Sue GreckiWorkplace Educator

Formulas at Work

Tradesworkers on the Job

SkillPlan Formulas at Work

Library and Archives Canada Cataloguing in Publication

Grecki Sue, 1956-Formulas at Work : Tradesworkers on the Job, Sue Grecki.

ISBN 978-0-9739232-6-1

1. Building--Mathematics.2.Carpentry--Mathematics.I.SkillPlan(Program)II.Title

QA141.G7372007 513’.1402469 C2007-903074-2

Copyright © 2007SkillPlan – BC Construction Industry Skills Improvement Council

All rights reserved. Reprinted 2010

To order copies of this publication, please contact:

SkillPlanBC Construction Industry Skills Improvement CouncilSuite 405, 3701 Hastings StreetBurnaby, BC, V5C 2H6

Order online: www.skillplan.ca

Coverdesignby LayoutandDesignbyHallographixDesign&Multimedia >Greater Than Graphics

The price of this publication is below market value to make it affordable for individual apprentices and to encourage purchase of class sets. No part of this material may be reproduced or repackaged without permission in writing from SkillPlan.

SkillPlan Formulas at Work

AcknowledgementsAppreciationisextendedtoallthosewhoassistedwiththispublication.WeappreciatetheassistanceofBenandKenBackman,ownersofKingstonConstruction,whowelcomedustooneoftheirconstructionsiteprojectsandallowedustotakephotographs.ThankstoGordonLindbergofOperatingEngineers,JakeLeBlancofSheetMetalandRobBradburyofPacificVocationalCollegeforhelpingwithadditionalphotographsandtradesexpertise.SkillPlanacknowledgesthefinancialcontributionoftheNationalLiteracySecretariat,HumanResourcesandSkillsDevelopmentCanadaforthedevelopmentoftheselearningmaterials.Weareappreciativeoftheirsupportforinitiativesthatcontributetoaskilledworkforce.Theproductionofthispublicationalsorepresentsthecollaborationofdedicatedprofessionals.SkillPlanWorkplaceEducatorsincludeLyndaFownes,VanyaWong,JuliaLewandCorinneVolpatti.Theyhaveallcontributedtothefinalproduct.

About SkillPlan

SkillPlan,ajointlabourandmanagementinitiativeoftheBCconstructionindustry,wasestablishedasanot-for-profitsocietyinMarch1991.TheCouncilistheindustry’sresponsetoanevolvingworkplacethatrequiresgreaterwriting,numeracy,problemsolvingandoralcommunicationskills.SkillPlanbelievesthatasolidfoundationoftheseskillsistheVelcro™towhichallotherskillsstick.Werecognizethattheseskillsarepartofanadult’slifenotonlyatworkbutintheirunionsandthewidercommunity.SkillPlan’sWorkplaceEducatorsareprivilegedtotutorhundredsofbuildingtradesapprenticesandinteractwithtechnicalinstructors,trainingcoordinatorsandthecontractorswhoemploythem.SkillPlanpublicationsaredependantonthisnetworktoaccuratelyreflecttheEssentialSkillsneededonthejob.

SkillPlan Formulas at Work

SkillPlan Formulas at Work

ContentsIntroduction .............................................................................................................. i

How to use the posters and this workbook ..............................................ivSection 1: Calculating Area .................................................................................... 1

Applications for the Warehouse Questions1–4:Roofing Question 5: Paving Asphalt Questions 6 – 10: Using DrawingsOther Applications Question11:Roofing Question 12: Landscaping Questions 13 – 14: Bricklaying

Question 15: Painting Question 16: FloorlayingAnswer Key ............................................................................................ 16

Section 2: Calculating Volume .............................................................................. 23Applications for the Warehouse Questions 1 – 5: Pouring Concrete Questions 6 – 9: Plumbing Question 10: Paving Asphalt

Question 11: LandscapingOther Applications Question 12: Plumbing Questions 13 – 14: Estimating Volume

Question 15: Calculating WeightAnswer Key ............................................................................................ 41

Section 3: Calculating Right-Angle Triangles ....................................................... 49Applications for the Warehouse Questions 1 – 2: Squaring Corners Question 3: Bracing Wall Panels Question 4: Bridging in Joists

