Republic of the Philippines
Department of Education
PUBLIC TECHNICAL-VOCATIONAL
HIGH SCHOOLS
PUBLIC TECHNICAL-VOCATIONAL
HIGH SCHOOLS
Unit of Competency: Perform Mensuration and Calculation
Module No.: 1
Module Title:
Performing Mensuration and
Calculation
Table of Contents
INTRODUCTION .......................................................................................... 1
TECHNICAL TERMS .................................................................................... 2
LEARNING EXPERIENCES / ACTIVITIES ................................................. 4
INFORMATION SHEET # 1 ....................................................................... 5
SELF CHECK # 1.1 ................................................................................ 11
INFORMATION SHEET # 2 ..................................................................... 12
SELF CHECK # 2.1 ................................................................................ 16
INFORMATION SHEET # 3 ..................................................................... 17
SELF-CHECK # 3.1 ................................................................................ 20
LEARNING EXPERIENCES / ACTIVITIES ............................................... 22
INFORMATION SHEET # 2.1 .................................................................. 24
SELF-CHECK # 2.1 ................................................................................ 26
OPERATION SHEET # 2.1 ...................................................................... 27
SELF-CHECK # 2.2 ................................................................................ 29
INFORMATION SHEET # 2.3 .................................................................. 30
SELF-CHECK # 2.3 ................................................................................ 39
INFORMATION SHEET # 2.4 .................................................................. 41
SELF-CHECK # 2.4 ............................................................................... 43
INFORMATION SHEET # 2.5 .................................................................. 44
SELF-CHECK # 2.5 ............................................................................... 47
INFORMATION SHEET # 2.6 .................................................................. 48
SELF-CHECK # 2.6 ................................................................................ 49
ASSESSMENT PLAN.................................................................................. 50
ANSWER KEY ........................................................................................... 54
HOW TO USE THIS MODULE
Activities are properly arranged in this module to help you work at
your own pace, this module also covers the knowledge, skills, and proper
attitudes you need in Drafting Technology.
A pre-assessment precedes the learning activities in each module to
determine your level and need.
The learning activity page gives the sequence of the learning task. This
page serves as the road map in achieving the desired objectives.
After you accomplished all the tasks required, a post-assessment is
given to check if you are already competent with the specified learning
outcome/s and are ready for the next task.
Definitions of terms are provided in this module for your better
understanding.
Program/Course
:
DRAFTING TECHNOLOGY
Unit of Competency
:
PERFORM MENSURATION AND
CALCULATION
Module Title
:
Performing Mensuration and
Calculation
INTRODUCTION
This module is designed to familiarize students with mensuration and
calculation. A description of shape is valueless without proper and complete
indication of size. The shop worker preferably the draftsman must know the
exact width, height and depth of a work piece, as well as the diameter and
precise location of holes.
Accuracy of measurements depends on one's
ability to use measuring tools correctly.
Proper practice in holding different tools, instruments and materials
as well as safety measures are also included in this module.
SUMMARY OF LEARNING OUTCOMES
Upon the completion of this module, you should be able to:
LO1. Select measuring instruments; and
LO2. Carry out measurements and calculation
1
TECHNICAL TERMS
Aligned system is a dimensioning system where all dimensions are parallel
to the line being measured.
Angle is a geometrical figure composed of two straight lines intersecting at
one of their extremities.
Circle is a closed curvewhere all points are equally distant from the center.
Concentric circles consist of two or more circles with a common center.
Cone is generated by a straight line moving in contact with a curved line in
passing through a fixed point.
Dodecahedron is a solid shape with twelve pentagons.
Eccentric circles are circles having no common center.
Heptagon is a polygon with seven sides.
Hexahedron is a solid cube.
Hexagon is a polygon with six sides.
Icosahedron is a solid shape with twenty triangles.
Nonagon is a polygon with seven sides.
Octagon is a polygon with eight sides.
Octahedron is a solid shape with eight triangles.
Pentagon is a polygon with five sides.
Polygon is a plane geometric figure bounded by straight lines.
Prism has two bases which are parallel equal polygon.
Pyramid has a polygon for a base and triangular lateral faces intersecting at
a common point called vertex.
Quadrilateral is a four-sided plane geometrical figure.
Radius is the length of a straight line connecting the center of a circle with a
point on the circumference of a circle.
Sector is a portion of a circle bounded by two radii and the intercepted arc.
Segment is a portion of a circle bounded by an arc and a chord.
Solid is a three-dimensional figure.
Sphere is generated by a circle revolving around each diameter.
Tetrahedron is a solid with four triangles.
2
Program/Course
:
DRAFTING TECHNOLOGY
Unit of Competency
:
PERFORM MENSURATION AND
CALCULATION
Module Title
:
Performing Mensuration and Calculation
Nominal Duration
:
20 hours
Learning Outcome 1
:
Select measuring instruments
Assessment Criteria
1. Objects or components to be measured are identified, classified
and interpreted according to appropriate regular geometric shape.
2. Measuring tools are selected/identified as per object to be
measured per job requirements.
3. Correct specifications are obtained from relevant sources.
4. Measuring instruments are selected according to job requirements.
5. Alternative measuring tools are used without sacrificing cost and
quality of work.
6. Measurements are obtained according to job requirements.
References:
Giesecke, Mitchell and Spencer. Technical Drawing; The Macmillan Company:
1999.
French and Vierck. Engineering Drawing 10th edition MacGraw, Hill Book
Company, 1960
German M. Manaois. Drafting 1 and 2 Phoenix Publishing:1983
Norman Stirling. Introduction to Technical Drawing Delmar Publishing: 1977
Competency Based Learning Material, Civil Technology
3
LEARNING EXPERIENCES / ACTIVITIES
Learning Outcome # 1: Select measuring instruments
Learning Activities
Special Instruction
1. Read Information Sheet No. 1
on geometric figures.
2. Answer Self Check No. 1.1
 Try to answer Self Check No. 1.1.
3. Check your answers using the
answer key.
4. Read Information Sheet No. 2
about measuring tools.
5. Perform task on Self Check No.
2.1

Try to perform the said task.

Ask your teacher on the items
which are difficult to perform.
6. Read Information Sheet No. 3
on
formulas
for
computing
volume, area and perimeter of a
plane and geometric figures.
7. Answer Self Check No. 3.1

