Republic of the Philippines Department of Education PUBLIC TECHNICAL-VOCATIONAL HIGH SCHOOLS PUBLIC TECHNICAL-VOCATIONAL

Learning Outcome 2: Carry out Mensuration and Calculations WEEK 5-8

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Unit of Competency: Perform Mensuration and Calculation

Module No.: 1 Module Title: Performing Mensuration and Calculation

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ACKNOWLEDGEMENT

Program/Course: FURNITURE MAKING NC II

Unit of Competency: PERFORM MENSURATION AND CALCULATIONS

Module Title: Performing Mensuration and Calculations

Learning Outcome 2: Carry out Mensuration and Calculations

ASSESSMENT CRITERIA

1. Calculations needed to complete work task are performed using the form basic process of addition ( + ), subtraction ( - ), multiplication (x), and division (÷) including, but not limited to: trigonometric, functional, algebraic computations. 2. Calculations involving fraction percentages and mixed numbers are used to complete work/task. 3. Numerical computations are self -checked and corrected for accuracy. 4. Accurate measurements are obtained. 5. System of measurement is identified and converted according to job requirements. 6. Work pieces are measured according to job requirements.

References:

1. Cabinet Making and Millwork, Second Edition, John L. Feirer 2. Exploring Woodworking, Fundamentals of Technology, B. Fred W. Zimmerman and Larry J. Mc Ward 3. Handicrafts Handbook, 1975, Tomas M. Quilang 4. Reader’s Digest Book of Skills and Tools 5. Working with Wood, 1982, Gilbert Hutching, Eugene Martin and Mario Coleman 6. Wood Technology and Processes, John L. Feirer 7. Fundamental Woodworking, 1976, Gregorio T. Amano

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LEARNING EXPERIENCES/ACTIVITIES

Learning Outcome 2: Carry-out Mensuration and Calculation

Learning Activities Special Instructions

1. Read the attached information sheet No. 2.1 on System of measurements 2. Answer Self Check No. 2.1

3. Read Information Sheet No. 2.2 Refer the illustration given to an on reading of measurements. actual measuring tool.

4. Answer Self-Check No.2.2

5. Read Operation Sheet No. 2.1 on converting fraction to decimal.

6. Answer Self-Check No. 2.3 on Refer your answer in every self- Let your teacher check your check to respective answer keys answer sheet.

7. Read Information Sheet No. 2.3 on Conversion of linear measurements.

8. Answer Self-Check No. 2.4

9. Read information sheet 2.4 on taking dimensions

10. Answer Self-Check 2.5

11. Read information sheet no.2.5 on calculating board foot of lumber

12. Solve for self-check 2.6 Let your teacher check your computation

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INFORMATION SHEET 2.1

SYSTEM OF MEASUREMENTS

The 2 systems of measurements are: the English and the Metric Systems. The English system originated in England and also known as the U.S. customary system of measurement while the Metric System was developed in France and also known as the S. I. (International Standard).

( UNIT OF MEASURES )

LINEAR MEASUREMENT

ENGLISH METRIC

Yard ( yd ) Meter Foot ( ft ) / („ ) decimeter 1/10 meter Inch (in. ) / (“ ) centimeter 1/ 100 meter Millimeter 1 / 1000 meter

SELF-CHECK 2.1

Directions: Enumerate the ff.

1-2 – 2 systems of measurements

3-5 - Give at least 3 units of linear measurements in the English system

6-9 – Give at least 3 units of linear measurements in the Metric System

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INFORMATION SHEET 2.2

READING OF MEASUREMENTS

A. Reading the inch: The inch is divided into segments called graduations. Each graduation represents a measurement in form of a proper fraction. The inch can be divided into 16, 8,4 and 2, equal parts.

1 3 5 7 9 11 13 15 1 1 1 1 16 16 16 16 16 16 16 16 16 16

1 3 5 7 1 1 1 3 8 8 1 8 8 1 4 4 8 1 0 2 1 4

Note : The illustration is not the actual length of an inch.

B. Reading the centimeter and centimeter

mm mm mm 1 2 3 4 5 6 7 8 910 20 30

0 1 2 3 cm cm cm

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SELF-CHECK 2.2

Direction: Read the following measurements.

1 – 5.

2 5 1 3 4 0 1 2

6 – 10 7 6 8 9 10

0 1 2 3 4

6. cm 7. mm 8. mm 9. mm 10. cm

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OPERATION SHEET 2.1 CONVERTING FRACTION TO

DECIMALS

In converting fractions to decimals, divide the numerator by its denominator whether it is proper, improper or mixed fraction.