Question 5: Building Trusses Question 6: Calculating a Rolling Offset

Other Applications Question 7: Ironwork Questions 8 – 10: Carpentry

Questions 11 – 12: Plumbing Questions 13 – 14: Sheet Metal

Answer Key ............................................................................................ 62

Glossary ............................................................................................................... 67

SkillPlan Formulas at Work

Introduction

SkillPlan Formulas at Work i

IntroductionNumeracyisoneofthenineEssentialSkillsdefinedbyHumanResourcesandSkillsDevelopmentCanada(HRSDC).EssentialSkillsareneededtosuccessfullycompletetasksatwork,athomeandinthecommunity.Formulas at WorkpresentstheEssentialSkillofnumeracyinaconstructionsettingbyconnectingmathoperationswithtrades-relatedworkplacetasks.Theaimofthisresourceistoprovidepracticeinsettingupworkplaceproblemsusingmathoperationsassociatedwitharea,volumeandright-angletriangles.

Formulas at Workdemonstratesatransitionfromworkplaceexamplesfromtypicaljobsitestoabstractformulas.Thisresourcegivesauthenticexamplesofhowarea,volumeandright-angletrianglesareusedbyapprenticesandtradesworkersinconstructiontrades.Forexample,painterscalculateareatodeterminetheamountofpaintneededandplumbersuseright-angletrianglestocalculatethelengthofapipe.Workersfacedwithataskonthejobtranslatetheproblemintosequentialmathematicaloperationsandthencalculatetofindtheinformationtheyneed.

Inthispublication,learnerssimulatethesameprocessoftranslationandcalculation.Someworkplaceproblemsrequireonlyminimaltranslationandonetypeofmathematicaloperation,forexample,calculatingtheareaofawarehouseroof.Othersrequiremultiplestepsofacalculationandacombinationofoperations.Forexample,usingareatodeterminethenumberofsheetsofdrywallorcalculatingthelengthofpipeinarolledoffset.

Althoughthisworkbookemphasizesnumeracy,otherEssentialSkillsarealsopracticed.LearnersuseReadingTextskillstofollowdirections,tolocatemultiplepiecesofinformationandtoidentifyrelevantandirrelevantinformation.TheyuseDocumentUseskillstoreaddrawingstogetoneormorepiecesofinformation.Thinkingskillsareusedtosolveproblemsandmakedecisions.

ThispublicationbringsEssentialSkillstolifeinthecontextofbuildingtradesoccupations.Wehopethatthoselearnerswhousethispublicationwillpracticethesenumeracyskillsandsucceedonthejob,regardlessoftheircareerchoice.

Introduction

ii SkillPlan Formulas at Work

For the InstructorSomeofthelearnersinyourinstructionalsettingmaybeinterestedinenteringanapprenticeshipintheconstructiontradesoryoumaybelookingforsomeworkplaceapplicationsforcalculatingarea,volumeandright-angletriangles.Thisworkbookgivespracticeusingtheseskillsinconstructiontradeapplications.Herearesomepossiblelearningobjectives:

• Increaseunderstandingofthenumeracyskillsusedintheconstructiontrades.

• Reviewandpracticecalculatingarea,volumeandright-angletrianglesasusedinthetrades.

• Familiarizelearnerswithconstructionterminology.• Practicetranslatingworkplaceproblemsintomathematicaloperations.• Demonstratehownumeracyisconnectedtoworkplacetasks.

Herearesomeexamplesofhowyoucanusethisbook:• Useallorsomeofthesectionstocomplementanexistingmathprogramby

providingextrapracticeandreallifeapplications.• Introducestudentswhoareinterestedinenteringatradetonumeracyused

inthetrades.• Buildonstudentwork-relatedexperiencetomotivatelearning.• Useaspartofcurriculumunitorwithotherresources.

Acompanionbook,From the Ground Up: Tradesworkers on the JobprovidesopportunitiestopracticenumeracyandotherEssentialSkillsinaconstructioncontext.AdultswithaninterestinconstructionwilllearnabouttradescareersandthelanguageofCanadianconstructionsitesinthisresource.