Try to answer Self Check No. 3.1
4
INFORMATION SHEET # 1
LO1. Select measuring instruments
GEOMETRIC FIGURES
The geometric figures commonly used in drawing pictures are lines,
angles, triangles, quadrilaterals, regular polygons, circles and arcs and
solids.
LINE.
A line is a set of points. A portion of the line between two distinct
points is a called a line segment. The following are the different kinds of
lines.
1. Straight line. It is the shortest distance between two points.
2. Parallel lines. These are lines on the same plane which will not
meet no matter how long you extend them.
3. Perpendicular lines. These are two intersecting lines which form
right angles.
STRAIGHT LINES
PARALLELL LINES
PERPENDICULAR
LINES
ANGLE. An angle is a figure formed by two rays with common end point.
Angles are classified according to their measures. The following are the
different kinds of angles.
1. Straight angle. It is an angle whose measure is 1800.
2. Right angle. It is an angle whose measure is 900.
5
3 Acute angle. It is an angle whose measure is less than 900.
4. Obtuse angle. It is an angle whose measure is more than 900 but
less than 1800.
5. Complementary angles.
These are two angles whose sum
measures 900.
6. Supplementary angles.
These are two angles whose sum
measures 1800.
180
A
0
0
90
LESS THAN 900
B
STRAIGHT ANGLE
MORE THAN 900
RIGHT ANGLE
180
A
ACUTE ANGLE
0
0
90
A
B
B
OBTUSE ANGLE
SUPPLEMENTARY
ANGLES
COMPLEMENTARY
ANGLES
POLYGON. A polygon is a closed figure formed by line segments intersecting
at end points. The line segments are called sides of the polygon. Polygon is
classified according to the number of sides. The following are the different
kinds of polygon.
1. Triangle. It is a three-sided polygon. The different kinds of triangles are
as follows:
a. Equilateral has all three sides equal.
b. Isosceles has two of the sides equal.
c. Scalene- has three sides of unequal length.
d. Right is where one of the angles is a right angle
6
QUADRILATERALS AND TRIANGLES
RECTANGLE
TRAPEZOID
TRAPEZIUM
SQUARE
ISOSCELES
TRIANGLE
RHOMBUS
RIGHT
TRIANGLE
EQUILATERAL
TRIANGLE
2. Quadrilateral. It is a four sided polygon. The different kinds of
quadrilaterals are as follows:
a.
Parallelogram is a quadrilateral with two pairs of opposite sides
parallel and equal.
b.
Rectangle is a parallelogram with a right angle.
c.
Square is a rectangle with four equal sides.
d.
Rhombus is a parallelogram with a right.
e.
Trapezoid is a quadrilateral with one pair of opposite sides
parallel in which one of them is longer than the other.
f.
Isosceles trapezoid is a trapezoid with its nonparallel sides
equal.
g.
Trapezium is a quadrilateral with no parallel sides and no equal
angles.
3. Pentagon. It is a five-sided polygon. If all the sides and angles of the
pentagon are equal, it is a regular pentagon. The measure of each included
angle is 1080.
4. Hexagon. It is polygon with six sides. If all the sides and angles are equal,
it is a regular hexagon. The measure of each included angle of a regular
hexagon is1200.
7
5. Heptagon. It is a polygon with seven sides. If all the sides and angles are
equal, it is a regular heptagon and the measure of each angle is
approximately equal to 128.560.
6. Octagon. It is a polygon with eight sides. If all the sides and angles are
equal, it is a regular octagon and the measure of each angle is 1350.
7. Nonagon. It is a polygon with nine sides. If all the sides and angles are
equal, it is a regular nonagon and the measure of each angle is 1400.
8. Decagon. It is a polygon with ten sides. If all the sides and angles are
equal, it is a regular decagon and the measure of each angle is 1440.
REGULAR POLYGONS
PENTAGON
HEXAGON
EQUILATERAL
TRIANGLE
OCTAGON
SQUARE
CIRCLE. A circle is a closed curve, all points are equally distant from the
center. An arc is a portion of the circumference of the circle. The following
are terms related to a circle or parts of a circle.
1. Concentric circles consist of two or more circles with a
2. Eccentric circles are circles having no common center.
3. Ellipse is an oblique circle with two axes, the minor axis and the
major axis.
4. Radius is a line segment from the center to any point on the circle.
5. Chord is a line segment whose endpoints lie on the circle.
6. Diameter is a chord that passes through the center.
8
7. Sector is a portion of a circle bounded by two radii and the
intercepted arc.
8. Segment is a portion of a circle bounded by an arc and a chord.
9. Circumference is the distance around the circle. The circumference
is equal to the diameter multiplied by 3.1416.
10. Quadrant is one-fourth of the entire area of the circle.
KINDS AND PARTS OF CIRCLE
CIRCUMFERENCE
ANGLES
CHORD
QUADRANT
0
90
RADIUS
CENTER
RADIUS
TANGENT
ARC
SEGMENT
SECTOR
DIAMETER
CONCENTRIC CIRCLES
ECCENTRIC CIRCLES
SOLID. A solid is a three-dimensional figure. The three dimensions are the
length, width and height. The following are the different kinds of solids.
1. Sphere is a three dimensional figure whose points are located at a
constant distance away from the center.
2. Prism is a three dimensional figure with a polygonal base and
triangular lateral faces.
3. Cube is a prism whose faces are congruent squares. An example of a
cube is a dice.
9
4. Cylinder is a solid figure with two circular bases in parallel plane
and parallel line segments connecting to these bases. An example of a
cylinder is a tin can.
5. Cone is solid figure with a circular base and a surface formed by line
segments joining every point on the edge of the base to a common point
in a parallel plane.
6. Tetrahedron is a solid figure composed of four equilateral triangles.
7. Dodecahedron is a solid figure bounded by twelve equal regular
pentagons.
8. Icosahedron is a solid figure bounded by twenty equilateral triangles.
COMMON GOEMETRIC SOLIDS
CYLINDER
TETRAHEDRON
HEXAHEDRON
SPHERE
DODECAHEDRON
ICOSAHEDRON
OCTAHEDRON OCTAHEDRON
PRISM
CONE
PYRAMID
10
SELF CHECK # 1.1
LO1. Select measuring instruments
Directions:
A. Identify the correct word that has the same relationship to the word as
the first pair. Write the answer on a separate sheet of paper.
1. Quadrilateral: Rhombus
; ____________: Isosceles
2. Circle: Sphere
; Square: ____________
3. 1080: Hexagon
; 1440: ____________
4. Straight: Polygon
; ____________: Circle
5. Line: Triangle
; ____________: Compass
B. Identify the following geometric figures and solids below.
6._____________
7._____________
8._____________
9._____________
10._____________
11.____________
12.____________
_
13.____________
_
14.____________
_
15.____________
_
11
INFORMATION SHEET # 2
LO1. Select measuring instruments
Measuring Tools used for the purpose of measuring dimensions,
measuring tools are imperative for implementing any work with precision.
The measuring tools are also used largely for carrying out different types of
measurements.
Importance of measuring tools
Measuring tools are essential
for examining a finished product or
semi- finished product. The inspection or examination operations include
checking, or testing an object based on the required dimensions given on a
diagram or a sketch. Again the measurements taken must be accurate.
Types of measuring tools
1. T-Square is used a guide in drawing horizontal lines and in
measuring up to 48” straight line.
12
2. Triangles are used for drawing vertical and oblique lines. They are
usually made of celluloid or plastic and come in various sizes. The
most commonly used triangles are the 45 and the 30x 60.
Illustrations below show the proper use of drawing lines and
measuring angles using the T-square and triangle.
TRIANGLE
3. Ruler is the most popular type of measuring tool. It is usually 6 or 12
inches in length. It is needed for measuring sizes and distances.
13
4. Triangular Scale is used in general drawing. Its main purpose is to
reproduce the dimension in full size or to reduce or enlarge them on a
drawing.
TRIANGULAR SCALE
5. Protractor is used for measuring and setting of angles other than
those obtainable with the triangles.
PROTRACTOR
6. Tape or tape ruler is a concave, spring-steel blade ranging from 1/4"
to 1" wide and 6 to about 300 feet in length, coiled inside a carrying
case. Metric tape ruler comes in comparable widths and lengths up to
10 meters. It provides an easy means for accurately measuring curved
surfaces.
14
How to Take Care of Drafting Measuring Tools
Tools will last longer when properly kept and maintained. A good
worker or draftsman keeps and takes care of these tools. The following are
some pointers:
1. Be sure to inspect tools before using them. This is to check if they are
in working condition.This can be detected when there is ease and
speed when in use.
2. After using a tool, clean it thoroughly with a damp cloth. Wipe it dry
with another piece of cloth before keeping it.
3. When not in use, the T-square is preferably hung by inserting the hole
to a nail (attached to a wall) at the end of its blade.
4. Do not abuse or misuse any piece of drawing instruments.
5. Avoid throwing tool to anybody instead hand it over
6. Avoid setting off the distances individually by moving the scale to a
new position each time, because slight errors in the measurements
may accumulate and give rise to a large error.
7. Avoid unnecessary sliding of T-square or triangles across the drawing.
Pick up the triangle by their tips and tilt the T-square blade upward
slightly before moving.
8. Report defective tool and any hazard to instructor immediately.
15
SELF CHECK # 2.1
LO1. Select measuring instruments
A. Directions: Match Column A with Column B. Write only the letter of
the correct answer on a separate sheet of paper.
Column A
1. A measuring tool used to layout an angle or
an arc.
2. Most popular type of measuring tools, usually
6 or 12 inches in length.
3. Its main purpose is to reproduce, reduce or
enlarge the dimension of size on a
drawing.
4. It is used for drawing vertical and oblique
lines.
5. It provides an easy means for accurately
measuring curved surfaces.
Column B
a. Triangle
b. Tape Ruler
c. T-Square
d. Scale
e. Ruler
B. List down at least five uses and care of
drafting or measuring tools.
1. _______________________________________________________________
_______________________________________________________________
2. _______________________________________________________________
_______________________________________________________________
3. _______________________________________________________________
_______________________________________________________________
4. _______________________________________________________________
_______________________________________________________________
5. _______________________________________________________________
_______________________________________________________________
16
INFORMATION SHEET # 3
LO1. Select measuring instruments
Formulas for Computing Volume, Area and Perimeter of a Plane and
Geometric Figures
Perimeter formula
Square
4 x side
Rectangle
2 x (length + width)
Parallelogram
2 x (side1 + side2)
Triangle
side1 + side2 + side3
Regular n-polygon
n x side
Trapezoid
height x (base1 + base2) / 2
Trapezoid
base1 + base2 + height
x [csc(theta1) + csc(theta2)]
Circle
2 x pi x radius
Ellipse
4 x radius1 x E(k,pi/2)
E(k,pi/2) is the Complete
Elliptic Integral of the Second Kind
k = (1/radius1)
x sqrt(radius12 - radius22)
Area formula
Square
side2
or
S2
Rectangle
length x width
or LW
Parallelogram
base x height
or bh
Triangle
base x height / 2
or bh/2 or 1/2bh
Regular n-polygon
(1/4) x n x side2 x cot(pi/n)
Trapezoid
height x (base1 + base2) / 2
Circle
pi x radius2
Ellipse
pi x radius1 x radius2
Cube (surface)
6 x side2
Sphere (surface)
4 x pi x radius2
Cylinder (surface of
side)
perimeter of circle x height
or 6S2
or 4Пr2
2 x pi x radius x height
Cylinder (whole
surface)
Areas of top and bottom circles
+ Area of the side
17
2(pi x radius2) + 2 x pi x radius
x height
Cone (surface)
pi x radius x side
Torus (surface)
pi2 x (radius22 - radius12)
Volume formula
Cube
side3
or S3
Rectangular Prism
side1 x side2 x side3
Sphere
(4/3) x pi x radius3
Ellipsoid
(4/3) x pi x radius1 x radius2
x radius3
Cylinder
pi x radius2 * height
or Пr2h
Cone
(1/3) x pi x radius2 x height
or 1/3 Пr2h
Pyramid
(1/3) x (base area) x height
Torus
(1/4) x pi2 x (r1 + r2) x (r1 - r2)2
or 4/3Пr2
Using the precise measuring tools and accurate formulas, computing
for volume, area and perimeter of a plane and geometric figures can be
attained.
Example No. 1
Compute the volume of a rectangular prism with the given dimensions.
5.00 m
10.00 m
3.00 m
V= HxWxL
Given
H = 3.00 m
W = 5.00 m
L = 10.00 m
Solution:
V = HxWxL
= 3.00 x 5.00 x 10.00
V = 150.00 cu.m
18
Example No. 2
Compute the volume of a cylinder with the given dimensions.
5.00 m
10.00
m
V =
∏r2h where r is the radius of the cylinder and h is its height.
Given
r = 2.50 m
h = 10.00 m
Solution:
V = ∏r2h
= (3.1416)(2.50)2(10.00)
= (3.1416)(6.25)(10.00)
= (19.635)(10.00)
V = 196.35 m3
Example No. 3
Compute the area of a rectangle with the given dimensions.
6.00 m
3.00 m
Given: W= 8m
L=12m
Solution:
A
=
=
=
L x W
6.00m x 3.00m
18.00 m2
19
SELF-CHECK # 3.1
LO1. Select measuring instruments
Directions:
1. Find the total volume of columns located in your drafting room. Select
appropriate measuring tools to be used.
2. Compute the total area of your drafting board.
20
Program/Course
:
DRAFTING TECHNOLOGY
Unit of Competency
:
PERFORM MENSURATION AND
CALCULATION
Module Title
:
Performing Mensuration and
Calculation
Nominal Duration
:
20 hours
Learning Outcome 2
:
Carry out measurements and
calculation
Assessment Criteria
1. Calculation needed to complete workplace tasks are performed
using the four basic processes of addition (+), subtraction (-),
multiplication (x) and division (/) including but not limited to
trigonometric functions and algebraic computations.
2. Calculation involving fractions, percentages and mixed numbers
are used to complete workplace tasks.
3. Numerical computations are self-checked and corrected for
accuracy.
4. Accurate measurements are obtained according to job
requirements.
5. Systems of measurement are identified and converted according to
job requirements.
6. Workpieces are measured according to job requirements.
References:
Giesecke, Mitchell and Spencer. Technical Drawing; The Macmillan Company:
1999.
French and Vierck. Engineering Drawing 10th Edition; MacGraw Hill Book
Company: 1960
German M. Manaois. Drafting 1 and 2, Phoenix Publishing:1983.
Norman Stirling. Introduction to Technical Drawing, Delmar Publishing, 1977.
Competency Based Learning Material, Civil Technology
21
LEARNING EXPERIENCES / ACTIVITIES
Learning Outcome # 2: Carry out measurements and calculation
Learning Activities
Special Instruction
1. Read Information Sheet No. 2.1
on Trade and Mathematics (Two
systems of measurements).
 Answer Self-Check without looking
2. Answer Self Check No. 2.1.
at the information sheet.
3. Check your answers using the
answer key.
4. Read Operation Sheet No. 2.2
about constructing geometric
figures.
5. Perform task on Self Check No.
2.2.
 Try to perform the said task.
 Try to answer Self-Check No. 2.2.
6. Read Information Sheet no. 2.3
on Dimensions.
7. Answer Self Check No. 2.3.
 Try to answer Self-Check No. 2.3.
8. If you missed some of the items,
go over the Information Sheet
again very carefully.
9. Answer again Self-Check no.
2.3.
10. Read Information Sheet No,
2.4 on Ratio and Proportion.
11. Answer Self Check No. 2.4.
 Try to answer Self-Check No. 2.4.
12. Read Information Sheet no.
2.5 on Percentage, Fractions
and Decimal.
22
13. Answer Self Check No. 2.5.
 Try to answer Self-Check No. 2.5.
14. Read Information Sheet no.
2.6 on Unit of Conversion.
15. Answer Self Check No. 2.6.
 Try to answer Self-Check No. 2.6.
23
INFORMATION SHEET # 2.1
LO2. Carry out measurements and calculation
TRADE MATHEMATICS/MEASUREMENT
INTRODUCTION
The word measurement comes from the Greek word "metron,"
meaning limited proportion. The metre (U.S.: meter) was standardized as the
unit for length after the French Revolution, and it has been adopted
throughout the world. Metric scale is applied when the meter is used for
linear measurement. Accurate measurement is essential in many fields, and
since all measurements are necessarily approximations, a great deal of effort
must be taken to make measurements as accurate as possible.
Measuring accurately is a skill that should be developed. Inaccurate
measurement would mean waste of time, effort and materials. The
development of the skill in measuring starts with the ability to read
measurements.
Two systems of measurement
There are two systems of measurement: the English system which
originated in England and the Metric system or Systems International (S.I)
which originated in France.
The basic unit in the S.I. measurement is called the meter. The meter is
divided into 100 centimeters.
Each centimeter is divided into 10
millimeters. They are abbreviated as follows:
Millimeters
Centimeters
Decimeters
Meters
mm
cm
dm
m
In the English system , the inch is divided into 16 graduations and the
smallest graduation is read 1/16
24
In the English system , the inch is divided into 16 graduations and the
smallest graduation is read 1/16
1
16
3
16
1
8
5
16
1
4
7
16
9
16
3
8
11
16
5
8
3
4
1
2
0
13
16
15
16
1 1
1
6
7
8
11
8
1 3
1
6
1
4
1 INCH
To read measurement exceeding 1 inch say 2” and for smaller
graduations, it is read and written as: 2 4/16 or 2 ¼.
1 Foot + 2 inches + 3 smaller graduations, it is read and written as:
3/16
14
In the S.I measurement , the meter is divided into 10 millimeters. as
shown below:
0
mm
1 2 3 4 5 6 7 8 9 10
mm
20
mm
30
1
cm
2
cm
3
cm
25
SELF-CHECK # 2.1
LO2. Carry out measurements and calculation
Directions: Write the correct measurements starting from the end of ruler at
the left to the points as indicated by extension lines. Use a separate sheet of
paper.
A. English System
2
1
3
1 INCH
6
5
4
1
2 INCH
B. Metric System
8
7
2
1
3
4
5 CM
10
9
1
2 CM
OPERATION SHEET # 2.1
26
OPERATION SHEET # 2.1
LO2. Carry out measurements and calculation
One way to practice the use of drawing instruments and drawing
geometric figures mechanically is to solve geometrical problems graphically.
In fact, a concerned draftsman always applies the four (4) basic operations
of mathematics, such as addition, subtraction, multiplication and division.
The following problems include computations needed in drawing
geometric figures.
1.
Construct a hexagon with the given radius.
Given: 30 mm
Steps:
a. Draw a circle with the given radius equivalent to 30 mm.
b. Draw a horizontal line passing through the center of the circle until
it intersects the circumference at points 1 and 4.
c. With these two points as centers and with the same radius, draw
two arcs so that they will intersect the circumference at points 2,
3, 5, and 6.
d. The straight lines connecting all these points become the sides of
the polygon.
2
3
1
4
6
5
Constructing a regular hexagon
27
2.
Draw an arc tangent to two unequal circles.
Given 2 circles of unequal radii and the radius r
R1 =
; smaller circle
R2 =
; bigger circle
R =
: given radius
Steps:
a. Add the radius of the smaller circle R1 and the given radius r
b. Using this sum as the radius and point O1 as center, draw an arc
above and between the two given circles.
c. Add the radius of the larger circle R2 and the given radius r.
d. Using this sum as the radius and point O2 as center, draw an arc
so that it will intersect the other arc at point O3. The points of
tangency, P1 and P2 are found by drawing straight lines from the
centers of the two circles.
An arc tangent to two unequal arcs
28
SELF-CHECK # 2.2
LO2. Carry out measurements and calculation
A.
Directions: Solve the following geometric problems by applying the four
fundamental operations. Write the solution on a separate sheet of paper.
1. Given the diameter equal to 75 mm, draw a regular pentagon.
2. Draw an arc tangent to two unequal circles.
Given 2 circles of unequal radii and the radius r
R1 =
15 mm
R2 =
25 mm
R =
20 mm
B.
Directions: Draw the following geometric figures applying the freehand
drawing technique.
1. Square
2. Rectangle
3. Circle
4. Ellipse
5. Polygon
6. Simple geometric solids such as cube, prism, pyramid and
cylinder
29
INFORMATION SHEET # 2.3
LO2. Carry out measurements and calculation
DIMENSION
Dimension is the numerical value that is being assigned to the size,
shape or location of the feature being described. Dimensions are indicated in
drawings by dimension lines and numerical figures. A properly dimensioned
drawing helps ensure that the part produced in the manufacturing phase
matches the part asked for.
Before we begin to study the rules for dimensioning, let us learn first
the anatomy of a dimension (Please see figure below).
FIG. 1 Anatomy of a dimension.
30
KINDS OF DIMENSION
a. Size Dimension tells how large or small an object is.
b. Location Dimension locates a feature of an object.
Location and size dimension
DIMENSIONING SYSTEM
a. Aligned system are figures aligned with the dimension lines so that
they may be read from the bottom or from the right side of the sheet.
(Note: Dimensions and notes shown with leader lines are aligned with
the bottom of the page.)
b. Unidirectional system are figures and notes lettered horizontally on
the sheet and read from the bottom of the drawing.
/ ALIGNED
System of placing dimensions
31
OVERALL DIMENSIONS are the total thickness or height, width and
length of an object.
DETAILED DIMENSIONS are the thickness, length and width of each
part of the same object.
RULES IN DIMENSIONING
The following rules provide some simple guidelines to be followed when
placing dimensions on a drawing.

The dimension should be applied in the view that provides the best
description of the feature being dimensioned. For example, holes
should be dimensioned in a view where they appear round. Generally
the dimension is placed between views.
Sample illustration of placing dimensions

Apply dimensions in a view where the feature appears in its true size.

Reference dimensions should be placed in parenthesis. This means
that it is not required. The total length is known because the radius of
the curve on the left side is given.
32
Parenthesis is placed in reference dimension

The dimension should be centered between the extension lines.

The dimension may be placed outside of the dimension lines if there is
insufficient space. The arrows may point out depending on the
available space.
The dimension should be centered between the extension lines.

Place larger dimensions towards the outside so that extension lines
don’t cross dimension lines.
33
Avoid crossing dimension lines

Do not over-dimension. Each feature should be dimensioned once.

If aligned dimension is used, dimensions must be read from the lower
or right-hand side of the sheet. If unidirectional system is used, all
dimensions must be read from the bottom of the sheet.

Dimension lines should not end at object lines. Use extension lines to
relate the dimension to the feature being described.

Do not place dimensions in the view. Use extension lines from the
feature and locate the dimension outside of the view.
34
Using extension lines in dimensioning

Use the diameter dimension to specify the size of holes and cylinders.
Precede the dimension with the diameter symbol Ø.

Use the radius to dimension an arc. The radius dimension is preceded
by the symbol R.
For round holes, dimension with the diameter symbol Ø. For arcs, use
radius dimension preceded by the symbol r.

