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<Notes><![CDATA[The course you are about to complete contains narration.If you can hear the narration, click the 'Go to Next Page' button.]]></Notes>
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<SlideText><![CDATA[TCI/TA Training: Math for Measurement & Payment   This course you are about to complete contains narration.   If you can hear the narration, click the ‘Go to Next Page’ button.  If you cannot hear the narration, please turn on your speakers or connect your headphones, then click the ‘Repeat Narration’ button.  ]]></SlideText>
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<Title><![CDATA[Math for Measurement & Payment]]></Title>
<Notes><![CDATA[Welcome to the Math for Measurement and Payment course.  This course will provide you with an overview of mathematical operations you will need to apply on the job as a construction inspector.  ]]></Notes>
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<SlideText><![CDATA[Math for Measurement & Payment TCI/TA Training 11-30-2011 ]]></SlideText>
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<Notes><![CDATA[This course contains several navigation tools.On the left of the screen is the ‘Outline’ tab.  Clicking on a title in the ‘Outline’ tab will take you to that screen.If you click the ‘Transcript’ tab you will see a transcript for the screen.]]></Notes>
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<SlideText><![CDATA[Transcript For illustration purposes only.  This is an image of a sample screen. ]]></SlideText>
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<Notes><![CDATA[To adjust the volume of the narration, click the ‘volume’ button at the bottom of the screen or adjust the volume on your speakers.The ‘pause’ button will pause the course.The ‘previous’ and ‘next’ buttons will move to the previous or next screen.The ‘view’ button will toggle through 3 screen-viewing modes.To download attachments at any time, click ‘Attachments.’  Once you have finished viewing the attachments, click the ‘OK’ button to continue with the course.To exit the course, click ‘Exit.’  To confirm that you wish to exit the course, click ‘Exit now.’]]></Notes>
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<Notes><![CDATA[Before proceeding, you should note that you will need to print your results in order to receive credit from PennDOT. If you cannot print, please stop and try again from another computer that can.   You will also need to have a calculator nearby to help you with some of the calculations. ]]></Notes>
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<Notes><![CDATA[The objectives for this course are:To explain why construction inspectors perform calculations. To explain the units of measure commonly used by an inspector for documentation and payment.To explain rounding concepts and decimal measures used on a PennDOT construction project.To explain calculations and demonstrate how to apply them.Mastering these objectives will provide you with the skills you need to work as an effective Transportation Construction Inspector.]]></Notes>
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<SlideText><![CDATA[To explain why construction inspectors perform calculations. To explain the units of measure commonly used by an inspector for documentation and payment. To explain rounding concepts and decimal measures used on a PennDOT construction project. To explain calculations and demonstrate how to apply them.  Course Objectives ]]></SlideText>
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<Title><![CDATA[Section 1: Overview of Construction Project Math]]></Title>
<Notes><![CDATA[As an inspector you are required to measure work performed by the contractor to ensure compliance with specifications and to determine payment for items of completed work.   Some tools you will use are: a retractable tape measure, an engineer’s six foot rule, a calculator, and a measuring wheel.]]></Notes>
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<SlideText><![CDATA[Section 1: Overview of Construction Project Math  ]]></SlideText>
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<Notes><![CDATA[There are six basic types of measurements used by an inspector for project documentation: length, area, volume, liquid measure, weight (or mass) and angles. These measurements are displayed with their most commonly required units and on-the-job applications.   Please take a moment to review the items on the screen. When you are finished reviewing the items, click next to continue.]]></Notes>
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<SlideText><![CDATA[Measurement Unit Application     Length inch, foot, yard, and mile      Area square inch, square foot, and square yard      Volume cubic inch, cubic foot, and cubic yard       Liquid measure pint, quart, and gallon      Weight ounce, pound, and ton      Angle second, minute, and degree      guide rail, pipe paving, shoulder structure concrete,  excavation line paint, tack coat asphalt leveling, rebar survey Units of Measurement When you are finished  reviewing the items,  click ‘Next’ to continue.  ]]></SlideText>
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<Title><![CDATA[Inspector Responsibilities]]></Title>