Thebookisdividedintothreesections.Thefirstsectionisabouttheconstructionofatilt-upwarehouse,andintroducesthereadertotheterminologyusedonajobsite.Thesecondsectionisanintroductiontocareersinthetradesandfeaturesinterviewswithtradesworkersandinformationabouttheiroccupations.Essential

SkillssuchasReadingText,DocumentUseandNumeracyarethefocusofthethirdsection.Abackgroundinthetradesisnotrequiredtocompletetrades-relatedtaskssuchasinterpretingfloorplans,readingspecificationsforwiringandcalculatinglengthsoflumber.

Introduction

SkillPlan Formulas at Work iii

For the LearnerPerhapsyouarethinkingaboutenteringanapprenticeshipinoneoftheconstructiontradesandyouwanttolearnmoreaboutthenumeracyskillsrequired.Ormaybeyouaretakingamathcourseandwantsomeextrapracticeusingrealworkplaceapplications.Ifyouwanttolearnabouthowarea,volumeandtheright-angletrianglesareusedintheconstructiontradesandtopracticesomerealworkplaceapplications,thisworkbookisforyou.

r

PracticeworkplaceapplicationsusingArea.Forexample:

• Calculatetheamountofroofingmaterialneededforawarehouse.

• Calculatetheamountofpaintneededforaproject.

• Calculatethenumberofsheetsofdrywallneededforaroom.

L

W

H

PracticeworkplaceapplicationsusingVolume.Forexample:

• Calculatethevolumeofconcreterequiredtopourawallpanel.

• Calculatethevolumeofasphaltneededtopaveadrivewayandparkinglots.

• ConvertvolumetoweightandImperialgallons.

a

b

c

PracticeworkplaceapplicationsusingRight-AngleTriangles.Forexample:

• Determineifacornerissquare(90°).• Calculatethelengthofpipeneeded

inapipingoffset.• Calculatethelengthofarafter.

Introduction

iv SkillPlan Formulas at Work

How to use the posters and this workbookPosters

Fourpostersaccompanytheworkbook.Threeoftheposters,Area,VolumeandRight-AngleTriangles,givetheproblemsolvingstepstosettingupanumeracyproblemanduseworkplaceexamplestoillustratethem.Thefourthposter,FormulasforPerimeter,AreaandVolume,isatablewiththeformulasforperimeter,areaandvolumeforavarietyofshapes.Learnerscanchoosethe

appropriateformula,andthenrefertothespecificpostertolearnhowtosetupandsolvespecificproblemtypes.Instructorscanusethepostersforexamplesofhowtosetupandsolvenumeracyproblems.Instructorsinalleducationalsettingsarebestabletodecidehowtousetheseresourcesandtomaketheadaptationsininstructionneededtomeettheneedsoflearners.

WorkbookThisworkbookisdividedintothreesections.Eachsectionfocusesonaspecificmathconcept.Learnerscancompletetheentireworkbook,workononeofthesections,ortryspecificquestionsineachsection.Examplesofquestionsforarea,volumeandright-angletriangles:

Section 1

� SkillPlan Formulas at Work

Question 2. Calculate the number of sheets of Q Decking required for the roof.

Question 1. Calculate the area of the roof of the warehouse.

The roof of the warehouse is made up of � layers.

One of the layers that make up the roofis sheet metal called Q decking.

200'

6�'

Dimensions of the roof.Length = 200' Width = 6�'

12'

3'

Dimensions of one sheet of Q decking.Length = 12' Width = 3'

Section 2

32 SkillPlan Formulas at Work

Question 8b. Calculate the total amount of backfillrequired in cubic feet.Allow 25% more backfill for compaction.

After the pipe has been laid, the trench isfilled with backfill and compacted so theground is level.

Question 8a. The eight inch storm service pipe rests on a four inch layer of bedding material.Calculate the volume of bedding material required.Width of trench = diameter of pipe + 24".

The bedding material supports thepipe so it does not shift or crack.

8"

bedding material

backfill18"

4"

pipe 220' long

diameter of pipe plus 24"

Dimensions of trench.

Section 3

52 SkillPlan Formulas at Work

Question 3: Bracing Wall Panels How many feet from the edge of the floor slab should the embed be placed?

wallpanel

brace

floor slab

Diagonal distance (braces) = 25'Vertical distance = 20'Braces support the wall panels until the roof is

installed. The braces are attached to embeds thatare placed in the wall panel and the floor slab.

brace

embed

embed

Question 4: Bridging in Joists Calculate the length of the bridging pieces.

bridging

joists

Horizontal distance = 14 "Vertical distance = 9"

Diagonal pieces called bridging are nailedbetween the joists to add strength.

bridging

Steps: Example 1: Example 2: Example 3:

1. Read the problem. 1. Calculate the area of thewarehouse roof.

1. Calculate the area of theplayground.

1. Calculate the area of the parking lotand driveway.

2. Draw and label a diagram.

2. 2. 2.

