5 spatial sense
TRANSCRIPT
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 1/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 1
Spatial Sense
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 2/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 2
Table of Contents
Spatial Sense
Constructing Shapes from Mat Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
Constructing 3-view Orthographic Projections from Mat Plans . . . . . . . . . . . . . . . . . . . . 4-4
Constructing Mat Plans from 3-View Orthographic Projections . . . . . . . . . . . . . . . . . . . . 4-12
Constructing Isometric Drawings from Mat Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18
Matching Isometric Drawings with Mat Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19
Combining Isometric Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22
Hidden-View Lines and 3-View Orthographic Projections . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Matching Isometric Drawings with 3-view Orthographic Projections . . . . . . . . . . . . . . . . 4-30
Constructing Isometric Drawings from 3-View Orthographic Projections . . . . . . . . . . . . 4-32
Constructing 3-view Orthographic Projections from Isometric Drawings . . . . . . . . . . . . . 4-34
Surface Identification (Orthographic Projections - Isometric Drawings) . . . . . . . . . . . . . . 4-36
Dot Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38
Isometric Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39
Drawing Mat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 3/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 3
Constructing Shapes from Mat Plans
Being able to represent the shape of a three-dimensional object on a two-dimensional surface is very
important as it allows others to interpret the object’s shape. This information can then be used to
construct the object. Although not used in industry, mat plans are one of the simplest methods to
represent three-dimensional objects. They are ideal in developing a spatial awareness; however, they
have limitations which you will discover as you proceed through the following exercises.
1. Construct the building illustrated in the mat plan below using cube-a-links.
Orient your building correctly on the building mat provided. Turn the building mat so that you can look
at the front, back, left, or right side of your building straight on. You should see a 2-D pattern of squares.
Decide which side of the building (front, back, right, left, or top) matches each of the diagrams below.
a) b)
c) d)
e)
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 4/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 4
Constructing 3-view Orthographic Projections from Mat Plans
1. Shown below is the right side view of a cube building. Draw the left side view. Confirm
the accuracy of your drawing using cube-a-links.
2. Use the mat plan below to construct the building on a building mat. Draw the top, front,
and right views (3-view orthographic) .
Note: To assist in drawing these views for the first time, it may be helpful to tape three pieces of transparency
sheets together to form three sides (front, top, and right side view) of a cube. The construction can then be
placed neatly against the inside corner of the transparency to allow the three views to be drawn and
labelled. Once complete, remove the tape holding the transparency together to provide you with the three
views on a flat, two-dimensional, surface.
3. Use the mat plans below to construct the buildings on a building mat. Draw the top,
front, and right views (3-view orthographic) for each building.a) b) c)
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 5/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 5
4. Use the mat plans below to construct the buildings on a building mat. Match each
building with the correct set of 3-view orthographic drawings shown below.
a) b)
c)
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 6/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 6
5. Use the mat plans below to construct the buildings on a building mat. Draw the top,
front, and right views (3-view orthographic) for each building.
a) b)
c) Use the mat plan below to construct the building on a building mat. Draw the top, front,
and right views (3-view orthographic) for the building.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 7/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 7
6. On a building mat, use the mat plan below to construct a cube building.
Match the building constructed from the mat plan above to one of the three sets of 3-view
orthographic drawings below.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 8/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 8
7. Use cube-a-links and the provided mat plans to build each of the 5 buildings. Place each
building on a building mat and write the letter of the building in front of the building.
When all buildings have been constructed, match each building with one of the sets of
3-view orthographic drawings on the following page. Justify each match in writing.
Mat Plans
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 9/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 9
Front
Top
R ight
8. Match the buildings constructed (previous mat plans) with the 3-view orthographic
drawings given below.
3-view orthographic Set 1
3-view orthographic Set 2
3-view orthographic Set 3
3-view orthographic Set 4
3-view orthographic Set 5
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 10/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 10
9. Below are the mat plans for four different buildings. Construct a model of each building
on a building mat.
10. Match the buildings constructed above with the following 3-view orthographic
projections.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 11/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 11
10. (continued).
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 12/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 12
Constructing Mat Plans from 3-View Orthographic Projections
Note: There may be more than one mat plan that will represent each 3-view orthographic
projections in questions 1-9.
1. Use the 3-view orthographic projections given below to construct a model of each building on a building mat. Draw the corresponding mat plan for each building.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 13/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 13
1. (continued).
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 14/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 14
2. Construct a 3-D model using the following
views. Draw the corresponding mat plan.