Concentric circles should be dimensioned in a longitudinal view.
35
Dimensioning concentric circles.

Stagger the dimensions if they are stacked.

Dimensions should be uniformly spaced.

Circular features should be located by dimensioning the centerlines
Circles are located through dimensioning the centerlines.
36

Avoid dimensioning hidden lines. Create a section view if necessary to
dimension an object line.
Dimensioning hidden edges
OTHER DIMENSIONING RULES

Dimensions should generally be placed between views.

Avoid repetition of dimensions.

Dimension lines should be parallel to the edge or line being measured.

The flares of the arrowhead should be properly made.

The fine line in a dimension line must be strictly observed.

The figures or numbers in a dimension line should be legible and
properly located.

Use an outside dimension if the space is limited and use inside
dimension if the space is ample or wide.

Continuous dimensions should be used whenever possible.

Staggered dimensioning should be used when the spaces for the
dimensions are narrow.

A dimension line may be terminated by a projection or center line.

Dimension lines should not be extended beyond the edge of line being
measured.

Arrowheads should point to the terminating line and not to the
dimensional figure.
37

Let no workman add or subtract dimensions.

When giving the location dimensions for round holes, measure the
center-to-center distance between holes and from the center line of the
holes to the two nearest visible lines.

Never crowd dimensions.

Give the diameter of a circle or round hole and radii of arcs.

Projection or extension lines and other alphabet of lines used in
dimensioning should be properly drawn.
38
SELF-CHECK # 2.3
LO2. Carry out measurements and calculation
Directions: Write TRUE if the statement is correct and FALSE if it is wrong
then write the word/s that makes it correct. Use a separate sheet of paper.
1. All lettering and numerals must be perfectly legible.
2. Standard height of numerals is 1”.
3. Dimension should generally be placed between views.
4. Notes are not always placed parallel to the right side of drawing.
5. Use lower case letters in dimensioning notes.
6. Avoid repetitions of dimensions.
7. Use an outside dimension if the space is limited and an inside
dimension if the space is ample or wide.
8. Continuous dimensioning should be used whenever possible.
9. Extension lines should end exactly at the arrowhead.
10. A dimension line may be terminated by a projection, visible, hidden
or center line.
II. IDENTIFICATION
A. Identify the basic dimensions of an object
B. Name the elements of
dimension
14
11
_____ 11.
_____ 12.
2.00
12
15
_____ 13.
_____ 14.
_____ 15.
13
39
B.
Identify the kinds of dimension by placing L for location dimension and
S for size dimension
_____ 16.
Dimension A
_____ 17.
Dimension B
_____ 18.
Dimension C
_____ 19.
Dimension E
_____ 20.
Dimension F
A
B
C
E
A
D
A
F
A
E
A
G
H
G
A
40
INFORMATION SHEET # 2.4
LO2. Carry out measurements and calculation
RATIO AND PROPORTION
 Proportion
A proportion is an equation with a ratio on each side. It is a
statement that two ratios are equal. Example:
3 6

4 8
When one of the four numbers in a proportion is unknown, cross
products may be used to find the unknown number. This is called solving
the proportion. Question marks or letters are frequently used in place of the
unknown number.
Example:
Solve for n:
1 n
 .
2 4
Using cross products, we see that 2xn=1x4=4, so 2xn=4. Dividing
both sides by 2 n=4÷2 so that n=2.
 Ratio
A ratio is a comparison of two numbers. We generally separate the two
numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8
and 12. We can write this as 8:12 or as fraction 8/12, and we say the ratio is
eight to twelve.
Examples:
Jerson has a bag with 3 videocams, 4 marbles, 7 books, and 1 mango.
1.
What is the ratio of books to marbles?
Expressed as a fraction, with the numerator equal to the first quantity and
the denominator equal to the second, the answer would be 7/4.
Two other ways of writing the ratio are 7 to 4, and 7:4.
41
2.
What is the ratio of the videocams to the total number of items in the
bag? There are 3 videocams, and 3+4+7+1 = 15 items total.The answer can
be expressed as 3/15, 3 to 15 or 3:15.
42
SELF-CHECK # 2.4
LO2. Carry out measurements and calculation
I. Directions: Solve the following. Use a separate sheet of paper.
1. 1 = N
5
10
2. 3 = 6
4
N
3. 2 = N
5
20
II. Find the ratio of the following
Gemir has a box with 4 sets of drawing instruments,8 pcs of drawing
papers, 2 boxes of craypass and 7 drawing pencils
4. What is the ratio of the box to the drawing instruments?
5. What about the ratio of the box to the drawing pencils?
43
INFORMATION SHEET # 2.5
LO2. Carry out measurements and calculation
PERCENTAGE , FRACTION AND DECIMAL
How To Compute Percentage
The simplest way to compute percentage is to divide the given amount
by the total and then multiply the answer by 100.
The equation can be put up as follows:
(Given amount /Total amount) x100
For example, if John scores 60 out of 75 in Drafting Technology, we
can find the percentage of his marks by dividing 60 by 75 the answer is 0.8,
then multiplying it by 100 the percentage of his marks is 80%.
Example: (60/75) x 100= 80%
ROUNDING OFF DECIMALS
Metric measurements in decimals are often long numbers. They must
often be rounded to a convenient number of digits. In this text most metric
dimensions are either whole millimeter or two-places decimals that have
been rounded off. To help you round off your own calculation, rules of
rounding are discussed below.
1. If the first number to be eliminated is less than 5, simply drop it (and the
number to the right of it) and let the last significant digit stand.
Example:
Round off 25.4 mm to whole millimeter.
Solution: Simply drop the .4
Answer: 25
44
Example : Round off 0.3125 (5/16) into two significant digits.
Solution: The first number to be eliminated is 2: Simply drop it
and all numbers to its right(5)
Answer:0.31
2. If the number to be eliminated is 5 or more, drop the number, then add
one to the last digit retained.
Example:
a. Round off 78.6 into its nearest ones.
Solution:
The number to be rounded off is 6 which is greater than
5, drop 6 and add one to the last digit retained.
Answer: 79
b. Round off 92.65 into its nearest tenths.
Solution:
The number to be rounded off is 5, drop 5 and add one to
6 which is the last digit retained.
Answer: 92.7
Millimeters Equivalent of Decimals and Fractions of an Inch.
Fractions
Decimals
Millimeter
1/16
0.0625
1.588
1/18
0.1250
3.175
3/16
0.1875
4.762
1/4
0.2500
6.350
5/16
0.3125
7.938
3/8
0.3750
9.525
7/16
0.4375
11.112
1/2
0.5000
12.700
9/16
05625
14.288
45
5/8
0.6250
15.875
11/16
.0.6875
17.462
3/4
0.7500
19.050
13/16
0.8125
20.638
7/8
0.8750
22.225
15/16
0.9375
23.812
1
1.00
25.400
This table is used to find the equivalent decimal numbers and millimeters of
a given fraction
46
SELF-CHECK # 2.5
LO2. Carry out measurements and calculation
Directions: Convert the numbers into Decimals. Write your answer on a
separate sheet of paper.
Practice Activity
Sample :
½ =N
.5
2
1.
0
10
0
TEST I. Answer the next activity based from the sample
1. ¼ to decimal
2. ¾ to decimal
3. 7/16 to decimal
4. 3/8 to decimal
5. 1/8 to decimal
_____________
_____________
_____________
_____________
_____________
TEST II. Round off the following numbers to their nearest hundredths.
1. 76.3456
2. 93.674
3. 27.009
4. 4.6245
5. 5.2532
_____________
_____________
_____________
_____________
_____________
TEST III. Change the following decimals to percent.
1. 0.78
2. 8.2
3. 0.86
4. 9
5. 1
_____________
_____________
_____________
_____________
_____________
TEST IV. Change the following percent to decimals.
1. 92.5% _____________
2. 78% _____________
3. 2%
_____________
4. 50% _____________
5. 2. 5% _____________
47
INFORMATION SHEET # 2.6
LO2. Carry out measurements and calculation
UNIT OF CONVERSION
System International (SI) to English
1 meter
=
39.37
=
3.28083 Feet
0. 3048 meter
= 1 Foot
1 centimeters
= 0.3937 inch
2.54 Centimeters
= 1 inch
1 millimeter
= 0.03937 inch
2.54 millimeter
= 1 inch
1 Kilometer
= 1093.61 yards
COVERSION FROM INCHES TO METER
A simple guide is adopted so that anybody could easily determine the
equivalent values of the English to metric system or vice versa.
Example:
1. To convert meter to feet, divide the length by .30
say 6.0m = 20 ft.
.30
2. To convert feet to meter, multiply by .30
say 30ft x .30 =9.0 meters
3. To convert inches to meter, follow the additional conversion table
below:
1inch = .25m
2 inches= .050m
3inches = .075m
4inches = .10m
48
SELF-CHECK # 2.6
LO2. Carry out measurements and calculation
Directions: Convert the following. Write your answer on a separate sheet of
paper.Round off your answers into two decimal places.
1. 25 cm to ………………………………… inches
2. 63 mto …………………………………... feet
3. 50 ft to …………………………………… meters
4. 13 inches ……………………………….. meters
5. 10 mm to ……………………………….. inches
49
ASSESSMENT RESOURCES
Performance Assessment
Scoring Rubrics
Criteria
Score
(Tick the corresponding pts.)
Accuracy
50
45
40
Speed
10
6
8
Neatness
25
20
15
Lettering/Labeling
15
12
10
8
Total
Performance Criteria:
 Accuracy
50 pts
-
the output is accurately done
45 pts
-
two to five errors are observed on the output
40 pts.
-
six to ten errors are observed on the output
10 pts
-
the output is done 5 minutes before the time
8 pts
-
the output is done on time
6 pts.
-
the output is done after the allotted time
 Speed
 Neatness
25 pts.
-
has no error
20 pts
-
has two to three erasures
15 pts
-
has four or more erasures
50
 Lettering/Labeling
15 pts.
-
all pieces of information are completely indicated and legibly
printed.
12 pts
-
all pieces of information are legibly printed but some are
missing.
10 pts.
-
all pieces of information are legibly printed but some are
missing and misspelled.
8 pts
-
pieces of information are not legibly printed and words are
missing and misspelled
51
ASSESSMENT PLAN
Evidence Checklist
Competency standard:
Drafting Technology
Unit of competency:
Performing Mensuration and Calculation

Objects or components
Questioning
Written Test
LO1- Select Measuring Instrument
Direct Observation
Actual Demonstration
Title of Module
Perform Mensuration and Calculation
Ways in which evidence will be collected:
[tick the column]
to be measured are identified,
classified and interpreted according to the appropriate
regular geometric shape.

Measuring tools are selected/identified as per object to
be measured for job requirements

Correct
specifications
are
obtained
from
relevant
sources.

Measuring instruments are selected according to job
requirements

Alternative
measuring
tools
are
selected
without
sacrificing cost and quality of work.

Measurements are obtained according to job
requirements.
LO2. Carry out measurements and calculations

Calculation needed to complete workplace tasks are
performed using the four basic processes of addition (+),
subtraction (-), multiplication (x) and division (/)
including but not limited to trigonometric functions and
algebraic computations.
52

Calculation involving fractions, percentages and mixed
numbers are used to complete workplace tasks

Numerical computations are self-checked and corrected
for accuracy.