150'

50'

Length = 150' Width = 50'

3. Write the formula or formulas needed.

3. A = L × W

4. Calculate the answer. 4. A= 150' × 50' = 7,500 ft2

3. A = πr2

4. A= π × (8 ft)2

= 201.06 ft2

(rounded off to two decimal places)

3. A = L × W

4. Area 1 = 185' × 35' = 6,475 ft2

Area 2 = 65' × 150' = 9,750 ft2

Total Area =6,475 ft2 + 9,750 ft2 = 16,225 ft2

250'

150'

35'

65'

Warehouse

1

2

Dimension of playgroundradius = 8 ft

Diameter

r =

Introduction

SkillPlan Formulas at Work v

Section 1: AreaThissectiongivespracticecalculatingareawithquestionsthatmimicworkplacetasks.Inconstructionapplications,workerstypicallycalculateareatodeterminetheamountofmaterialsneededtocompleteatask.Howthissectionisorganized:

• Thereare16questions.Eachquestionisbasedonaworkplaceapplication.• Questions1–10useexamplesfromawarehouseconstructionsite.For

example,learnerscalculatetheareaoftheroofandthenusethisinformationtocalculatetheamountofroofingmaterialsneeded.Otherquestionsrequirethelearnertousedrawingstocalculatearea.

• Questions11–16useapplicationsfromotherjobsites.Forexample,learnerscalculatetheareaofacircularplaygroundtodeterminethecostoftherubbersurfacetiles.

Section 2: Volume Thissectiongivespracticecalculatingvolumewithquestionsthatmimicworkplacetasks.Inconstructionapplications,workerstypicallycalculatevolumetodeterminetheamountofmaterialsneededtocompleteatask.Howthissectionisorganized:

• Thereare15questions.Eachquestiongivesaworkplaceapplication.• Questions1–11useexamplesfromawarehouse.Forexample,learners

calculatethevolumeofconcreteinawallpanelandthenusethisinformationtocalculatetheweightofthewallpanel.

• Questions12–15useapplicationsfromotherjobsites.Forexample,learnerscalculatetheweightofasectionofaconcretewatermainthatwillbeliftedintoplacebyamobilecrane.

Section 3: Right-Angle TrianglesThissectiongivespracticeusingright-angletriangleswithquestionsthatmimicworkplacetasks.Inconstructionapplications,workerstypicallyuseright-angletrianglecalculationstocheckordeterminemeasurementstocompleteatask.Howthissectionisorganized:

• Thereare14questions.Eachquestiongivesaworkplaceapplication.• Questions1–6useexamplesfromawarehouse.Forexample,learnersuse

right-angletrianglestodetermineifthecornersonconcreteformworkaresquare.

• Questions7–14useapplicationsfromotherjobsites.Forexample,learnersuseright-angletrianglestocalculatethecentre-to-centrelengthforapieceofpipe.

Introduction

vi SkillPlan Formulas at Work

Quick ReferenceUsethisQuickReferencetofindpracticequestionsrelatedtospecificmathoperationsorconcepts.

Mathematical Foundation Section Question

Numeracy•Calculatelengths Section3:

Right-AngleTrianglesQuestions:1–14

•Calculateareasandvolumesofsimple,familiarshapes

Section1:AreaSection2:Volume

Questions:1–16Questions:1–15

•Calculateareasandvolumesofshapesthataresimplecompositesofsimple,familiarshapes

Section1:AreaSection2:Volume

Questions:5,7,8,10,16Questions:2,5a,10a,10b,

11a,11b•Convertbetweenmeasurement

systemsorbetweenunitsinonesystem,e.g.ft2toyd2,yd3tom3

Section1:AreaSection2:Volume

Questions:4,8,16Questions:3b,15

•Calculatequantitiesofmaterials Section1:AreaSection2:Volume

Questions:2–16Questions:1–5,8–10,11,

15•Estimatequantitiesofmaterials Section2:Volume Questions:13–14