Sample Solutions

1. Proper Fraction 2/5 = 0.4

0.4 5 2.0 0 20 20 0

2. Improper Fraction 11/3 = 3.66

3.66 3 11.00 9 20 18 20 18 2

3. Mixed Fraction 2 1 = 2.5 2

0.5 2 2 1.0 1.0 0

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SELF-CHECK 2.3

Directions: Convert the following fractions into decimals.

1. 1/4 2. 3/4 3. 5/8 4. 7/8 5. 9/16 6. 11/5 7. 13/4 8. 9/5 9. 6 3/5 10. 3 2/3 INFORMATION SHEET 2.3

CONVERTING UNITS OF MEASURE

GUIDE TABLE IN UNIT CONVERSION

English to English Metric to Metric

1foot = 12 inches 1 meter = 10 decimeter 1 dm = 10 centimeter 1 cm = 10 millimeter

English to Metric Metric to English

1 inch = 2.54 cm 1 meter = 3.28 feet 1 inch = 25.4 mm 1 meter = 39.37 inches 1 foot = 30.48 cm

Sample Solutions in Conversion

A. Foot to inches 3 ft = inches

Solution : Multiply 3ft by 12 inches / ft = 36 inches

B. Inch to feet 48 inches = Feet

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Solution: Divide 48 inches by 12 inches / feet = 4feet

C. Centimeter to millimeter 22 cm = millimeters

Solution: Multiply 22 cm by 10 mm / cm = 220mm

D. Inch to centimeter 6 inches = centimeter

Solution : Multiply 6 inches by 2.54 cm / inch = 15.24 cm

SELF-CHECK 2.4

Directions: Convert the following measurement into their unit equivalents .

1. 4 meter = cm. 2. 4 meter = ft. 3. 8 feet = inches 4. 20 inches = cm 5. 236.22 inches = meters

INFORMATION SHEET 2.4

TAKING DIMENSIONS

Ways of taking dimension

1. Measure end to end of stock.

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2. Measure edge to edge

3. Measure outside diameter of a cylindrical object.

4. Measure inside diameter

5. Lay-out width.

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SELF-CHECK 2.5

Directions: Identify the different ways of taking dimensions.

1.

2.

3.

4.

5.

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INFORMATION SHEET 2.5

CALCULATING BOARDFOOT OF LUMBER

Although the International System (SI) or Metric System already had and superseded the English System of measure, the board foot as a unit of measure for determining the volume of lumber is still being used by the furniture & cabinet making and construction industry. This is because lumbers are sold in terms of board foot.

A board foot is actually one square foot of lumber of one inch thick

1 foot 1 foot or 12”

1 inch

A board Foot

The formula used in computing board foot is:

Board foot (Bd.Ft.) = T x W x L 12

Where:

T = Thickness in inches W= Width in inches L = Length in feet

Note: This formula is being used for saved wood of commercial dimension.

Example: Compute the board foot of lumber whose dimension is 2” x 4 “ x 12”

Steps 1. Identify the given data Given. T = 2” W = 4” L = 12‟

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Step 2 : Determine what is being asked

Find the Bd. Ft. = ?

Step 3 State the formula

Formula: Bd.Ft. = T x W x L 12

Step 4. Substitute the given data in the formula, then solve.

Solution:

Bd.Ft. = T x W x L 12

= 2” x 4” x 12 “ 12

= 96 12

= 8 Bd.Ft.

SELF-CHECK 2.6 Directions: Compute the number of board feet of the following dimensions.

1. 2” x 6” x 12‟ 2. 3” x 4” x 10‟ 3. 2” x 2” x 16‟

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ANSWER KEY 2.1

1. English System 2. Metric System 3. Inch 4. Foot 5. Yard 6. millimeter 7. centimeter 8. decimeter 9. meter

ANSWER KEY 2.2

1. 3/8” 2. 13/16” 3. 1 ¼ 4. 1 ½ 5. 1 11/16 6. 2 cm 7. 15 mm 8. 28 mm 9. 36 mm 10. 4 cm

ANSWER KEY 2.3

1. .25 2. .75 3. .625 4. .875 5. .563 6. 2.2 7. 3.25 8. 1.8 9. 6.6 10.3.67

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ANSWER KEY 2.4

1. 400cm 2. 13.12 ft. 3. 96 inches 4. 50.8 6. 6 meters

ANSWER KEY 2.5

1. Measure end to end of stock. 2. Measure edge to edge. 3. Measure outside diameter of a cylindrical object 4. Measure inside diameter of a circular object. 5. layout- out width

ANSWER KEY 2.6

1. 12 Bd.Ft.

2. 10 Bd.Ft.

3. 5.33 Bd. Ft.

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