<Notes><![CDATA[One of your primary responsibilities as an inspector is to measure and document completed work in order to pay the contractor. ]]></Notes>
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<SlideText><![CDATA[Inspector Responsibilities ]]></SlideText>
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<Title><![CDATA[The Decimal System]]></Title>
<Notes><![CDATA[In basic highway mathematics, there are no operations more common than working with and rounding decimals, so let’s focus on working with decimals first.   The entire decimal system is based on tens.  When you view the numbers in the standard way, whole numbers are to the left of the decimal point, and fractions are to the right. Most typically, inspectors will record measured values to the nearest tenth (0.0); perform calculations for payment of that item of work to the nearest thousandth (0.000); and round the result of those calculations to the nearest hundredth (0.00) to arrive at the final pay quantity.  These calculations are completed in your daily PSA or in an I-Book. ]]></Notes>
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<SlideText><![CDATA[The Decimal System Decimals In basic highway mathematics, there are no operations more common than working with decimals. Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Ones (units) . – Decimal Point Tenths Hundredths Thousandths Ten thousandths Hundred thousandths millionths 1246231.1245967 ]]></SlideText>
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<Title><![CDATA[Required Accuracy]]></Title>
<Notes><![CDATA[The required level of accuracy for measurement and payment of items of work are defined in Publication 2, the Project Office Manual (or POM), page B.2.2; in Publication 408, Section 109.01; and under each item’s measurement and payment section within Publication 408.   It is important to discuss any significant differences between plan quantity and actual quantity with your supervisor and to document an explanation that makes reference to where the differences occurred.]]></Notes>
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<SlideText><![CDATA[Required Accuracy ]]></SlideText>
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<Notes><![CDATA[At times you will also need to simply count in order to enumerate item quantities.  The most common types of enumerations are: Set, Bag, Lump Sum, Each, Dollar, and Predetermined Amount (or PDA). These measurements are displayed with their most commonly required units and on-the-job applications.Please take a moment to review the items on the screen. When you are finished reviewing the items, click ‘Next’ to continue.]]></Notes>
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<SlideText><![CDATA[Measurement Unit Application    Set Measured as a unit consisting of two or more parts.     Bag Measured as an item unit bag.     Lump Sum Not measured. Paid as estimated percentage of completed work     Each Measured as the number of individual items      Dollar / PDA A predetermined amount       A pair of bridge supports A bag of bolts Maintenance & Protection of Traffic (MPT), Mobilization, Inspector’s Field Office Bolts, bearing pads survey Counting & Enumeration Measures Specialty item, survey When you are finished  reviewing the items,  click ‘Next’ to continue.  ]]></SlideText>
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<Title><![CDATA[Section 1 Quiz: Construction Project Math]]></Title>
<SlideText><![CDATA[Section 1 Quiz: Construction Project Math]]></SlideText>
<Notes><![CDATA[Please take a moment to answer some review questions from section 1.]]></Notes>
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<Title><![CDATA[Section 2: Construction Project Specifics]]></Title>
<Notes><![CDATA[Every calculation you perform will have a unit of measure associated with it; without it the numbers are meaningless.   Many of the standards and specifications provide both English and Metric values.  For construction projects, all calculations should be done within the system of units of the contract (for example English jobs should be measured, calculated, and paid in English units and vice-versa).  Most calculations you will utilize will be in English and the level of accuracy should be maintained as specified for that item of work.  ]]></Notes>
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<SlideText><![CDATA[Section 2: Construction Project Specifics 17.375 1   22 8.5   31   17.375 feet 22 square yards  8.5 inches  1 ton  31 cubic yards  ]]></SlideText>
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<Title><![CDATA[NICET]]></Title>
<Notes><![CDATA[In addition, if you choose to advance your career by pursuing certification through the National Institute for Certification in Engineering Technologies (or NICET), proficiency with conversions is a required element in your NICET Certification advancement.  It is mandatory that the NICET work element for conversions is successfully completed in order to obtain certification. ]]></Notes>