Accurate measurements are obtained according to job
requirements

Converted
system
of
measurements
are
identified
according to job requirements

Workpieces are measured according to job requirements.
Prepared by:
Date:
Checked by:
Date:
NOTE: *Critical aspects of competency
53
ANSWER KEY
Self -Check 1.1
A.
1. Triangle
2. Cube
3. Decagon
4. Curve
5. Arc
B.
6. Cylinder
7. Cube
8. Dodecahedron
9. Pyramid
10. Pentagon
11. Cone
12. Icosahedron
13. Octahedron
14. Rectangle
15. Sphere
Self -Check 1.2
1. B
2. E
3. D
4. A
5. F
Self -Check 1.3 ( Teacher’s Check)
Self -Check 2.1
A. English System
1. 9/16”
2. 13/16”
3. 3/8”
4. 15/16”
5. 1 7/8”
6. 2 ¼”
B. Metric System
7. 1.30 cm or 13 mm
8. 3.70 cm or 37 mm
9. .40 cm or 4mm
10. .75 cm or 7.5 mm
54
Self -Check 2.2 ( Teacher’s Check)
Self -Check 2.3
I.
1. True
2. False – 1/8” or 3mm
3. True
4. False – left side
5. False – capital letters/ uppercase
6. False – repetition
7. True
8. True
9. True
10. True
II. A.
11. Depth
12.Height
13.Width
14.Number or figure
15.Extension line
B.
16. S
17. S
18. L
19. L
20. S
Self -Check 2.4
1. N = 2
2. N = 8
3. N = 4
4. 4;8
5. 2;7
Self -Check 2.5
I.
1. 0.25
2. 0.75
3. 0.43
4. 0.37
5. 0.125
II.
1. 76.35
2. 93.67
55
3. 27.01
4. 4.62
5. 5.25
III.
1. 78%
2. 820%
3. 86%
4. 900%
5. 100%
IV.
1. .925
2. .78
3. .002
4. .50
5. .0025
Self -Check 2.6
1. 9.84 inches
2. 206.74 feet
3. 15.24 meters
4. 0.33 meter
5. 0.39 inch
56
ACKNOWLEDGEMENT
We, the teachers assigned to work on the Competency Based
Curriculum (CBC) and Contextual Learning Material (CLM) and
Competency – Based Learning Modules (CBLM) particularly in Drafting
Technology, wish to express our gratitude and appreciation for having been
given the chance to take part in this educational breakthrough. With high
hopes we look forward to the improvement of the Technical-Vocational
Education of the country through the development of functional materials
such of this kind.
Marikina Hotel
Marikina City
May 25-30, 2009
June 5-7, 2009
Technology Writers
Conrado C. Casulla
Pangasinan School of Arts and Trades
Lingayen, Pangasinan
Region I
Mirasol F. Dasig
San Pedro Relocation Center National High School
San Pedro, Laguna
Region IV-A, Calabarzon
Rolando V. Inay
E. Rodriguez Vocational High School
Nagtahan,Sampaloc,Manila
Mario S. Gregorio
Tagum National Trade School
Tagum City, Davao Del Norte
Region XI
Alexander M. Latoga
Manuel S. Enverga Memorial School of Arts and Trades
Mauban, Quezon
Ariel F. Maglalang
Assemblywoman Felecita G. Bernardino Memorial Trade School
Lias, Marilao, Bulacan
57
English Teacher
Mercy F. Divina
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Math Teacher
Emmanuel V. Dionisio
Assemblywoman Felecita G. Bernardino Memorial Trade School
Lias, Marilao, Bulacan
Science Teacher
Ma. Lenalyn Q. Manzano
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Editorial Specialist
Estrelita Y. Evangelista Ed.D. (Ret.)
CESO VI
DepED-Director, BSE
Beatriz A. Adriano
Principal III
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Carolina F. Chavez
Principal II
Muntinlupa Business High School
Facilitator
Orlando E. Manuel Ph.D.
Principal I
Cabarroguis National School of Arts and Trades
Gundaway, Cabarroguis, Quirino
Region II
Math Specialist
Jesus L. Huenda
Senior Education Program Specialist
DepED-BSE
58
Encoders
Eduardo B. Dicion Jr.
Integrative School of Quezon City
U.P. Village, Diliman, Quezon City
Jomel Gail O. Ponce
One World Connection
31/F Wynsun Corporate Plaza
Ortigas Center, Pasig City
Percival Magaway
Cabarroguis Natural School of Arts and Trades
Gundaway, Cabarroguis, Quirino
Region II
59
Republic of the Philippines
Department of Education
PUBLIC TECHNICAL-VOCATIONAL
HIGH SCHOOLS
PUBLIC TECHNICAL-VOCATIONAL
HIGH SCHOOLS
Unit of Competency: Interpret technical drawings and plans
Module No.: 2
Module Title: Interpreting technical drawings
and plans
HOW TO USE THIS MODULE
Activities are properly arranged in this module to help you work
at your own pace, this module also covers the knowledge, skills, and
proper attitudes you need Drafting Technology.
A pre-assessment precedes the learning activities in each
module to determine your level and need.
The learning activity page gives the sequence of the learning
task. This page serves as the road map in achieving the desired
objectives.
After you accomplished all the tasks required, a postassessment is given to check if you are already competent with the
specified learning outcome/s and are ready for the next task.
Definitions of terms are provided in this module for your better
understanding.
Table of Contents
INTRODUCTION ......................................................................................... 1
TECHNICAL TERMS ................................................................................... 3
DRAFTING TECHNOLOGY...................................................................... 5
INFORMATION SHEET # 1.1 ................................................................. 6-8
SELF CHECK # 1.1 .................................................................................. 9
INFORMATION SHEET # 1.2 ............................................................. 10-14
SELF CHECK # 1.2 ........................................................................... 15-16
DRAFTING TECHNOLOGY............................................................... 17-21
INFORMATION SHEET # 2.1 ............................................................. 22-29
SELF CHECK # 2.1.1 ............................................................................. 30
OPERATION SHEET # 2.1 ................................................................. 31-37
SELF-CHECK # 2.1.2............................................................................. 38
INFORMATION SHEET 2.2 ............................................................... 39-40
OPERATION SHEET # 2.2.1 .............................................................. 41-42
SELF CHECK # 2.2.1 ............................................................................. 43
OPERATION SHEET # 2.2.2 .............................................................. 44-46
SELF CHECK # 2.2.2 ............................................................................. 47
OPERATION SHEET # 2.2.3 .............................................................. 48-49
SELF CHECK # 2.2.3 ............................................................................. 50
INFORMATION SHEET # 2.2.4 .......................................................... 51-53
OPERATION SHEET # 2.2.4 .............................................................. 54-58
SELF CHECK # 2.2.4.1 ..................................................................... 59-60
SELF CHECK # 2.2.4.2 .......................................................................... 61
INFORMATION SHEET 2.3 ............................................................... 62-63
OPERATION SHEET # 2.3 ................................................................. 64-65
SELF CHECK # 2.3 ................................................................................ 66
INFORMATION SHEET 2.4 ............................................................... 67-69
OPERATION SHEET # 2.4 ................................................................. 70-72
SELF CHECK # 2.4.1 ............................................................................. 73
SELF CHECK # 2.4.2 ............................................................................. 74
INFORMATION SHEET # 2.5 ............................................................. 75-82
SELF CHECK # 2.5.1 ............................................................................. 83
OPERATION SHEET # 2.5.2 .............................................................. 86-87
SELF CHECK # 2.5.2 ............................................................................. 88
SELF CHECK # 2.5.3 ............................................................................. 89
INFORMATION SHEET # 2.6 ............................................................. 90-93
SELF CHECK # 2.6.1 ............................................................................. 94
SELF CHECK # 2.6.2 ............................................................................. 95
INFORMATION SHEET # 2.7 ............................................................. 96-97
SELF CHECK # 2.7 ................................................................................ 98
INFORMATION SHEET # 2.8 .................................................................. 99
SELF CHECK # 2.8 .............................................................................. 100
INFORMATION SHEET # 2.9 ......................................................... 101-107
SELF CHECK # 2.9 .............................................................................. 108
ACTIVITY SHEET # 2.9 ................................................................. 109-114
ANSWER KEY .............................................................................. 115-124
ACKNOWLEDGEMENT ................................................................ 125-127
PROGRAM COURSE
:
DRAFTING TECHNOLOGY
UNIT OF COMPETENCY :
INTERPRET TECHNICAL DRAWINGS
AND PLANS
MODULE TITLE
Interpreting technical drawings
and plans
:
INTRODUCTION:
This module is designed to familiarize student in drawing
mechanically the orthographic and pictorial projection using compass,
triangle, T-square, pencils, erasers, and technical pens. It is important
to have basic knowledge and skills in orthographic projection because
this can be used or applied construction to be undertaken.
This is also designed to teach students how to interpret
simple working drawing.
SUMMARY OF LEARNING OUTCOMES
Upon completion of the module, you should be able to:
LO1 Analyze signs, symbols and data; and
LO2 Interpret technical drawings and plans.
1
TECHNICAL TERMS
Alphabet of lines are set of conventional line symbols used in orthographic
drawings.
Assembly Drawing is an orthographic drawing of an object with its parts
assembled.
Auxiliary view is an extra or helping view of an orthographic drawing
perpendicularly projected from an inclined surface.
Detail Drawing is a large-scale drawing that shows of part of a machine,
device, or building.
Exploded Drawing is the showing of items in a diagram, but with their
relative maintained positions.
Frontal plane is a plane where the front view is projected
in a single viewing.
Ground plane is the edge view of the ground upon which the object usually
rests.
Hem is used to strengthen the lips of sheet metal objects, made in 4 mm,
6mm, 10 mm, etc standard sizes.
Horizon represents the eye level of the observer.
Horizontal plane is a plane where the top view is projected approximately
as appear to the observer.
Isometric drawing is one view drawing showing its three faces with equal
measure.
Oblique projection is a kind of pictorial drawing of an object which surface
is parallel to the front plane while the others are oblique or inclined to it.
Parallel Development refers to measuring lines parallel to one another.
Examples are cube, cylinder and prism.
Pattern is a part or model used a s a guide for making something.
Offset Section shows the zigzag direction of the cutting plane if the
principal interior features of an object are not located in a straight line.
Orthographic is a graphic presentation of an object showing the three space
dimensions of an object in its true shape and size.
Pictorial drawing shows several faces of an object at once.
Projection is a view conceived to be drawn or projected onto a plane.
Radial development refers to measuring lines that converge at a certain
points for example are the pyramid and cone.
2
Seams are used to strengthen sheet metal sections. They are usually joined
by soldering and/ or riveting process.
Section is an orthographic view showing the inside view or construction of
an object.
Sectional view is a method of drawing presentation showing the interior
parts of the building especially when the inner parts is
complicated.
Vanishing point represents the center of vision.
3
Program/Course
:
DRAFTING TECHNOLOGY
Unit of Competency
:
INTERPRET TECHNICAL DRAWING
AND PLANS
Module Title
:
Interpreting technical drawing and
Plans
Nominal Duration
:
10 hours
Learning Outcome 1
:
Analyze signs, symbols and data
Assessment Criteria:
1. Signs, symbols, and data are identified according to job
specifications.
2. Signs, symbols and data are determined according to
classification or as appropriate in drawing.
3. Signs and symbols in trade mathematics are identified
according to their applications.
References:
Giesecke, Mitchell, and Spencer. Technical Drawing; The Macmillan
Company: 1949.
French and Vierck. Engineering Drawing; MacGraw, Hill Book Company,10th
editon: 1960
German M. Manaois. Drafting 1 and 2; Phoenix Publishing:1983
Norman Stirling. Introduction to Technical Drawing; Delmar Publishing:
1977
Jun B. Principe, Corazon A. Garcia, Carlos S. Asuncion, Cresencio M.
Viernes and Trinidad S. Flores. Technology and Home Economics for
Secondary Schools: Revised Edition; FNB Educational, Inc.:1999
http://www.roymech.co.uk/Useful_Tables/Drawing/ABREV.html
Microsoft® Encarta® 2007. © 1993-2006 Microsoft Corporation.
4
LEARNING EXPERIENCES/ ACTIVITIES
Learning Outcome # 1: Analyze signs, symbols and data.
Learning Activities
1. Read
or
presentation
view
PowerPoint
on
Information
Special Instruction
Sheet No.1.1 about Alphabet of
Lines
2. Answer Self Check No. 1.1
 Try to answer Self Check No. 1.1
3. Check your answers using the
Answer Key
4. Read
or
presentation
view
PowerPoint
on
Information
Sheet No.1.2 about Mensuration
5. Answer Self Check No. 1. 2
 Try to answer Self Check No. 1.2
 Try to perform the said task
Be guided by your teacher on the
difficult tasks.
5
INFORMATION SHEET # 1.1
LO1. Analyze signs, symbols and data
Drafting is said to be the universal language of industry and
modern technology. It is through the application of special lines and
symbols that drafters use so that technical people can communicate.
Through drawings, ideas and designs are transferred between
draftsmen, architects and engineers.
The uniformity of lines and
symbols makes it possible to be widely accepted, thus, making
graphic technical drawing understandable anywhere in the world.
In a fast-developing country like the Philippines, many investors
are coming in so they need technical people to supervise factories and
offices. New products are introduced, hence, there is a great demand
for designs.
The production of goods always starts from a design.
Ideas are presented by pictorial sketches in the initial stages of
creative work. Detailing is done with lines to represent all the features
of an object, such as its edges, surfaces and contours. Lines also form
the sizes, dimensions, symbols and notes to complete a description.
To understand the fundamental principles of drawing, acquired
desirable values are necessary. A draftsman should possess the ability
and the skills in using different drawing instruments. In general, it
helps him construct output with accuracy and speed.
6
Below are signs and symbols used in Drawing:
ALPHABET OF LINES
Alphabet of lines are set of conventional line symbols
which have different weights, thickness, forms and uses.(Please
refer to CBLM in Technical Drawing I for the illustrations of
Alphabet of Lines)
Line Applications
Line widths and recommended pen sizes
Name of Line
Dimension
Approximate
Recommended
Width
Pen Size and
Number
Visible line
Thick
0.032” (.7 mm)
.50 mm 2
Hidden line
Thin
0.016”(0.35 mm)
.35 mm 0
7
Center line
Thin
0.016”(0.35 mm)
.35 mm 0
Section line
Thin
0.016”(0.35 mm)
.35 mm 0
Dimension line
Thin
0.016”(0.35 mm)
.35 mm 0
Extension line
Thin
0.016”(0.35 mm)
.35 mm 0
Leader line
Thin
0.016”(0.35 mm)
.35 mm 0
Cutting plane line
Thick
0.032” (.7 mm)
.50 mm 2
Long break line
Thin
0.016”(0.35 mm)
.35 mm 0
Phantom line
Thin
0.016”(0.35 mm)
.35 mm 0
8
SELF-CHECK #. 1.1
LO1. Analyze signs, symbols and data
Directions: Identify the alphabet of lines used in the illustration
below. Use a separate sheet of paper.
10______________
_____
3________________
_
7________________
__
9___________________
_
2__________________
_
4_________________
_
8_________________
5_______________________
__
1____________________
________
6__________________
_
9
INFORMATION SHEET # 1.2
LO1. Analyze signs, symbols and data
MENSURATION
Every nation in the world has different ways of measuring
quality, weight and volume.
This is necessary to carry out trade,
business or any form of economic exchange.
In 1960, countries from all over the world had started to use the
standard Metric System International d’ Unites or SI to promote
international trade. This is also called International Organization of
Weights and Measures. The basic units of SI are shown below.
Units
Same
Symbol
Length
Metre
M
Mass
Kilogram
Kg
Time
Second
S
Electric current
Ampere
A
Temperature
Kelvin
K
Luminous intensity
Candela
Cd
Mensuration Formulas
A. Length of Lines or Edges
1. Perimeter of plane figures with straight sides=sum of all
sides
2. Length of arc = number of degrees in arc x circumference
360
3. Circumference of circle = πD or 2πR
Π = 3.1416
4. Diameter of a circle = circumference
Π
5. Diameter= 2 area of circle
Π
6. Radius = diameter or circumference
2
2π
7. Arc of sector = area of sector x360
10
area of circle
8. Height of prism or cylinder = volume
area of base
9. Major diameter of ellipse = area ; b is minor diameter
Πb
10. Minor diameter of ellipse = area ; a is major diameter
Πa
11. Height of frustum of cone or pyramid
= 3 x volume
B+b= Bxb
B = area of lower base
B = area of upper base
h
h
FRUSTUM OF A
CONE
12.
13.
FRUSTUM OF A
PYRAMID
Altitude of triangle = area x 2
Base
Hypotenuse H of right triangle =
A 2 + B2
A = H2 – B2
B = H2 – B2
H
A
B
14.
Sum of three angles in a triangle = 1800
B. Area of Geometrical Figures
a.
Square or rectangle, A = length x width
b.
Parallelogram, A = average of bases x altitude (alt)
11
b
alt
alt
base
b
c.
d.
e.
Circle, A = Π r2
Triangle, A = base x altitude
2
Ellipse, A = Π ab a = ½ major diameter
B = ½ minor diameter
b
a
f.
Sector, A = number of degrees in sector
360
h.
Trapezoid, A = average width x altitude
SECTOR
W1
alt
W2
g.
Area of base of prism or cylinder = volume
Height
12
h.
i.
j.
k.
l.
Lateral surface of cylinder = circumference x height
Lateral surface of prism = perimeter of base x height
Lateral surface of pyramid = number of sides x area of a
side
Lateral surfaces of sphere = 4 Π R2
Lateral surface of frustum of a cone = average perimeter of
bases x slant height
C. Volume of Geometrical Solids
1.
Prism, V = area of base x height
2.
Upright cylinder, V = area of base x height
3.
Upright cone or pyramid, V = area of base x height
3
4.
Sphere, V = 4 Π R2
3
5.
Frustum of cone or pyramid, V = 1/3h(B+b)+ Bxb
h= height
B = area of larger base
B = area of smaller base
D. Miscellaneous
1. Board feet = number of pieces x T” x W” x L’
12
2. Board meters = number of pieces = Tcm x Lcm x Lm
100
3. Stair tread T and riser R
2R” +T” = 24” (English)
2R cm + Tcm = 61 cm (metric)
4. Approximate number of steps = stair rise in inches or
7”
= stair rise in meters
0.175
T
H
H
STAIR RISE
STAIR RUN
5. Height of step(riser)= stair rise in inches or stair rise in mts
Number of steps
Number of steps
13
6. Conversion Formulas
a. Length in inches x 0.0254
b. Length in inches x 2.54
c. Length in feet / 3.28
d. Length in meters x 39.37
e. Length in inches /39.37
f. Length in feet x 0.305
g. Length in feet x 30.5
7. Pitch of roof
= rise
= span
= length in meters
= length in centimeters
= Length in meters
= Length in inches
= Length in inches
= Length in meters
= Length in centimeters
RISE
SPAN
14
SELF-CHECK # 1.2
LO1. Analyze signs, symbols and data
Directions: Write the letter that corresponds to your answer. Use a
separate sheet of paper.
A. Match the formula in Column A with the geometric figures in
Column B.
Column A
Column B
1.
2.
a.
b.
c.
d.
length x width
average width x altitude
Π r2
base x altitude
2
e.
f.
g.
average of base x altitude
Π ab
No. of deg. in sector
360
Volume
height
2
3.
h.
4.
360
5.
B. Find the correct formula of the length of lines or edges
of the geometric plane figures as illustrated below. Write only
the letter of the correct answer.
SECTOR
b
a
15
alt
base
H
A
h
h
B
CONE
PYRAMID
1. Circumference of circle
a. πD or 2πR
b. circumference
π
c. 3 x volume
B+b+ Bxb
2. Altitude of triangle
3. Major diameter of an ellipse
4. Hypotenuse H of right triangle
5. Height of frustum of a cone
d. A2 + B2
e. πD or 2πR
f. area x 2
base
g. area
πb
h. area
πa
360
16
Program/Course
:
DRAFTING TECHNOLOGY
Unit of Competency
:
INTERPRET TECHNICAL DRAWING
AND PLANS
Module Title
:
Interpreting technical drawing and
Plans
Nominal Duration
:
330 hours
Learning Outcome 2
:
Interpret technical drawings and
plans
Assessment Criteria
1. Necessary tools, materials and equipment are identified
according to the plan.
2. Components, assemblies or objects are recognized as per job
requirement.
3. Dimensions and specifications are identified according to job
requirements.
References:
Giesecke, Mitchell, and Spencer. Technical Drawing; The Macmillan
Company: 1949.
French and Vierck. Engineering Drawing; MacGraw, Hill Book Company,10th
editon: 1960
German M. Manaois. Drafting 1 and 2; Phoenix Publishing:1983
Norman Stirling. Introduction to Technical Drawing; Delmar Publishing:
1977
Jun B. Principe, Corazon A. Garcia, Carlos S. Asuncion, Cresencio M.
Viernes and Trinidad S. Flores. Technology and Home Economics for
Secondary Schools: Revised Edition; FNB Educational, Inc.:1999
Microsoft®
Encarta®
2007.
©
1993-2006
Microsoft
Corporation.
17
LEARNING EXPERIENCES/ ACTIVITIES
Learning Outcome # 1: Analyze signs, symbols and data.
Learning Activities
1. Read
or
Special Instruction
view
PowerPoint
presentation
on
Information
Sheet
2.1
regarding
No.
Orthographic Projection
2. Answer Self Check No. 2.1.1
 Try to answer Self Check No. 2.1.1
6. Check your answers using the
Answer Key
3. Perform Operation Sheet No. 2.1
 Ask your teacher on the task which
are difficult to you
4. Answer Self Check No. 2.1.2
 Try to answer Self Check No. 2.1.2
7. Check your answers using the
Answer Key
5. Read
or
presentation
view
PowerPoint
on
Information
Sheet no. 2.2 about Pictorial
Drawing
6. Perform Operation Sheet No.
 Ask
your
teacher
how
to
accomplish some difficult tasks.
2.2.1
 Try to answer Self Check No. 2.2.1
7. Answer Self Check No. 2.2.1
8. Check your answers using the
Answer Key
8. Perform Operation Sheet No.
 Try to perform the said task
2.2.2
 Try to answer Self Check No. 2.2.2
9. Answer Self Check No. 2.2.2
9. Check your answers using the
Answer Key
10. Perform
2.2.3
operation
Sheet
No.
 Try to perform the said task
18
11. Answer Self Check No. 2.2.3
 Try to answer Self Check No. 2.2.3
10. Check your answers using the
Answer Key
12. Read
or
presentation
Sheet
no.
view
PowerPoint
on
Information
2.2.4
about
Perspective Drawing.
13. Perform Operation Sheet no.
2.2.4
 Try to perform the said task
 Ask
your
teacher
how
to
accomplish some difficult tasks.
14. Answer Self Check No. 2.2.4.1
and 2.2.4.2
 Try to answer Self Check
No.
2.2.4.1 and 2.2.4.2
11. Check your answers using the
Answer Key
15. Read
or
View
PowerPoint
on
Information
Presentation
Sheet no. 2.3 about Auxiliary
View.
16. Perform Operation Sheet no. 2.3
 Try to perform the said task
 Ask
your
teacher
how
to
accomplish some difficult tasks.
17. Answer Self Check No. 2.3
 Try to answer Self Check No. 2.3
18. Check your answers using the
Answer Key
19. Read
or
presentation
view
PowerPoint
on
Information
Sheet no. 2.4 about Pattern
Development.
20. Perform Operation Sheet No. 2.4
 Try to perform the said task
21. Answer Self Check No. 2.4.1
 Try to answer Self Check No. 2.4.1
22. Check your answers using the
19
Answer Key
23. Please perform Activity Sheet
 Please perform the said task
2.4.1 on Pattern Development.
24. Answer Self Check No. 2.4.2
 Try to answer Self Check No. 2.4.2
25. Check your answers using the
Answer Key
26. Read
or
Presentation
View
PowerPoint
on
Information
Sheet no. 2.5 about Sectional
View
27. Answer Self Check No. 2.5.1
 Try to answer Self Check No. 2.5.1
28. Check your answers using the
Answer Key
29. Perform Operation Sheet No.
 Please perform the said task

