reight

s senger line

2. Computing basicfare

3. Nautical mile

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E. To demonstrate an under-standing of traveling bytrain, the student shouldbe able to:

1. Interpret a train,schedule.

2. Compute basic fareand baggage charges.

3. Compare cost and/oradvantages of travelby train with thoh oftravel by plane.

F. To demonstrate a basicunderstanding of travelingby passenger ship, thestudent should be able to:

1. Distinguish betweenmodes of sailing such asa cruise luxury linerand a freight passengerliner.

2. Compute lsic fare andexpress in terms ofdollars per day.

3. Compare the cost and/oradvantages of travelingon a luxury liner withthose of travqing on afreight passenger liner.

4. Determine the distancebetween,two ports innautical miles.



E. A consumer makes acomparison betweentraveling by bus andby train.

4.

F. Many Americanstravel to Europe eachyear for vacation. Thetrip usually involvesseveral modes oftransportation.

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E.

F.

Compare a trip from New Orleansto New York City by bus with'thesame trip by train.

Using brochures obtained froma travel agency, plan a trip toEurope. Estimate the cost ofthe trip if fourteen days areto be spent in Europe. Determinewhat mode of transportation isfeasible at a designated pointduring the trip.

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G. International travel

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G. To demonstrate an under-standing of internationaltravel, each student shouldbe able to convert Americandollars to currency of othercountries, using thecurrent rate of exchange.



G. A worker at a moneyexchange stationconverts Americandollars to foreignmoney.

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G. Convert $100 to Mr-lrig,Francs, Drachmas, Lire,and Pounds, using the currentrate of exchange.

cr,

It STIIMTION REPORT NO . May 74

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