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<SlideText><![CDATA[Proficiency with conversions is not only required to perform payment calculations, but is also a required element in your NICET Certification advancement.  It is MANDATORY that the NICET work element for conversions is successfully completed in order to obtain certification.   This does reinforce why it's important to be proficient in conversions, but the NICET certification is not discussed anywhere else, so these needs a bit more transition.  NICET National Institute for Certification in Engineering Technologies ]]></SlideText>
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<Title><![CDATA[Units]]></Title>
<Notes><![CDATA[The most important thing to remember in any calculation is that you cannot work with more than one type of unit at one time.  For instance, you cannot subtract 5 inches from 17 feet for an answer of 12.     ]]></Notes>
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<SlideText><![CDATA[               17 -5 12 17 feet  -5 inches 12 units ? Units ]]></SlideText>
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<Title><![CDATA[Unit Conversions]]></Title>
<Notes><![CDATA[But you can subtract 5 inches from 16 feet, 12 inches.  By converting one of the feet into inches we arrive at the correct answer of 16 feet, 7 inches. ]]></Notes>
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<SlideText><![CDATA[               17 feet =  16 feet ,12 inches  -                      5 inches 16 feet ,    7 inches Unit Conversions ]]></SlideText>
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<Title><![CDATA[Percentage Conversions]]></Title>
<Notes><![CDATA[Percentages are closely related to decimals.  76% means 76 parts of a hundred, or 76 over 100, or 76 hundredths.  Follow along as we show how to change a percentage to a decimal.  First drop the percent sign and show the number as a fraction over 100, then move the decimal point two places to the left.  Eliminate the fraction and you have the answer of .76.]]></Notes>
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<SlideText><![CDATA[               76% 0.76 76   76   100 Percentage Conversions ]]></SlideText>
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<Title><![CDATA[Decimal Conversions]]></Title>
<Notes><![CDATA[You will do this in reverse when converting decimals to percentages.Starting with a decimal number, first drop the decimal point and view the number as a fraction over 100.  84 over 100, or 84 hundredths, can be read as 84%. ]]></Notes>
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<SlideText><![CDATA[               76% 84% 0.84 84   84   100 Decimal Conversions ]]></SlideText>
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<Title><![CDATA[Working with Fractions]]></Title>
<SlideText><![CDATA[Working with Fractions]]></SlideText>
<Notes><![CDATA[Please take a moment to answer these review questions.]]></Notes>
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<Title><![CDATA[Fractions]]></Title>
<Notes><![CDATA[A simple fraction is a number that shows some amount that is less than a whole number.  Here we start with a whole apple pie.  If you cut it into four big slices, and take one, you have taken one quarter of the pie. Two of the slices would be 2 quarters of the pie.  When this occurs we usually describe it in the simplest terms, here as one half the pie. In fractions, the bottom half shows how many parts the whole unit has been divided into, and the top half shows the number of parts at hand.  When adding or subtracting fractions, it is important that the bottom numbers be the same.]]></Notes>
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<SlideText><![CDATA[Fractions Mixed numbers are whole numbers displayed with a fraction (for example 18’-9 ¾”).   When dealing with mixed numbers, always work from smallest to largest converting the fraction first and then adding the whole number to it.  Use a calculator and follow the procedure described. Many plans and standard drawings you will regularly encounter display dimensions in feet, inches, and fractions of an inch. It is important that you are able to read common fractions on a tape measure and convert these fractions into decimals prior to performing your computations.   3/4 1/4 2/4 = 1/2 ]]></SlideText>
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<Notes><![CDATA[You may sometimes need to add or subtract fractions. When dealing with fractions always start by converting the bottom numbers, the denominators, so that you are working with the same number of parts.  Work from smallest to largest to convert all the fractions and then add them up.  Here the number that will work for all three fractions is twelfths. So ½ will become 6/12, 1/3 becomes 4/12 and ¼ becomes 3/12. When you add the top numbers together the total is 13/12.  When the top number is larger than the bottom, it means that there is a whole number and a fraction.  In this case this is 1 and 1/12.  This is also called a mixed number.     ]]></Notes>
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<SlideText><![CDATA[               1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = = 13/12 =1  1/12  Adding Fractions ]]></SlideText>
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<Title><![CDATA[Mixed Numbers]]></Title>