2.5.1
30. Perform Operation Sheet No.
 Please perform the said task
2.5.2
31. Answer Self Check No. 2.5.2
 Try to answer Self Check No. 2.5.2
12. Check your answers using the
Answer Key
32. Answer Self Check No. 2.5.3
33. Read
or
Presentation
Sheet
no.
View
PowerPoint
on
Information
2.6
about
 Try to answer Self Check No. 2.5.3
Detail
Drawing
34. Answer Self Check No. 2.6.1
 Try to answer Self Check No. 2.6.1
13. Check your answers using the
Answer Key
35. Answer Self Check No. 2.6.2
 Try to answer Self Check No. 2.6.2
36. Check your answers using the
Answer Key
37. Read
or
Presentation
View
PowerPoint
on
Information
Sheet no. 2.7 about Working
Drawing with Bill of Materials.
20
38. Answer Self Check No. 2.7
 Try to answer Self Check No. 2.7
14. Check your answers using the
Answer Key
39. Read
or
Presentation
View
PowerPoint
on
Information
Sheet no. 2.8 about Exploded
Drawing.
40. Answer Self Check 2.8
 Try to answer Self Check No. 2.8
15. Check your answers using the
Answer Key
41. Read
or
Presentation
Sheet
no.
View
PowerPoint
on
Information
2.9
about
other
symbols used in Drafting.
42. Answer Self Check No. 2.9
 Try to answer Self Check No.2.9
16. Check your answers using the
Answer Key
43. Perform Activity Sheet No. 2.9
 Perform the said task
 Ask
your
teacher
how
to
accomplish some difficult tasks.
21
INFORMATION SHEET # 2.1
LO 2. Interpret technical drawings and plans
Early Technical Drawing
Perhaps the earliest known technical drawing in existence is a
plan view of a fortress designed and engraved on a stone tablet by the
Chaldean engineer named Gudea. It is remarkable how similar this
plan is to those made by modern architects, although it was “drawn”
thousand of years before paper was invented.
Modern Technical Drawing
The first printed form of technical drawing was the Geometrical
Drawing published in 1849 by William Minifie. In 1876 the blueprint
process was introduced at the Philadelphia Centennial Exposition. Up
to this time, the graphic language is considered more or less an art.
Some works were characterized by fine line drawings which were
made to resemble copper-plate engraved while others , by the use of
shade lines and water color “washes.” These technique become
unnecessary
after the introduction
of blueprinting. This was the
beginning of modern technical drawing . The graphic language now
became a relatively exact method of representation.
ORTHOGRAPHIC PROJECTION
An orthographic projection is a representation of separate views
of an object on a two-dimensional surface. It reveals the width, depth
and height of an object.
The projection is achieved by viewing the object from a point
assumed to be at infinity (an indefinitely great distance away). The line
of sight or projectors are parallel to each other and perpendicular to
the plane of projection.
22
VISUALIZING ONE VIEW OF AN ORTHOGRAPHIC PROJECTION
Three plane of projection
One can develop the skill in visualizing the views of an object by
imagining that the object is enclosed in a “glass box”. Each face of the
object is viewed perpendicularly to the projection plane. The views are
obtained by projecting the lines of sight to each plane of the glass box.
Since the glass box have six sides, six views of the object can be seen.


Frontal Plane. The projection shown in the frontal plane is
called front view or front elevation.
Horizontal Plane. The projection shown in this plane is called
top view or plan view.
23

Profile Plane. A projection at this plane is called the side view
or end view, or side or end elevation.
THE GLASS BOX
REPRESENTING THE
PLANES OF PROJECTION
Six principal views of an object
As we unfold the glass box, six views of the object are revealed:
top, front, right-side, left-side, rear, and bottom view. We assumed
that all of the pieces of the glass box are hinged to the front plane
except the rear plane being hinged to the left-side plane, as shown in
the illustration.
UNFOLDING THE GLASS BOX IN ONE PLANE SHOW
24
THE SIX PRINCIPAL VIEWS OF AN OBJECT
The object is to be presented in two or more separate views
showing the three space dimension, the width, height and depth of
length. This drawing will be the source of information on the true
shape of the object on its top, front and side view of the objects.
In this projection the position of the three main views will be in
L shape. The top and front view is vertically aligned together while the
front view and right side view are horizontally aligned.
Fig.1
Fig. 2 with hidden line
FRONT VIEW
RIGHT SIDE VIEW
Fig 3- cylinder
Top view
FRONT VIEW
RIGHT SIDE VIEW
Fig. 4- with hole
Top view
+
25
COMMON METHODS OF TRANSFERRING DEPTH DIMENSIONS
(Note: Projection lines are used to transfer height and width dimensions to other views,
but depth dimensions require other methods.)
A. 45º MITER LINE
45º miter line
B. DIVIDERS
C. SCALE
26
First and Third Angle Projection.
When an object is viewed through a plane of projection from a
point of infinity, an accurate outline of the visible face of the object is
obtained. However, the projection of one face usually will not provide
an overall description of the object so other planes of projection must
be used. Establishing an object’s true height, width, and depth
requires front, top, and side views, which are called the Principal
Planes Of Projection. These include the Vertical, Horizontal, and
Profile Planes, previously explained in Technical Drawing I. The angles
formed between the horizontal and the vertical planes are called the
FIRST, SECOND, THIRD, and FOURTH ANGLES. Currently, for
technical reasons, only the use of first- and third-angle projection is
practical to use.
In orthographic projection, drawings are referred to as “firstangle” or “third-angle” projections. These two projections are derived
from a theoretical division of all space into four quadrants by a
vertical plane and a horizontal plane. The quadrants are numbered
from 1 to 4, starting from the upper front quadrants and continuing
clockwise when viewed from the right side. The viewer of the four
quadrants is considered to be in front of the vertical or frontal plane,
and above the horizontal plane.
VIEWS ARE PROJECTED FORWARD IN THIRD-ANGLE PROJECTION
27
The position of the profile plane is not affected by the quadrants. It is
considered to be either to the right or left of the object as desired.
Third-angle projection is used in the United States and Canada. Most
European countries use first-angle projection. The difference between the
two is how the object is projected and the position of the views on the
drawing.
In third-angle projection, the projection plane is considered to be
between the viewer and the object, and the views are projected forward to
that plane. The top view appears above the front view, the right-side view is
to the right of the front view, the left view to the left of the front view, and so
on.
VIEWS ARE PROJECTED BACKWARD IN FIRST-ANGLE PROJECTION
In first-angle projection, the projection plane is on the far side of
the object. The views of the object are projected to the rear and onto
the projection plane instead of being projected forward.
The individual views are the same as those obtained in the
third-angle projection.
28
Carefully study the symbols shown below. Normally a symbol is
drawn underneath that clearly shows which angle of projection has
been used.
SYMBOL FOR FIRST-ANGLE AND THIRD-ANGLE PROJECTION
The final arrangements of the views are shown in the drawing
below. Notice how the symbol for first angle orthographic projection
has been added to the drawing.
SYMBOL FOR FIRST-ANGLE PROJECTION HAS BEEN ADDED TO THE
DRAWING
29
SELF-CHECK # 2.1.1
LO 2. Interpret technical drawings and plans
Direction: Fill in the blanks with the correct answers and write it
on a separate sheet of paper.
__________ 1. It is a thick heavy line used to represent the visible edges
of an object.
__________ 2. It is a view vertically aligned with the top view in its
projection.
__________ 3. It is the terminating point of dimension line.
__________ 4. They are light penciled line used in blocking-in the
views.
__________ 5. It is the standard height of numerical figures in
dimensioning.
__________ 6. They are dashes of lines representing hidden edges or
contour of the object.
__________ 7. It is a view in the orthographic views which is
horizontally aligned with the front view.
__________ 8. It is the sum total of detailed dimensions.
__________ 9.
__________ 10. They are the symbols of first and third-angle projection
9.
10.
30
OPERATION SHEET # 2. 1
LO 2. Interpret technical drawings and plans
Orthographic Projection
1. Prepare the following tools and materials.
-
T-square
-
Triangle (30x60 & 45x45)
-
French curve
-
Compass
-
Pencil
-
Technical pen
-
Drawing paper
-
Eraser
-
Masking tape
2. Procedures in constructing orthographic projection.
To draw orthographic views of the given pictorial drawing, first
determine the number of views needed, then decide which surface will
become the front view. Establish the space needed between views for
dimensioning and calculate the center of the drawing. Then proceed to
the following steps.
10
40
20
20
10
40
10
20
10
20
30
10
PICTORIAL DRAWING
31
Step1. Draw the vertical and two horizontal axis with at least 2cm
or more apart
2 cm
Step 2. Indicate or supply marking lines according to the given
dimension of the width of the top view, height of the front and
depth of the top view.
2 cm
FRONT VIEW
Step 3. Construct the enclosing box of the top view and front view by
projecting the marking lines horizontally and vertically
2 cm
FRONT VIEW
32
Step 4. Construct diagonal line at 450 angle using 450 x 450 triangle
from the upper right corner of the enclosing box of the front view
2 cm
FRONT VIEW
Step 5. Project down the two intersecting points to get the width of the
right side view and to form its enclosing box
2 cm
FRONT VIEW
33
Step 6. Divide proportioning distance of top view and front view by
indicating marking lines
2 cm
FRONT VIEW
Step7.Draw the details of top view, front view, and right side view by
projecting the marking lines horizontally and vertically
2 cm
FRONT VIEW
34
Step8. Darken the final edges of the top view, front view, and right
side view
2 cm
Step9. Divide the space provided for dimensioning by indicating
marking lines
2 cm
35
Step10. Draw the line for dimension and extension lines by projecting
the marking lines horizontally and vertically, and supply
arrows on the tip end of dimension lines
Step11 Indicate both detail and overall numerical dimension.
10
40
10
30
0 10
20
40
10
36
Step12. Label the top, front and right side views, finally erase the
construction lines
TOP VIEW
10
40
10
30
10
20
40
10
FRONT VIEW
SIDE VIEW
37
SELF-CHECK # 2.1.2
LO 2. Interpret technical drawings and plans
Orthographic Projection
Direction. Draw the orthographic views applying the First angle
and Third angle projection on the given pictorial view below. Use a
separate sheet of paper.
10
15
12
10
10
10
10
10
PICTORIAL DRAWING
38
INFORMATION SHEET NO. 2.2
LO 2. Interpret technical drawings and plans
PICTORIAL DRAWING
Pictorial drawings are important elements of working drawing
because they show the graphic representation of an object as it
appears on the observer’s eyes.
Even a person who has no technical knowledge in technical
drawing, can easily understand the object being presented in the
drawing.
Three types of pictorial Projection
Axonometric- projection
Kinds of axonometric projection