3. Construct a 3-D model using the followingviews. Draw the corresponding mat plan.
4. Construct a 3-D model using the following
views. Draw the corresponding mat plan.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 15/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 15
5. Construct a 3-D model using the following views. Draw the corresponding mat plan.
6. Construct a 3-D model using the following views. Draw the corresponding mat plan.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 16/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 16
7. Construct a 3-D model using the following views. Draw the corresponding mat plan.
8. Construct a 3-D model using the following views. Draw the corresponding mat plan.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 17/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 17
9. Construct a 3-D model using the following views. Draw the corresponding mat plan.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 18/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 18
Constructing Isometric Drawings from Mat Plans
Isometric drawing are an excellent way to represent three-dimensional objects because, unlike
mat plans and orthographic projections, they give the illusion of three-dimensionality.
1. Using isometric paper, construct an isometric drawing for each of the following mat plans:
2. Use the isometric drawing tool at
http://illuminations.nctm.org/tools/isometric/isometric.asp#ft to draw an isometric
drawing of each mat plan above.
( Hint: Viewing Isometric Drawings on this website...when you are looking up and to the left you are
seeing the front view; when you are looking up and to the right you are seeing the right side view.) Use
the “eye” icon to check the mat plan and the top-front-right side orthographic views for agreement).
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 19/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 19
Matching Isometric Drawings with Mat Plans
1. Which of the following is not a corner view of the building represented by the mat plan?
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 20/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 20
2. On a building mat, build a cube model of each of the following three buildings.
Identify which building is represented by each of the corner views (left front, front right,
back left, and right back) illustrated in isometric drawings A- L.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 21/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 21
3. Which corner of this building was the artist viewing to make the drawing at the right?
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 22/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 22
Combining Isometric Drawings
1. Which of these buildings can be made from the two basic shapes given?
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 23/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 23
2. Using cube models, show how the two basic shapes can be put together to make each of
the buildings shown below?
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 24/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 24
Hidden-View Lines and 3-View Orthographic Projections
Hidden-view lines are represented by broken line segments on an orthographic projection. Unlike
solid object lines, hidden-view lines allow an orthographic projection to represent the edges of
voids (hollow spaces) of an object that is not visible by the face being viewed.
To assist in visualizing these objects it may be useful to use cube models to represent their shape
Draw in the missing object lines or hidden-view lines on the orthographic projection.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 25/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 25
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 26/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 26
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 27/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 27
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 28/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 28
Enrichment
The following problems involve slanting surfaces and are considered to be very challenging. To
assist in visualizing these objects it may be useful to use malleable materials, as opposed to rigid
cube models, to represent their shape
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 29/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 29
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 30/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 30
Matching Isometric drawings with 3-View Orthographic Projections
Match the letter of the set of orthographic views below to the number representing the correct
isometric view on the following page.
1 ---letter answer--- 6 ---letter answer---
2 ---letter answer--- 7 ---letter answer---
3 ---letter answer--- 8 ---letter answer---
4 ---letter answer--- 9 ---letter answer---
5 ---letter answer--- 10 ---letter answer---
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 31/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 31
Matching isometric views with 3-view orthographic projections continued...
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 32/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 32
Constructing Isometric Drawings from 3-View Orthographic Projections
1. Use the orthographic views of the set of stairs shown below to construct an isometric view
and to build a cube-a-link model.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 33/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 33
2. Use the orthographic views (top, front, right) of the machine component shown below to
construct an isometric views and to a build cube-a-link model.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 34/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 34
Constructing 3-View Orthographic Projections from Isometric Drawings
1. Draw three orthographic views (top, front, right) of the object below. Use the positions
indicated by the short darkened line segments to position the views.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 35/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 35
2. Draw three orthographic views (top, front, right) of the object below. Use the positions
indicated by the short darkened line segments to position the views.
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 36/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 36
Surface Identification (Orthographic Projections - Isometric Drawings)
1. Find the numbers in the top, front, and right side views that correspond to the lettered
surfaces in the isometric drawing. Create a table similar to the one below to record your
answers.
Top Front Right
A
B
C
D
E
F
G
H
J
K
L
M
N
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 37/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 37
2. Find the numbers in the top, front, and right side views that correspond to the lettered
surfaces in the isometric drawing. Create a table similar to the one below to record your
answers.
Top Front Right
A
B
C
D
E
F
G
H
I
J
K
L
M
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 38/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 38
Dot Paper
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 39/40
PRINCE EDWARD ISLAND APPLIED MATHEMATICS 801A
4 - 39
Isometric Paper
7/27/2019 5 Spatial Sense
http://slidepdf.com/reader/full/5-spatial-sense 40/40
Drawing Mat