<Notes><![CDATA[When dealing with mixed numbers, always convert the fractions first and then add the whole number to it, working from left to right.  Use a calculator and follow the procedure described. In order to add the fractions of inches we need to convert them to a common denominator.  In this example we will use 4.  Now we add 2/4 to ¼ and get ¾.  Next we add 7 inches to 2 inches and get 9 inches.  Finally, we add 27 feet to 32 feet and get 59 feet. ]]></Notes>
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<SlideText><![CDATA[                     27 Feet, 7 1/2 inches + 32 Feet, 2 1/4 inches Mixed Numbers       27 Feet, 7 2/4 inches + 32 Feet, 2 1/4 inches       27 Feet, 7 2/4 inches + 32 Feet, 2 1/4 inches                                3/4  9  59 Feet, 9 3/4 inches ]]></SlideText>
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<Title><![CDATA[Dimensions with Fractions]]></Title>
<Notes><![CDATA[Many plans and standard drawings you will regularly encounter display dimensions in feet, inches, and fractions of inches.  It is important that you are able to read common fractions on a tape measure and convert these fractions into decimals prior to performing your computations.  For example, you will work with feet and hundredths or thousandths of a foot in your computations.  This requires that you first convert foot-and-inch measurements into foot-and-decimal measurements.      ]]></Notes>
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<SlideText><![CDATA[Dimensions with Fractions This requires that you first convert foot-and-inch measurements into foot-and-decimal measurements.       ]]></SlideText>
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<Title><![CDATA[Converting Fractions to Decimals]]></Title>
<Notes><![CDATA[In order to convert the number 2 and 3/8 to a decimal first take the fraction, 3/8 and follow this procedure.3/8 means 3 divided by 8.  When you do this division you get .375.  Put back the 2 we started with and the complete answer is 2.375. ]]></Notes>
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<SlideText><![CDATA[                     = 0.375 Converting Fractions to Decimals       3/8 = 3 ÷ 8          2 3/8 Converting Fraction to Decimals For mixed numbers, always convert the fraction first, and then add the whole number.  Use a calculator and follow the procedure described.        2.375 ]]></SlideText>
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<Title><![CDATA[Math Skills]]></Title>
<Notes><![CDATA[Since the conversion of fractions of inches to decimals is performed so often, you may find it helpful to use a prepared table.  In this example, by first reading across for whole inches and down for fractions, you can get the decimal equivalent. Here you see the decimal equivalent of 3 and 1/32 inches is 0.2526.Since this operation is commonly performed when calculating payments, you will most often convert and round to the thousandths (0.000) of a foot. ]]></Notes>
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<SlideText><![CDATA[Math Skills Converting Inches and Fraction of Inches to Decimals of a Foot Inch 0″ 1″ 2″ 3″ 0 .0000 .0833 .1667 .2500 1/32 .0026 .0859 .1693 .2526 1/16 .0052 .0885 .1719 .2552 3/32 .0078 .0911 .1745 .2578 ]]></SlideText>
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<Title><![CDATA[Rounding]]></Title>
<Notes><![CDATA[Now let’s look deeper into rounding and levels of accuracy. Everyone working for or with the Department must follow the same, specific procedures for rounding.  PennDOT has adopted the American Association of State Highway and Transportation Officials (or AASHTO) guideline, R 11.  This is the Standard Recommended Practice for Indicating Which Places of Figures Are to Be Considered Significant in Specified Limiting Values.  See page 7 of Publication 19, the Field Test Manual, for this reference. Rounding always involves a loss of accuracy.  The Department evaluates the required level of accuracy by asking themselves one question.  “Is it worth the effort?”  Simply put, is it worth the time and effort to calculate a payment past a certain level of accuracy? ]]></Notes>
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<SlideText><![CDATA[Rounding Everyone in the Department must follow the same, specific procedures for rounding. American Association of State Highway and Transportation Officials (AASHTO) R 11: Standard Recommended Practice for Indicating Which Places of Figures Are to Be Considered Significant in Specified Limiting Values Rounding always involves a loss of accuracy, but eases calculations.  Most numbers in highway work are rounded.  Is it worth the effort? ]]></SlideText>
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<Title><![CDATA[Rounding Up]]></Title>
<Notes><![CDATA[To round any number, you first need to determine the last digit that will be kept as determined by the level of accuracy you need.  Once you determine this digit,  look at the next number to the right of it.  Let’s round the number you see to the nearest tenth.  If the next number to the right of the digit to be kept is 4 or lower, drop it and all the other numbers to the right.  If it is 5 or higher, raise the number that shows the level of accuracy you need. Here, since the number to the right of our desired level of accuracy is 8, when rounded to the nearest tenth, our original number becomes 352.3. ]]></Notes>