isometric pictorial projection

dimetric pictorial projection

trimetric pictorial projection
Oblique pictorial drawing
Kinds of oblique pictorial drawing
Cavalier-refers to measurements of width,
height and depth/ length in full size
General- refers to measurements of width, and
height are full size while its depth or length
2
is two third  
3
39
Cabinet- refers to measurements of width and height
in full size while its depth or length is one half
1
 
2
Two common types of perspective pictorial drawing
Parallel or one point perspective
Angular or two point perspective
Note:
A perspective can be identifies as:
Worms eye view
Men’s eye view
Bird’s eye view
40
OPERATION SHEET # 2.2.1
LO 2. Interpret technical drawings and plans
Isometric pictorial drawing
1. Prepare the following tools and materials
-
T-square
-
Triangle (30x60 & 45x45)
-
Compass
-
Pencil
-
Technical pen
-
Drawing paper
-
Eraser
-
Masking tape
Steps in isometric drawing
1. Draw the three isometric axes using 30 x 60 triangle
300
300
2. From the given orthographic views indicate the measurements
of the width, height and length on the isometric axes.
41
3. Draw the isometric box and complete the construction lines.
4. Darken the edges/ contour of the object, and apply
shading if required
42
SELF-CHECK # 2.2.1
LO 2. Interpret technical drawings and plans
Isometric Pictorial Drawing
Direction: Draw the isometric pictorial drawing based on the
dimensions given below. Use a separate sheet of paper.
TOP VIEW
6 10
8
30
40
15
10
30
10
FRONT VIEW
SIDE VIEW
43
OPERATION SHEET # 2.2.2
LO 2. Interpret technical drawings and plans
Constructing Isometric Circles
Circle or Ellipse in Isometric Drawing.
300
Orthographic Circle
300
Isometric of Circles
1. Prepare the following tools and materials
-
T-square
-
Triangle (30x60 & 45x45)
-
Compass
-
Pencil
-
Technical pen
-
Drawing paper
-
Eraser
-
Masking tape
44
2. Procedure:
1. Draw an isometric box using a 30 x 60 triangle
2. Draw a 60 degree line from the upper and lower corner of the
Isometric box
3. Draw arcs using x and y as the centers.
45
4. Draw arcs using A and B as center
5. Draw a vertical lines connecting the two ellipse in order to
produce the outline of the cylinder
46
SELF-CHECK # 2.2.2
LO 2. Interpret technical drawings and plans
Isometric Pictorial Drawing with Circular Features
Direction: Draw the Isometric Pictorial drawing based on the given
dimensions in the Orthographic views with circular features below.
TOP VIEW
7
20
34
28
7
10
10
17 R
44
15
20 O
12
FRONT VIEW
SIDE VIEW
47
OPERATION SHEET # 2.2.3
LO 2. Interpret technical drawings and plans
Constructing Oblique Pictorial Drawing
Given Orthographic Views
20
40
TOP VIEW
20
40
40
FRONT VIEW
SIDE VIEW
Procedure:
1. Draw oblique pictorial axes using either 30°, 60° or 45°
45°
2. Supply measuring marks on the axes base on the given
dimensions of the object
48
3. Form the oblique pictorial box by constructing lines projected
from the markings
4. Add or complete the construction lines.
5. Outline the object using construction line as group guide.
Darken the lines. Label the drawing. If required, erase
construction lines.
CAVALIER PICTORIAL DRAWING
49
SELF-CHECK # 2.2.3
LO 2. Interpret technical drawings and plans
OBLIQUE PICTORIAL DRAWING
Direction: Construct an Oblique pictorial drawing at 30° based
on the Orthographic views below.
A.
TOP VIEW
30
42
12
10
10
10
10
30
10
SIDE VIEW
FRONT VIEW
B.
TOP VIEW
5
5
40
20 R
20
20 O
35
20
FRONT VIEW
SIDE VIEW
50
INFORMATION SHEET # 2.2.4
LO 2. Interpret technical drawings and plans
Perspective Drawing is the most natural presentation of an
object as it appear on the viewer’s eye.
Principles of Perspective Drawing.
1. All receding lines converge on a vanishing point.
2. The farther color, the lighter it appears.
3. The farther the object, lines, edges, the smaller they appears.
4. The object can be viewed in either birds eye view, men’s eye view
and worms eye view.
Bird’s Eye View
Man’s Eye View or Eye level View
Ant’s Eye View or Worm’s Eye View
5. The vanishing point and station point must be vertically aligned
together.
6. The two vanishing point must be located in the horizon.
7. The farther station point from the top plan, the bigger will the
perspective become.
Two Techniques of Perspective Presentation
1. Artist Method
2. Mechanical Method
51
Types of Perspective Drawing
1. Parallel or One Point Perspective – its receding lines will
converge on a single vanishing point.
2. Angular or Two Point Perspective – its receding lines will
converge on two vanishing point.
3. Three Point Perspective – its receding lines converges on three
vanishing point.
I.
PARALLEL OR ONE POINT PERSPECTIVE
II.
ANGULAR OR TWO POINT PERSPECTIVE
52
III.
THREE POINT PERSPECTIVE
53
OPERATION SHEET # 2.2.4
LO 2. Interpret technical drawings and plans
Construct Perspective Drawing
I.
Procedure in constructing
(Mechanical Method).
one
point
perspective
1. Draw three horizontal lines representing picture plane, ground
line and horizon. In the picture plane draw the top and front
view on the ground line.
TOP VIEW
Picture
Plane
Horizon
Ground
Line
2. Locate station point on the ground line and project lines of
vision from the corner of the top view to the station point.
TOP VIEW
Picture
Plane
Horizon
Ground
Line
54
3. Establish the vanishing point by projecting vertical lines from
the station point.
TOP PLAN
VP
SP
4. Draw projectors to the vanishing point and from the piercing
point project vertical lines downward.
TOP PLAN
PICTURE PLANE
HORIZON
GROUND
LINE
FRONT VIEW
VP
SP
PERSPECTIVE
55
II.
Procedure in Constructing Angular or Two Point
Perspective
1. Draw the horizontal lines representing picture plane, ground
line and horizon. In the picture plane draw top plan using
30ox60o triangle and front view in the ground line.
o
o
30
60
2. Locate the station point.
The size of perspective drawing
depends on the distance of station point from the top plan.
o
o
30
60
PP
H
GL
SP
56
3. From the station point, draw two lines, one at 30o and the
other at 600, then mark their meeting points with the picture
plane and from that mark draw vertical line up to horizon plane,
Their meeting point with the horizon will serve as left and right
vanishing points.
30o
PP
60o
H
RVP
LVP
GL
SP
4. Project corners of the top plan to form visual rays which will
converge at the station point, Then, mark the meeting point.
Project vertical line which will become the measuring lines.
PIERCING POINT
Visual Rays
PP
H
LVP
RVP
MEASURING LINES
GL
SP
57
5. From corners of the height of the object extend projectors to the
left and right of the vanishing point to form its construction
lines.
VISUAL RAYS
PIERCING POINT
MEASURING LINES
PP
H
LVP
RVP
PROJECTORS
GL
SP
6. Since the construction line for the perspective is already
complete, darken now the object lines.
VISUAL RAYS
PIERCING POINT
MEASURING LINES
PP
H
RVP
LVP
PROJECTORS
GL
SP
58
SELF-CHECK 2.2.4.1
LO 2. Interpret technical drawings and plans
One Point Perspective
Directions. Convert the following Oblique Pictorial Drawings into
One-Point Perspective Drawing. Follow the given dimensions.
Note: Measurements are in millimeter
A.
30
15
15
10
20
10
30
40
OBLIQUE PICTORIAL DRAWING
59
B.
8
13
10
20 0
5
2
6
38 0
14
8
14
36
OBLIQUE PICTORIAL DRAWING
(CIRCULAR OBJECT)
60
SELF-CHECK 2.2.4.2
LO 2. Interpret technical drawings and plans
Two Point Perspective or Angular Perspective
Directions. Convert the given Isometric Pictorial Drawings into OnePoint Perspective Drawing. Follow the given dimensions.
Note: Measurements are in millimeter
20
24
8
8
32
10
5
10
40
25
5
10
35
10
ISOMETRIC DRAWING
61
INFORMATION SHEET 2.3
LO 2. Interpret technical drawings and plans
AUXILIARY VIEWS
In the three main views or orthographic projection, the true
shape and size of an inclined surface is not clearly shown, so in order
to show it, an auxiliary view is needed to be presented.
Two Options in drawing auxiliary views
1. Partial Auxiliary – refers only to the inclined surface of the
object.
2. Complete Auxiliary – refers to the whole view that can be seen
in viewing inclined surface.
Six Types of Auxiliary Views
1
2
62
3
4
5
6
63
OPERATION SHEET # 2.3
LO 2. Interpret technical drawings and plans
AUXILIARY VIEWS
Procedure:
1. Study the given orthographic views. Identify the type of
auxiliary view used for the given problem.
2. From the inclined surface draw two straight lines at 90o
90o
90o
3.
Transfer all dimensions of the object on the lines projected
from the inclined surface.
5
o
20
10
5
90
90o
4. Draw additional construction line projected from the marking of
the measurements.
64
5. Draw out the object lines from the construction lines to show
the auxiliary views.
FRONT
VIEW
R-SIDE
VIEW
65
SELF CHECK # 2.3
LO 2. Interpret technical drawings and plans
Auxiliary Views
A.
Directions: Choose the letter of the best answer
and write it on a separate sheet of paper.
_____ 1. A type of a drawing used to represent the exact shape and
size of an inclined surface.
a. Orthographic drawing
c. Auxiliary drawing
b. Vertical drawing
d. Perspective drawing
_____ 2. A surface that needs an auxiliary view.
a. Circular features
c. Horizontal surface
b. Vertical surface
d. Inclined surface
_____ 3. A view which only the inclined surface can be drawn in an
auxiliary view.
a. Partial auxiliary view
c. Complete auxiliary view
b. Exploded view
d. Sectional view
_____ 4. It is not preferred option to draw an auxiliary view.
a. Complete auxiliary view
c. Perspective view
b. Orthographic view
d. Partial auxiliary view
_____ 5. It is the opposite of front elevation.
a. Left auxiliary view
c. Right auxiliary elevation
b. Rear auxiliary view
d. Right auxiliary view
B. From the given set or orthographic drawings, what type of
auxiliary drawing will be produced based on the position of the
inclined surface.
________________ 1.
_________________ 3.
_________________ 2.
_____________4.
66
INFORMATION SHEET 2.4
LO 2. Interpret technical drawings and plans
PATTERN DEVELOPMENT
A pattern is a full size drawing of the various surfaces of an
object stretch-out on a flat surface.
Pattern development is used only for flexible materials such as
carton sheet material or anything that can be folded. Product
packages for stoves and refrigerators are produced by this pattern
development.
Sample development objects.
CUBE
CONE
PYRAMID
CYLINDER
PRISM
Two types of Pattern Development
1. Parallel development – refers to the object whose measuring
lines are parallel to one another. Examples are cube, cylinder
and prism.
3
2
4
1
PICTORIAL
COVER
1
2
3
LAP SEAM
BASE
GIRT LINE
4
4
FRONT VIEW
SIDE VIEW
SEAM
STRETCH-OUT PATTERN
PARALLELL DEVELOPMENT
67
1. Radial development – Their following or measuring lines will
converge at a certain points and example of this is pyramid and
cone.
TOP VIEW
6
5
1
4
2
3
TRANSFER
MEAUREMENTS
PICTORIAL
1
6
2
3
4
5
FRONT VIEW
BASE
STRETCH-OUT PATTERN - RADIAL DEVELOPMENT
Hem. Edges and Seams
Hem is used to strengthen the edges of sheet metal objects. It is
made in standard sizes, 4 mm, 6mm, 10 mm, etc.
SINGLE SEAM
DOUBLE SEAM
68
Wired edge gives an extra strength and rigidity to sheet metal edges
WIRED EDGE
Seams are used to strengthen sheet metal sections. They are usually
joined by soldering and/ or riveting process.
GROOVED SEAM
COUNTER SUNK
LAP SEAM
LAP SEAM
69
OPERATION SHEET # 2.4
LO 2. Interpret technical drawings and plans
PATTERN DEVELOPMENT
Procedures In Constructing Parallel Development
1. Draw the top and front view of the prism. Divide the top view into
eight equal divisions and number each part.
TOP VIEW
TOP VIEW
45
0
FRONT VIEW
FRONT VIEW
2. From the front view, project its height horizontally for the stretchout pattern. Set the measurements of the numbered segments and
transfer them to draw the folding lines of the stretch-out pattern.
TOP VIEW
4
5
3
6
2
7
1
TRANFER
MEASUREMENTS
HERE
8
1
2
3
4
5
6
7
8
FRONT VIEW
70
3. Darken the girth line and folding lines of the pattern.
TOP PLAN
4
5
3
6
2
7
1
8
2
1
3
4
5
6
7
8
FRONT VIEW
4. Draw two circles of the same size with the top view to form the
cover and the base. Divide the circumference of the circle into
eight equal parts.
TOP PLAN
4
5
3
6
2
7
1
8
1
2
3
4
5
6
7
8
FRONT VIEW
71
5. Darken the lines for the cover and base of the stretch-out pattern
TOP PLAN
4
5
3
6
2
7
1
8
1
2
3
4
5
6
7
8
FRONT VIEW
6. Add seams and lap seam on the stretch-out pattern.
TOP PLAN
4
5
3
6
2
7
1
COVER
8
FOLDING
LINE
1
2
3
4
5
6
7
8
FRONT VIEW
LAP SEAM
GIRTH LINE
BASE
STRETCH-OUT PATTERN
72
SELF-CHECK # 2.4.1
LO 2. Interpret technical drawings and plans
Pattern Development
Directions: Choose the letter of the best answer and write it on a
separate sheet of paper.
____1. It is a full size drawing of the various surfaces of an object
stretch out on a flat surface.
a. Pattern b. Hem
c. Fabrication
d. Cylinder
____2. It is used to strengthen the edges of sheet metal object. It is
made in standard sizes, 4.8mm, 6.0mm, 10,0mm etc.
a. Seam
b. hem
c. edge
d. Wedge
____3. A type of pattern development whose measuring or folding lines
are parallel to each other.
a. Isometric
b. Parallel c. Orthographic d. Radial
____4. Pattern development of figure A
A
C
B
A
D
____5. Pattern development of figure B.
A
C
B
D
73
SELF-CHECK # 2.4.2
LO 2. Interpret technical drawings and plans
Pattern Development
Directions: Develop the correct pattern of the model or object below.
Use a separate sheet of paper.
10
10
40
30
30
74
INFORMATION SHEET # 2.5
LO 2. Interpret technical drawings and plans
Sectional View
Sectional view is a method of drawing presentation showing the
interior part part of the building especially when the inner parts are
complicated. The direction of the cutting plane line is the major
reference to consider in determining the form to be drawn. The parts
or portion of the object being imagined to be cut will be represented by
section lines.
Alphabet of lines needed in the construction of sectional views.
1. Visible-edge is a heavy line that can
be seen when viewing an object.
2. Cutting plane line is a thick short
dash line representing the imaginary
cut in the object.
3. Section line is a thin solid line at 450
representing solid parts of the object
that are being cut.
4. Short break line – thick solid lines
used for broken out section.
Principles of Sectioning
1. It shows the type of sectional view of the entire cut surface of
the view.
2. It shows more detailed illustrations particularly on the interval
parts of the object.
3. It describes the shape of the internal parts.
75
Types of Sectional Views
1. Full Section is obtained when the cutting-plane extends
entirely through the object in a straight line and the front half of
the object is totally.
TOP VIEW
A
A
CROSS SECTION
B
TOP VIEW
B
LONGITUDINAL SECTION
FULL SECTION VIEW
76
2. Half Section refers to one quart of the object to be cut or removed.
TOP VIEW
CUTTING PLANE LINE
SECTION LINES
HALF SECTION
HALF SECTION DRAWING
3. Broken – out Section refers to the portion of the object to be
taken out
77
4. Removed Section is generally used in furniture, machine , and
architectural drawing. The appearance of the sectional view depends
on the location of the cutting-plane lines.
B
A
B
A
SECTION A-A
SECTION B-B
5. Revolved Section is a type of section applied to a circular object.
The resulting view is similar to full section view.
6. Offset Section shows the zigzag direction of the cutting plane if
the principal interior features of an object are not located in a
straight line. It is necessary to offset the cutting-plane to allow
to pass through as many of the principal features of the object,
78
CUTTING
PLANE
LINE
In order to include features that are not in a straight line, the cutting-plane
may be offset or bent, so as to include several planes or curved surfaces.
OFFSET SECTION
79
7. Assembly Section is made up of a combination of all the parts
previously mentioned. This section may be used to increase the
clarity and readability of assembly drawings.
TYPES OF ASSEMBLY DRAWING