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<SlideText><![CDATA[                     5 or higher -> Raise it Rounding Up       4 or lower -> Drop it         352.2862      352.3 ]]></SlideText>
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<Title><![CDATA[Rounding Down]]></Title>
<Notes><![CDATA[Let’s round the number you see to the nearest whole number.  Remember, if the next number to the right of the digit to be kept is 4 or lower, drop it and all the other numbers to the right.  If it is 5 or higher, raise the number that shows the level of accuracy you need.  Here, since the number to the right of our desired level of accuracy is 2, when rounded to the nearest whole number, our original number becomes 352.]]></Notes>
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<SlideText><![CDATA[                     5 or higher -> Raise it Rounding Down       4 or lower -> Drop it         352.2862      352 ]]></SlideText>
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<Title><![CDATA[Examples]]></Title>
<Notes><![CDATA[Let’s practice some rounding! Remember, to round any number, you first need to determine the last digit you will keep, as determined by the required level of accuracy for the operation.  Once you determine this digit, look at the next number to the right of it in the expression.  If it is 4 or lower, drop it. If it is 5 or higher, raise it. So looking at the first example, when rounded to the nearest hundred, our number becomes 500. The same number, when rounded to the nearest ten, becomes 470.When rounded to the nearest whole number it becomes 472.  The way you round remains the same when working to the right of the decimal point.  When rounded to the nearest tenth, the number becomes 472.4. When rounded to the nearest hundredth, it becomes 472.39, and when rounded to the nearest thousandth, it becomes 472.386.  Please take a moment to review the items on the screen. When you are finished reviewing the items, click next to continue. ]]></Notes>
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<SlideText><![CDATA[Examples Rounding Numbers Original Number Round to the nearest Answer     472.3862 hundred      472.3862 ten      472.3862 whole number      472.3862 tenth      472.3862 hundredth      472.3862 thousandth      500 470 472 472.4 472.39 472.386 When you are finished  reviewing the items,  click ‘Next’ to continue.  ]]></SlideText>
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<Title><![CDATA[Section 2 Quiz: Construction Project Specifics]]></Title>
<SlideText><![CDATA[Section 2 Quiz: Construction Project Specifics]]></SlideText>
<Notes><![CDATA[Please take a moment to answer some review questions from section 2.]]></Notes>
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<Title><![CDATA[Section 3: Practical Calculations]]></Title>
<Notes><![CDATA[In this section we will apply some of what you have learned to practical uses on the project. This will include:Stationing and offsets;Construction area and volume calculations;Average end area calculations; and,Calculating yields of various materials.  ]]></Notes>
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<SlideText><![CDATA[Section 3: Practical Calculations	 Stationing and offsets Construction area & volume calculations Average end area calculations Calculating yields of various materials ]]></SlideText>
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<Title><![CDATA[Stationing]]></Title>
<Notes><![CDATA[A station, when used as a term of measurement, is a horizontal distance equal to 100 linear feet. A station shown on plans as 0+00 indicates a starting point of 0.  One hundred feet ahead of this starting point will be Station 1+00; two hundred feet ahead will be 2+00, and so on….   These references can be displayed to a level of accuracy of 1+02.33 which equals a distance of 102.33 feet from a starting point of 0+00. ]]></Notes>
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<SlideText><![CDATA[A station = a horizontal distance equal to 100 linear feet.   A station shown on plans as 0+00 indicates a starting point of 0. One hundred feet ahead of this starting point will be Station 1+00; two hundred feet ahead will be 2+00. Stationing ]]></SlideText>
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<Title><![CDATA[Stationing for Payment]]></Title>
<Notes><![CDATA[Each project requires the contractor to provide visible stationing by marking it on the roadway or shoulder with paint, or on stakes which are offset away from the active work area.   As the inspector, you will be required to make payments for the contractor’s work by referencing ‘plan stations,’ the stationing in the plans and tabulations, and documenting the ‘actual stations,’ the locations marked by the contractor, where the work was performed.   The recorded difference between stations should equal the measured distance you are reporting for payment.  This is important when measuring work performed on a curve because the measured distance could be greater than the recorded distance between stations.  This is a common occurrence at intersections.  The reasons for any differences must be reported on your Project Site Activity, or PSA.]]></Notes>
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<SlideText><![CDATA[Stationing for Payment Images Needed:    Stationing (painted on roadway 	and  on stakes) Show PSA payment entry for specific stations  Show stationing depicted on curve ]]></SlideText>
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<Title><![CDATA[Cross Sections]]></Title>
<Notes><![CDATA[Publication 408 defines ‘cross sections’ as a ‘graphic representations of the original ground and the proposed highway, at right angles to the centerline or base line.’  Think of it as taking a slice of the roadway to reveal the various layers of existing ground and proposed construction as well as the location and elevation of underground utilities.     Typically cross sections are shown in increments of 50-feet for the length of the project and have a common centerline, or baseline, which is the center of the proposed work.  Offsets are distances measured from the right or left of the roadway’s centerline, or baseline.   Cross sections are designed to scale, meaning that approximate distances and depths can be measured using an engineer’s scale or other electronic device or program.   Cross sections are commonly used to approximate the location of underground utilities, determine the planned location of storm sewer drainage facilities, such as pipe, inlet types and inlet elevations, as well as calculating volumes of excavation.	   ]]></Notes>
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<SlideText><![CDATA[Cross Sections	 ]]></SlideText>
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<Title><![CDATA[The Use of Geometry in Inspection]]></Title>
<Notes><![CDATA[All highway work revolves around three dimensions:Length is the first dimension.Width, which allows us to define perimeters and areas, is the second dimension.Depth or height, which defines volumes, is the third dimension.These dimensions are used to determine linear distances, and calculate areas and volumes which will then be applied to generate payment for the contractor’s completed work.]]></Notes>
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<SlideText><![CDATA[36 The Use of Geometry in Inspection Length Width Depth ]]></SlideText>
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<Title><![CDATA[Area]]></Title>
<Notes><![CDATA[‘Area’ is the size of a figure on a 2-dimensional surface, that is length and width.  The measurement is in square units. The area formula of an object varies based on its shape and generally involves some multiplication of both the length and width of the object.  ]]></Notes>
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<SlideText><![CDATA[Area Area Area – The size of a figure on a 2-dimensional surface, as measured in square units. The area formula of an object varies based on its shape and generally involves some multiplication of both dimensions of the object. Area is the basis for volume calculations. 1 4 Feet 6 Feet 4 Feet X 6 Feet = 24 Square Feet ]]></SlideText>
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<Title><![CDATA[Area Formulas]]></Title>
<Notes><![CDATA[Area formulas for shapes commonly used in construction are shown.To calculate the area of a square or a rectangle, multiply one side by the other.To calculate the area of a circle, square the radius, that is, multiply the radius by itself, and then multiply the result by Pi, which is 3.14.The area of a triangle is ½ of the base times the height. Please take a moment to review the items on the screen. When you are finished reviewing the items, click next to continue.]]></Notes>
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<SlideText><![CDATA[Area Formulas A Heading for Stuff if Needed a a Square = a2 a Rectangle = a X b b Circle = ∏ r2 (∏ = 3.14)  r b h Triangle = ½ b X h When you have finished reviewing all 5 unsafe actions, click on the ‘Go to Next Section’ button.  When you are finished  reviewing the items,  click ‘Next’ to continue.  ]]></SlideText>
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<Title><![CDATA[Area Formulas (2)]]></Title>
<Notes><![CDATA[The formulas for irregularly shaped objects may seem slightly more difficult, but working through them should prove no more difficult than any other shape. The area of a parallelogram is simply the base times the height.  A trapezoid multiplies the height by the average of the top and bottom.  ]]></Notes>
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<SlideText><![CDATA[Area Formulas (2) A Heading for Stuff if Needed b a Parallelogram = b X h b1 Circle = ∏ R2 (∏ = 3.14)  r Triangle = ½ b X h h Trapezoid = ½ (b1+b2) X h  b2 h ]]></SlideText>
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<Title><![CDATA[Irregular Shapes]]></Title>
<Notes><![CDATA[Another common calculation that relates to both bituminous and concrete paving is the calculation of areas for driveways and side road approaches.  When you have a large and irregularly shaped area, you will need to break it up into smaller pieces that can be calculated more easily.  You can see an example of this in the sketch. By calculating and adding these smaller areas together, you should be able to calculate the total area.Take a moment to review the sketch on your screen, when you have finished reviewing the sketch, click next to continue.]]></Notes>