General Assembly
GENERAL ASSEMBLY DRAWING OF A TABLE

Layout Assembly
PRESENTS THE LAYOUT ASSEMBLY OF FM RADIO.
80

Pictorial Exploded Assembly
PICTORIAL EXPLODED ASSEMBLY OF SHOCK SUPPORT
FOR SCREW MACHINE
SECTION LINING
Section lining, sometimes referred to as cross-hatching, can serve
a double purpose. It indicates the surface that has been theoretically cut
and make it stand out clearly, thus helping the observer to understand
the shape of the object. Section lining may also indicate the material
from which the object is to be made.
81
DIRECTION OF SECTION LINING
SYMBOLS FOR MATERIALS IN SECTION
82
SELF-CHECK # 2.5.1
LO 2. Interpret technical drawings and plans
Directions : Fill in the blanks. Write the correct answer on a separate
sheet of paper.
__________ 1. It is an imaginary line that shows the part of the object
that is being cut.
__________ 2. It is a kind of section whose cutting plane passes
through the different feature of the subject.
__________ 3.It is a portion of the object taken out so that part of its
inner part can shown.
__________ 4. It is the object to be cut in its full length.
__________ 5. These are solid lines at 45˚ indicating parts of the object
is being cut in the sectional views.
__________ 6. It is a portion of the object taken depending on the
location of the cutting plane.
__________ 7. It is the method of drawing presentation showing its
interior features.
__________ 8-10.Give at least three(3) kinds of alphabet of lines used in
sectional views.
83
OPERATION SHEET # 2.5.1
LO 2. Interpret technical drawings and plans
Steps in Constructing Full Section:
1. Imagine the object is cut in a straight line along its full length
2. Imagine the half of the object nearest the viewer has been
removed then view the remaining half isometric.
84
3. The result is a full sectional view of the object that clearly
describes its interior feature.
85
OPERATION SHEET # 2.5.2
LO 2. Interpret technical drawings and plans
Steps in Constructing Half-Section
1. Imagine the object is cut into a quarter or one fourth of its
portion.
2. Since one fourth or a quarter of the object is taken away, then
view the part in pictorial form.
86
3. The result is half-sectional view of the object that clearly shows
its interior features.
87
SELF-CHECK # 2.5.2
LO 2. Interpret technical drawings and plans
Direction: Given the pictorial drawing, draw the half section following
the instructions below. Use a separate sheet of paper.
20
5
20
10
5
20
20
5
30
Draw the following:
1.
2.
3.
4.
The plan or top view and indicate the cutting plane line.
The front view
The half-sectional view
The oblique pictorial drawing
88
SELF-CHECK # 2.5.3
LO 2. Interpret technical drawings and plans
Directions: Draw the cross and longitudinal section using scale 1:20
based on the orthographic views given.
TOP VIEW
1.00
.48
.02
.02
.02
.72
.56
.02
.48
.14
.02
.50
.23
FRONT VIEW
RIGHT – SIDE VIEW
89
INFORMATION SHEET # 2.6
LO 2. Interpret technical drawings and plans
Detail Working Drawing is a technical drawing of a single part of
a machine or mechanism which is complete in dimension. It provides
sufficient technical foundation to allow the part to be made. This
drawing also show the details on how joints or fittings were executed
based on the drawings which were done in large scale.
Thing to be considered in making detailed drawings

Identify the parts or joints to be drawn in detail.

Encircle the parts to be drawn.

Use leader line to pinpoint parts to be drawn in detail.