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<SlideText><![CDATA[Irregular Shapes When you have finished  reviewing the sketch,  Click ‘Next’ to continue.  When you are finished  reviewing the items,  click ‘Next’ to continue.  ]]></SlideText>
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<Title><![CDATA[Volume Formulas]]></Title>
<Notes><![CDATA[Volume is the amount of space occupied in all three dimensions: length, width, and height or depth, and applies to many construction operations including pipe excavation and backfill.  These measurements are shown in cubic units. Area is the basis for determining volume.  Calculating the volume of a solid object involves finding the area of one side (remember that is done by multiplying the length by the width), and then multiplying that area by the third dimension, height.   ]]></Notes>
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<SlideText><![CDATA[Volume Formulas Cube = a3 a Rectangular prism  = l X w X h h l w ]]></SlideText>
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<Title><![CDATA[Volume Formulas Continued]]></Title>
<Notes><![CDATA[With “non-square” solids (such as columns), it is best to find the area of either the top or bottom and then multiply that by the length of the object.  Here the radius is 3 and the height is 9. First find the area of the circle.  Pi is 3.14, so we multiply 3.14 X 3 X 3 and get 28.26.Next take the area you just calculated and multiply it by the height of the cylinder, which is 9. The volume of the cylinder is 254.34 cubic feet.Remember that as you add a dimension, you will move from the linear measure to a square measure and finally to a cubic measure.  ]]></Notes>
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<SlideText><![CDATA[Volume Formulas Continued r 1. Area of Circle =  ∏ r2,  ∏ = 3.14 r h Radius = 3 ft Height = 9 ft  Area = 3.14 X 3 X 3        = 28.26 SF 2. Volume of Cylinder 	= area X h 	= 28.26 X 9 	= 254.34 CF ]]></SlideText>
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<Title><![CDATA[Average End Area Method]]></Title>
<Notes><![CDATA[The Average End Area method is commonly used in conjunction with the project’s cross sections to calculate the volume of excavations in cubic yards, and area of pavement and subbase in square yards.   Most projects establish a template using a Microsoft Excel spreadsheet that allows the inspector to input measurements directly into a program that performs the average end area calculations automatically.  However, it is important to understand how it is being calculated.  ]]></Notes>
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<SlideText><![CDATA[Average End Area Method ]]></SlideText>
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<Title><![CDATA[Average End Area Calculations]]></Title>
<Notes><![CDATA[The following is an example of measurements taken from project cross sections to calculate square yards of subbase.  After entering the applicable date, plan and actual locations, items and item numbers, the inspector records the stations, the actual distance between stations, and the width of subbase at each station.  If cross sections are available on the project, use the widths shown on the cross sections to calculate the square yards of subbase.  Document actual field measurements in the comments section or indicate that field measurements ‘met or exceeded’ cross section widths. Between each station the widths are averaged to obtain an average width for the measured distance between stations.  That average width is then multiplied by the distance between the stations to calculate the square feet of subbase.  Each area of subbase is then totaled and the sum (which will be in decimal feet) is then divided by 9 to determine the square yards for that plan station. Should your result be considerably more or less than the plan quantity, review your calculations.  If there still is a considerable difference, have your supervisor review the calculations and the designer’s calculations that were used to determine the plan quantity for that location.  Explanations for substantial differences between plan and final field-measured quantities must be documented. ]]></Notes>
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<SlideText><![CDATA[Average End Area Calculations ]]></SlideText>
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<Title><![CDATA[Area &amp; Volume Practice]]></Title>
<SlideText><![CDATA[Area  amp; Volume Practice]]></SlideText>
<Notes><![CDATA[Please take a moment to answer these review questions.]]></Notes>
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<Title><![CDATA[Calculating Yields]]></Title>
<Notes><![CDATA[While assigned to bituminous paving operations, the inspector should be familiar with calculating the yields of placed materials to ensure that the proper amount of material is being placed. Even though the work may be paid for as an area, such as a square yard item, yields are calculated to determine if the proper tonnage was placed as represented by the material certifications received by project personnel.  While inspecting a bituminous paving operation you must calculate how far the paver will travel to place a known tonnage of bituminous material.   To calculate the distance that the paver travels with a load of material, the easiest method is to calculate how many tons are placed per foot and then divide the result into the number of tons in the load. You can also assure that placement is at the proper depth by taking random loose depth checks of the material and measuring the compacted depth of the cores that are extracted for testing purposes. ]]></Notes>
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<SlideText><![CDATA[Calculating Yields ?      ?        ?           ?   ]]></SlideText>
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<Title><![CDATA[Yield Example]]></Title>
<Notes><![CDATA[For example, a truck delivers 20 tons of bituminous wearing material and the paver places the material at a width of 12 feet and at a compacted depth of 2 inches.  The weight of your bituminous mixture is indicated on the approved mix design for the project.  For this example, we will use 153 pounds per cubic foot.  First calculate the weight of the material in the delivery truck by converting the load from tons to pounds.  2,000 pounds in 1 ton multiplied by 20 tons in the load is 40,000 pounds.  That result is then divided by the pounds per cubic foot, 153, to give you the volume, 261.44 cubic feet.  You can then calculate the yield by determining how many cubic feet are placed for every foot the paver advances by multiplying the width of the paving, 12 feet, by the depth, 2 inches or 0.17 feet, to get 2.04 cubic feet per linear foot of paving.  Dividing the total volume, 261.44 cubic feet, by the yield, 2.04 cubic feet per linear foot, gives you 128 feet.  This is how far the paver will travel to place the 20 ton load of material. ]]></Notes>
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<SlideText><![CDATA[Yield Example 20 Tons of Bituminous material,  w = 12 ft, d = 2 in  Weight is153 lbs per cubic foot (153 lbs/CF) Multiply 2,000 lbs/ton by 20 tons = 40,000 lbs 40,000 lbs ÷ 153 lbs/CF = 261.44 CF For every 1’ the paver advances, multiply width of paving by depth  of paving.  1 ft X 12 ft X 0.17 ft  = 2.04 CF/LF  This means you will use 2.04 CF of material per linear  foot of paving.    261.44 CF ÷ 2.04 CF/LF  = 128 LF per truck    ]]></SlideText>
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<Title><![CDATA[Section 3 Quiz: Practical Calculations]]></Title>
<SlideText><![CDATA[Section 3 Quiz: Practical Calculations]]></SlideText>
<Notes><![CDATA[Please take a moment to answer some review questions from section 3.]]></Notes>
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<Title><![CDATA[Summary]]></Title>
<Notes><![CDATA[The objectives for this course were:To explain why construction inspectors perform calculations. To explain the units of measure commonly used by an inspector for documentation and payment.To explain rounding concepts and decimal measures used on a PennDOT construction project.To explain calculations and demonstrate how to apply them.]]></Notes>
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<SlideText><![CDATA[To explain why construction inspectors perform calculations. To explain the units of measure commonly used by an inspector for documentation and payment. To explain rounding concepts and decimal measures used on a PennDOT construction project. To explain calculations and demonstrate how to apply them.  Summary ]]></SlideText>
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<Title><![CDATA[Completion]]></Title>
<Notes><![CDATA[You have successfully completed the course materials, but you have not yet finished the course.In order to receive credit you must complete the module test. Once you pass, you will receive instructions on how to send your results to PennDOT.]]></Notes>
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<SlideText><![CDATA[Completion You have successfully completed the course materials, but you have not yet finished the course.     In order to receive credit you must complete the module test. Once you pass, you will receive instructions on how to send your results to PennDOT.  ]]></SlideText>
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<Notes><![CDATA[Congratulations! You have successfully completed the Math for Measurement and Payment course.Please click on the attachments tab, complete the cover sheet, then print and send it to PennDOT, along with the results of your final exam.]]></Notes>
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<SlideText><![CDATA[Completion Congratulations! You have successfully completed the Math for Measurement & Payment course.  Please click on the attachments tab, complete the cover sheet, then print and send it to PennDOT, along with the results of your final exam.     ]]></SlideText>
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<Notes><![CDATA[If your computer system can print to a PDF file, or if you can scan your results to a file, you can email them to PennDOT. The email address is on the cover sheet.]]></Notes>
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<SlideText><![CDATA[Completion via Email  If your computer system can print to a PDF file, or if you can scan your results to a file, you can email them to PennDOT.  The email address is on the cover sheet. Keep the hard copy of your completion until you receive confirmation from PennDOT.  ]]></SlideText>
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