Indicate notes that serve as reference of the part to be drawn in
detail.
Purposes of a Detailed Drawing
1. It describes the shapes of the object drawn.
2. It indicates the dimensions of the object drawn.
3. It provides any additional information that is required to make
the object drawn. Such additional information is usually shown
in the form of one or more notes.
Characteristics of a Detailed Working Drawing:
1. A detailed drawing can be drawn on a separate sheet.
2. Detailed drawing can usually be found beneath the assembly
drawing.
3. Detailed drawing should be drawn in larger scale to clearly show
the parts
4. Dimension in detailed drawing should be shown clearly.
90
TOP PLAN
LEGS
TOP BOARD
SEE
DET. A
.25
1.20
.20
.20
.05 .10 .05 .10 .05
.05 .10
.30
2” THK.
BRACE - B
.10
SEE
DET - C
.40
.10 .05
BRACE-A
2” X 2” BRACE
2” X 2” LEGS
SEE
DET - B
RIGHT – SIDE VIEW
FRONT VIEW
DETAIL OF JOINTS
DETAIL B
DETAIL A
DETAIL C
91
1.20
1.50
.10 .05
..05 .10
.02
25
.02
DETAIL PARTS
25
.02
.05
DETAIL OF TOP BOARD
.05
.05
.05
.05
.32
.05
.025
DETAIL OF LOWER BASE
.05
.40
.25
SCALE 1 : 05
.30
.05
.05
.05
.020
DETAIL OF LEGS
DETAIL OF DIAGONAL SUPPORT
SCALE 1 : 05
SCALE 1 : 05
92
.05
.025
SCALE 1 : 10
Required illustrations to be prepared in Working Drawing.
1. Three main views of the object
2. Assembly pictorial drawing
3. Details of joints.
4. Other details of the different parts of the object if needed.
Note:
The detail drawing maybe drawn in a large scale in a form of sectional
views, exploded view or orthographic views.
93
SELF CHECK # 2.6.1
LO 2. Interpret technical drawings and plans
Direction: Given the three orthographic views, draw the assembly
pictorial drawing. (Use scale 1:10)
TOP VIEW
.60
1.00
.32
.02
.02
.32
.02
.56
.02
.74
.12
.32
.10
.02
FRONTVIEW
RIGHT-SIDEVIEW
94
SELF CHECK # 2.6.2
LO 2. Interpret technical drawings and plans
Direction: Answer the following questions. Use a separate sheet of
paper.
1. What are the three purposes of detailed working drawing?
a. _________________________________________________________
b. _________________________________________________________
c. _________________________________________________________
2. What are the four (4) characteristics of detailed working
drawing?
a. _________________________________________________________
b. _________________________________________________________
c. _________________________________________________________
d. _________________________________________________________
95
INFORMATION SHEET # 2.7
LO 2. Interpret technical drawings and plans
WORKING DRAWING WITH BILL OF MATERIALS
Bill of materials is a list of items needed in the construction of a
piece of work or project. It includes the amount of each material in the
production of the structure.
The following steps in computing bill of materials.
1. Determine the measurement of the width, depth, length and
height of the project.
2. Total the length of all parts having the same sizes but differ in
length.
3. Convert the total length into foot/feet, by dividing the total
number of centimeter by 30.5
Example:
500 cm
30.5
=
16.39 ft.
4. Each piece of lumber should be converted to board foot / feet in
order to determine its price/amount.
Example:
2”x4”x16”
12
=
10.67 board feet (1piece only)
5. Number of board foot/feet should be multiplied by the unit price
per board foot in order to get the amount.
Example:
Unit price per board foot – P 40.00
P40.00 x 16.39 = P 655.60
6. For the other materials, know the unit price according to the
description of the item.
7. After computing the amount of various materials add them all to
determine the total amount .
96
TOP VIEW
.10
DE
VI
E
W
.40
DE
VI
E
W
.20
.375
.30
DE
VI
E
W
.05
DE
VI
E
W
2X2
2X2
2X2
2X3
1X3
2X2
2X2
FRONT VIEW
.22
.13
.375
.40
DE
1.00
VI
0VIE
.05
EW
W
.15
.30
DE
VI
.10 E
DE W
VI
E
W
2X2
2X3
SIDE VIEW
PICTORIAL VIEW
97
SELF-CHECK # 2.7
LO 2. Interpret technical drawings and plans
WORKING DRAWING WITH BILL OF MATERIALS
Directions: A pictorial drawing of a chalkboard with dimensions is
given. Draw the orthographic views ( Top view and Front View only)
and compute its bill of materials by completing the table below.
Show your computations on a separate sheet of paper.
1.20 m
2.30
m
1” X 3” FRAME
¼” THK MARINE PLYWOOD
BIII OF MATERIALS
Qty.
Description of Materials
1 pc
2 pcs
¼ liter
¼ liter
¼” thk. 4’x 8’ Marine Plywood
1”x3”x12’ Good lumber
Slating Paint, green
Quick drying enamel (QDE),
Chocolate brown
#1” Common nail
#1-1/2 ” Common nail
# 100 Sandpaper pad
# 500 Sandpaper pad
Paint thinner
# 3” Paint brush
# 1” Paint brush
# 1” Paint brush
1/8kg
1/8kg
1foot
1 foot
1 bot
1 pc
1 pc
1 pc
No. of
Bf.
----_______
-----------------------------------------
Unit
Total
Price
Price
490.00 _______
41.00 _______
85.00 _______
80.00 _______
7.00
7.00
35.00
35.00
35.00
35.00
25.00
25.00
_______
_______
_______
_______
_______
_______
_______
_______
Total Estimated Cost ………………. __________
98
INFORMATION SHEET # 2.8
LO 2. Interpret technical drawings and plans
Exploded view are drawn in disassembled pictorial form
showing the sequence of assembly of parts of an object that fit
together. Even a person who has no knowledge in technical drawing
can easily understand the mechanics of its assembly.
Principles of Exploded Pictorial Drawing
1. The exploded drawing is pictorial drawn in is disassembled
pictorial form.
2. The disassembled parts are arranged in orderly manner.
3. It supplies information on how the assembly will be undertaken.
99
SELF CHECK # 2.8
LO 2. Interpret technical drawings and plans
Exploded Drawing
Direction: Given the three orthographic views, draw its exploded
pictorial drawing using scale 1:10. Use a separate sheet of paper.
TOP VIEW
4 mm THK METAL PLATE
10
50
10
70
15
29
7
2
15 O
55
20 O
7 mm THK BLADE
METAL RING
FRONT VIEW
HARD WOOD HANDLE
SIDE VIEW
100
INFORMATION SHEET 2.9
LO 2. Interpret technical drawings and plans
OTHER SYMBOLS
STANDARD SYMBOLS AND ABBREVIATIONS. TO BS8888
Term
Abbreviation
or Symbol
Term
Abbreviation
or Symbol
AF
Maximum
Material
Condition..In a
note
Assembly
ASSY
Maximum
Material
Condition..(Geom.
tol)
Centers
CRS
Minimum
MIN
Not to Scale (In a
note and
underlined
NTS
Across Flats
Center Line ..On View
MMC
Center line ..On Note
CL
Number
NO.
Centre Of Gravity
CG
Pattern Number
PATT NO.
Chamfer of
Chamfered..In a Note
CHAM
Pitch Circle
Diameter
PCD
Countersunk/
Countersink
CSK
Radius..In a note
RAD
Countersunk Head
CSK HD
Radius..Preceding
R
a dimension
Counterbore
CBORE
Reference
REF
Cylinder or
Cylinderical
CYL
Required
REQD
Diameter..in a note
DIA
Right hand
RH
Round Head
RD HD
Diameter..preceding a
dimension
Drawing
DRG
Screw of Screwed SCR
Equally Spaced
EQUI SP
Sheet (Drawing
SH
101
Number)
External
EXT
Sketch (prefix to
SK
Drawing Number)
Figure
FIG
Specification
SPEC
Hexagon
HEX
Spotface
SFACE
Hexagon Head
HEX HD
Square ..In a note SQ
Insulated or
Insulation
INSUL
Square
..Preceding dim
Internal
INT
Standard
Least Material
Condition..In a Note
LMC
Taper.. On Dia or
Width
Least Material
Condition..(Geom.Dim)
STD
Thread
THD
Left hand
LH
Thick
THK
Long
LG
Tolerance
TOL
Machine
MC
Typically OR
Typical
TYP
Material
MAT
Undercut
UCUT
Maximum
MAX
Volume
VOL
Electronic and Electrical Symbols
We use graphic symbols on electrical and electronic diagrams to
show the components and workings in a circuit. Graphic symbols for
electrical engineering are shorthand way to show through drawings
how a circuit works or how the parts of the circuit are connected. A
graphic symbol shows what part it does in the circuit. Drafters use
graphic symbols on single-line (one-line) diagrams, on schematic
diagrams, or on connection or wiring diagrams. You can relate graphic
symbols with part lists, descriptions, or instructions by marking the
symbols.
102
103
104
NAME
ABBREV
SYMBOL
ELEVATION
PICTORIAL
DOUBLE
DB FACILITIES SYMBOLS JOINT SYMBOLS
SANITARY
BRANCH
BR EL
ELBOW
STRAIGHT
CROSS
SFTY
X
SAFETY
VALVE
SFTY
V
GATE
VALVE
GV
HANG
VALVE
P
PIPE
OUTLET
DOWN
P
NAME
ABBREV
COUPLING
SYMBOL
ELEVATION
PICTORIAL
CPLG
0
ELBOW 90
EL
0
TEE 90
T
LATERAL
0
45
LAT
REDUCER
RED
PIPE INTERSECTION SYMBOLS
105
NAME
ABBREV
FLANGED
FITTING
FL FT
ABBREV
SCREWED
FITTING
SC FT
WELDED
FITTING
WLD
FT
SOLDERED
FITTING
SLD
FT
EXPANSION
EXP
JT
JOINT
MOTOR
OPERATE
D VEHICLE
SYMBOL
SYMBOL
ELEVATION
ELEVATION
PICTORIAL
PICTORIAL
M OP
V
PIPE JOINT SYMBOLS
NAME
METER
ABBREV
FD
DRY
WELL
DW
SEPTIC
TANK
DISTRIBUTION
BOX
ELEVATION
PICTORIAL
M
FLOOR
DRAINED
SEPTIC
TANK
SYMBOL
SEP
TNK
SEP
TNK
DIS
BX
SANITARY FACILITIES SYMBOLS
106
COMMON ELEVATION SYMBOLS
COMMON SECTION SYMBOLS
107
SELF-CHECK #. 2.9
LO 2. Interpret technical drawings and plans
Electrical and Electronic Symbols
Identify the name of the component that each symbol represents. Use
a separate sheet of paper.
1.
____________________
6.
___________________
2.
___________________
__________________
3.
___________________
__________________
4.
___________________
5.
___________________
7.
8.
9.
__________________
10.
___________________
108
ACTIVITY SHEET # 2.9
LO 2. Interpret technical drawings and plans
Other Drawing Symbols
Since topics A to F consist of numerous groups of symbols, the
activity for each category of symbols shall be done every meeting .
Directions: Draw the following symbols as specified below.
The subsequent resources needed are:
Tools and materials
-
T-square
-
Triangle (30x60 & 45x45)
-
Compass
-
Pencil
-
Technical pen
-
Drawing paper
-
Eraser
-
Masking tape
A. Electrical and Electrical Symbols
B. Pipe Joint Symbols
C. Sanitary Facilities Symbols
D. Pipe Intersection Symbols
E. Common Section Symbols
F. Common Elevation Symbols
109
Performance Assessment
Scoring Rubrics
Criteria
Score
(Tick the corresponding pts.)
Accuracy
50
45
40
Speed
10
6
8
Neatness
25
20
15
Lettering/Labeling
15
12
10
8
Total
Performance Criteria:
 Accuracy
50 pts
-
the output is accurately done.
45 pts
-
two to five errors are observed on the output.
40 pts.
-
six to ten errors are observed on the output.
10 pts
-
the output is done 5 minutes before the time.
8 pts
-
the output is done on time.
6 pts.
-
the output is done after the allotted time.
 Speed
 Neatness
25 pts.
-
has no error.
20 pts
-
has two to three erasures.
15 pts
-
has four or more erasures
110
Lettering/Labeling
15 pts.
-
all pieces
of information are completely indicated and
legibly
printed.
12 pts.
-
all pieces of information are legibly printed but some are
missing.
10 pts.
- all pieces of information are legibly printed but some are
missing and misspelled.
8 pts.
- pieces of information are not legibly printed and words are
misspelled.
111
ASSESSMENT RESOURCES
Performance Assessment
Scoring Rubrics
Criteria
Score
(Tick the corresponding pts.)
Accuracy
50
45
40
Speed
10
6
8
Neatness
25
20
15
Lettering/Labeling
15
12
10
8
Total
Performance Criteria:
 Accuracy
50 pts
-
the output is accurately done.
45 pts
-
two to five errors are observed on the output.
40 pts.
-
six to ten errors are observed on the output.
10 pts
-
the output is done 5 minutes before the time.
8 pts
-
the output is done on time.
6 pts.
-
the output is done after the allotted time.
 Speed
 Neatness
25 pts.
-
has no error
20 pts
-
has two to three erasures
15 pts
-
has four or more erasures
112
 Lettering/Labeling
15 pts.
-
all pieces of information are completely indicated and
legibly printed.
12 pts
-
all pieces of information are legibly printed but some are
missing.
10 pts.
-
all pieces of information are legibly printed but some are
missing and misspelled.
8 pts
-
pieces of information are not legibly printed and words
are missing and misspelled.
113
ASSESSMENT PLAN
Evidence Checklist
Competency standard:
Drafting Technology
Unit of competency:
Performing Mensurations and Calculations
Questioning
Written Test
LO1- Select Measuring Instruments
Direct Observation
Actual Demonstration
Title of Module
Perform Mensurations and Calculations
Ways in which evidence will be collected:
[tick the column]
 Signs, symbols, and data are identified according to job
specifications.
 Signs, symbols and data are determined according to
classification or as appropriate in drawing.
 Signs and symbols in trade mathematics are identified
according to their applications.
LO2. Carry out measurements and calculations

Necessary tools, materials and equipment are identified
according to the plan.

Components, assemblies or objects are recognized as per
job requirement.

Dimensions and specifications are identified according to
job requirements.

Prepared by:
Date:
Checked by:
Date:
NOTE: *Critical aspects of competency
114
ANSWER KEY
SELF CHECK # 1.1
1. Section line
2. Cutting plane line
3. Dimension line
4. Visible line
5. Phantom line
6. Center line
7. Hidden line
8. Leader line
9. Short break line
10. Extension line
SELF CHECK # 1.2
A.
1. b
2. f
3. c
4. e
5. d
B.
1. a
2. f
3. g
4. d
5. c
SELF CHECK # 2.1.1
1. Visible line
2. Front
3. Extension line
4. Construction line or blocking lines
5. 3 mm
6. Invisible line
7. Side View
8. Over-all Dimension
9. First angle projection
10.
Third angle projection
SELF CHECK # 2.1.2
Teacher’s Check
115
SELF CHECK # 2.2.1
ISOMETRIC PICTORIAL
DRAWING
SELF CHECK # 2.2.2
ISOMETRIC PICTORIAL DRAWING
(with circular features)
116
SELF CHECK # 2.2.3
A. OBLIQUE PICTORIAL DRAWING
B. OBLIQUE PICTORIAL DRAWING
117
SELF CHECK # 2.2.4.1
A. ONE-POINT OR PARALLEL PERSPECTIVE DRAWING
B. ONE-POINT OR PARALLEL PERSPECTIVE DRAWING
(CIRCULAR OBJECT)
118
SELF CHECK # 2.2.4.2
ANGULAR PERSPECTIVE DRAWING
SELF CHECK # 2.3
A.
1. c
2. d
3. a
4. a
5. b
B.
1. Right auxiliary view
2. Front auxiliary view
3. Left auxiliary view
4. Rear auxiliary view
119
SELF CHECK # 2.4.1
11.
Pattern
12.
Hem
13.
Parallel line development
14.
b
15.
a
SELF CHECK # 2.4.2
TOP VIEW
2
c
d
10
30
b
10
a
10
1
3
4
10
10
30
1
a
VERTEX
b
a
a c
b d
c
d
2
1
1 3
2 4
4
3
FRONT VIEW
1
2
STRETCHOUT PATTERN
SELF CHECK # 2.5.1
1. Cutting plane line
2. Offset section
3. Broken-out section
4. Full Section
5. Section line
120
6. Removed section
7. Sectional View / Section Drawing
8. Cutting plane line
9. Visible line
10. Section line
in any order
Short break line
SELF CHECK # 2.5.2
TOP VIEW
B
A
OBLIQUE PICTORIAL
DRAWING
FRONT VIEW
HALF SECTIONAL VIEW
SELF CHECK # 2.5.3
LONGITUDINAL SECTION
CROSS SECTION
121
SELF CHECK # 2.6.1
ASSEMBLY PICTORIAL DRAWING
SELF CHECK # 2.6.2
1.
a. It describes the shape of the object
b. It indicates the dimension of the object
c. It provides additional information that is required to make
the object drawn.
2.
a. A detail drawing can be drawn on a separate sheet.
b. Detailed drawings can usually be found beneath the
assembly drawing.
c. Detailed drawing should be drawn in larger scale to clearly
show the parts.
d. Dimension in detailed drawing should be shown clearly.
SELF CHECK # 2.7
TOP VIEW
2.30 M
2.30
M
FRONT VIEW
122
BILL OF MATERIALS
Qty.
1 pc
2 pcs
¼ liter
¼ liter
1/8kg
1/8kg
1foot
1 foot
1 bot
1 pc
1 pc
Description of Materials
¼” thk. 4’x 8’ Marine
Plywood
1”x3”x12’ Good lumber
Slating Paint, green
Quick drying enamel (QDE),
Chocolate brown
#1” Common nail
#1-1/2 ” Common nail
# 100 Sandpaper pad
# 500 Sandpaper pad
Paint thinner
# 3” Paint brush
# 1” Paint brush
No. of
Bf.
-----
Unit
Price
490.00
Total
Price
490.00
6 bd.ft
---------
41.00
85.00
80.00
246.00
95.00
80.00
-----------------------------
7.00
7.00
35.00
35.00
35.00
35.00
25.00
9.25
9.25
35.00
35.00
35.00
35.00
25.00
Total Estimated Cost ……………….P 1,094.00
SELF CHECK # 2.8
EXPLODED DRAWING
OF A CHISEL
SELF CHECK # 2.9
1. Amplifier, general
2. Rectifier, bridge type
3. Transformer
4. Fuse, general
5. Capacitor, polarized
6. Switch, single throw,
single pole
123
7. Antenna, general
8. PNP type transistor
9. Speaker
10. Resistor, general
124
ACKNOWLEDGEMENT
We, the teachers assigned to work on the Competency Based
Curriculum (CBC) and Contextual Learning Material (CLM) and
Competency – Based Learning Modules (CBLM) particularly in
Drafting Technology , wish to express our gratitude and appreciation
for having been given the chance to take part in this educational
breakthrough. With high hopes we look forward for the improvement
of the Technical-Vocational Education of the country through the
development of functional materials such of these kinds.
Marikina Hotel
Marikina City
May 25-30, 2009
June 5-7, 2009
Technology Writers
Conrado C. Casulla
Pangasinan School of Arts and Trades
Lingayen, Pangasinan
Region I
Mirasol F. Dasig
San Pedro Relocation Center National High School
San Pedro, Laguna
Region IV-A, Calabarzon
Rolando V. Inay
E. Rodriguez Vocational High School
Nagtahan,Sampaloc,Manila
Mario S. Gregorio
Tagum National Trade School
Tagum City, Davao Del Norte
Region XI
Alexander M. Latoga
Manuel S. Enverga Memorial School of Arts and Trades
Mauban, Quezon
Ariel F. Maglalang
Assemblywoman Felecita G. Bernardino Memorial Trade School
Lias, Marilao, Bulacan
125
English Teacher
Mercy F. Divina
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Math Teacher
Emmanuel V. Dionisio
Assemblywoman Felecita G. Bernardino Memorial Trade School
Lias, Marilao, Bulacan
Science Teacher
Ma. Lenalyn Q. Manzano
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Editorial Specialist
Estrelita Y. Evangelista Ed.D. (Ret.)
CESO VI
DepED-Director, BSE
Beatriz A. Adriano
Principal III
E. Rodriguez Vocational High School
Nagtahan, Sampaloc, Manila
Carol F. Chavez
Principal I
Muntinlupa Business High School
Facilitator
Orlando E. Manuel Ph.D.
Principal I
Cabarroquis National School of Arts and Trades
Gundaway, Cabarroquis, Quirino
Region II
Math Specialist
Jesus L. Huenda
Senior Education Program Specialist
DepED-BSE
126
Encoders
Eduardo B. Dicion Jr.
Integrative School of Quezon City
U.P. Village, Diliman, Quezon City
Jomel Gail O. Ponce
One World Connection
31/F Wynsun Corporate Plaza
Ortigas Center, Pasig City
Percival Magaway
Cabarroguis Natural School of Arts and Trades
Region II, Quirino
127