Unit 5 notes - St John Brebeuf

Apprenticeship and workplace Math 11
St.John Brebeuf
Unit 5:
Mathematics
Scale Representations
Department
Goals:
In this chapter you will use some familiar concepts like fractions,
ratios, proportions and measurement to:
Make scale models
Create drawings that represent 2D and 3D
Calculate the full-size measurements of objects from drawings
Draw views and perspective drawings of objects and their
component parts
Key Terms: You will be able to define and use the following terms:
Component parts drawing
Elevation
Exploded view
Isometric drawing
One-point perspective
Scale factor
Scale statement
3-D representation
2-D representation
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Apprenticeship and workplace Math 11
St.John Brebeuf
5.1: Scale Drawings and Models
‣ Scale Statement: a ratio that expresses the size relationship
between2 objects.
‣ Scale Factor: a number by which all the dimensions of an original
figure are multiplied to produce an enlargement or a reduction.
5cm
10cm
5cm
Scale Factor = 2
Since the larger case is twice the size of the smaller case
Example 1:
Philippe is a cabinet maker with a contract to make wooden stereo
speaker cabinets. He receives the scale drawing below from the
speaker company.
How big will the actual speaker cabinet be
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Apprenticeship and workplace Math 11
St.John Brebeuf
5cm
Scale 1:14
2cm
3cm
Solution:
Example 2.
Antonio works as a truck driver. His truck is over 2 stories high and
can haul 360 tonnes of oil and sand. Antonio sends a photo of himself
standing next to his truck to his friend Martin. Martin wonders how
tall the truck is. He knows that Antonio is about 180cm . In the photo
he is 0.7cm tall. If the height of the truck in the photo is 2.5cm, how
high is the actual truck in metres
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Apprenticeship and workplace Math 11
St.John Brebeuf
Solution:
Actual height : Scale height
180cm : 0.7cm
x cm : 2.5cm
Use proportional reasoning
Complete notebook assignment page 2157 # 1-7
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Apprenticeship and workplace Math 11
St.John Brebeuf
5.2: 2-Dimensional Representations:
‣ View: A 2-D or flat geometric drawing that depicts one face of
an object
‣ Elevation: Another term for view, usually refers to a vertical
plane.
‣ Component Parts Diagram: 2 –D scale representation that shows
each part of an object.
Eg. Below is shown the different views of an information board
Insert diagram page 219
‣ A view can be drawn to scale or it can be an approximation.
‣ Looking at parts drawings can help you visualize how the pieces
fit together
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Apprenticeship and workplace Math 11
St.John Brebeuf
Example1:
Lori had a laneway house, a small house built near a back lane, built on
her property for her parents to move into. Now she wants to add a
sunroom to one side. You are a building surveyor who has been hired to
draw views of the existing laneway house.
Draw views of the 3 sides of the house that will be affected by the
addition.
Solution:
Insert page 220
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Apprenticeship and workplace Math 11
St.John Brebeuf
Example 2.
Have you ever had to assemble furniture or machinery
If so you have likely used instructions to help you figure out how to
put things together.
Instruction booklets usually contain scale component diagrams, so
people can see the number and type of materials needed to build
something.
You are the technical illustrator who’s job it is to draw a cabinets
component parts, at a scale of 1:10.
Label the components with their measurements.
45cm
30cm
40cm
Solution:
Identify the parts that make up the cabinet
Back…………………………………………………………………..
Calculate the scaled measurements
40cm 30cm 45cm
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Draw the component parts.
Back
Front
Top and Bottom
Sides
Complete notebook assignment page 226 # 1-7
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5.3: 3-Dimensional Representations:
‣ Perspective drawing: A representation
of a 3-D object in 2-D; objects appear proportionally smaller with
.
distance, and features including a foreground and vanishing point
are used to create a sense of depth and space.
The advantages of perspective drawings is that they try and
represent objects as you really see them.
In a one-point perspective drawing, a scene or object is
drawn as it looks from a single point. Parts of the scene or
object that are farther away and look smaller and parallel
lines converge towards the horizon.
‣ Isometric drawing: A representation of a 3-D object where the
same scale is used to draw the same object height, width and
depth; lines that are parallel in reality are shown to be parallel in
the drawing.
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Apprenticeship and workplace Math 11
St.John Brebeuf
The advantages of isometric drawings is that they show
parallel projection of an object, meaning that lines that are
parallel in reality are parallel in the drawings.
Use vertical lines to show the height of an object
Use lines measured 30° from a horizontal line to show width
and height
‣ Exploded Diagrams: A 3-D representation of an object that
shows how the components connect together; components are
shown separated but in their relative positions.
Insert page 233
‣ An exploded diagram can be either a perspective drawing or an
isometric drawing.
‣ In an exploded diagram the parts that are normally hidden in a
drawing are visible.
‣ Exploded diagrams may be used to show how furniture is
assembled.
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Apprenticeship and workplace Math 11
St.John Brebeuf
‣ Dotted lines are often used to show where the pieces connect to
one another.
Example 1.
Anthony is making an assembly kit for a French Canadian blanket box
that dates from the 1800’s. The finished box has a length of 89.5cm, a
width of 42.5cm and a height of 43.5cm (including the lid which is 2cm
thick). The kits use traditional construction techniques and materials.
Anthony needs to include an isometric drawing in the kit.
Prepare a scale drawing he can include.
Solution: Hint use a scale of 1:10
Step 1:
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Apprenticeship and workplace Math 11
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Step 2:
Step 3:
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St.John Brebeuf
Step 4:
Step 5:
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Step 6:
‣ Horizon line: A horizontal line (not always visible) that is at the
eye level of the observer in a perspective drawing.
‣ Vanishing Point: The point at which parallel lines appear to
converge in a perspective drawing.
Example 2.
Jillian is a designer who is making a one-point perspective drawing of a
juice box. The illustration will be used in a poster promoting recycling.
Draw the juice box that will be used in the poster.
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Apprenticeship and workplace Math 11
St.John Brebeuf
Solution:
Follow these steps:
Draw a horizon line or horizontal line
Draw a vanishing point on the horizon line
About
of the way down the page draw a rectangle
Draw 4 lines that start at the vanishing point and pass through
the 4 corners of the juice box
Draw a horizontal line between the 2 top lines that end at the
vanishing point. This line is parallel to the horizon line. It is also
the back of the juice box.
From the left edge of this line, draw a vertical line. This line
stops at the line drawn from the left corner.
The juice box is now complete and looks like
Erase the lines behind the juice box.
‣ If you shift the vanishing point to the right you will create a juice
box that looks like this:
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Apprenticeship and workplace Math 11
St.John Brebeuf
Example 3.
Michael is an instructor at Brooks Secondary School in Powell River,
BC. As the final project of the year, the students in his class are
building coffee tables. They have the option of including a glass or
wooden inlay in the top of the table.
Before the students assemble their table components, Michael
circulates a drawing that shows how the table parts will fit together to
make the completed object.
Make a drawing that Michael could use.
Solution:
Identify the components that make up the table:
__________________________________________
__________________________________________
__________________________________________
Draw the 9 component parts separately showing how they will fit
together.
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St.John Brebeuf
Draw dotted lines that show the relationship of the parts
Complete Notebook Assignment page 244 # 1-5
Complete Unit Review page 248 # 1-6
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Reflect on your learning
Now check the box that applies to you :
RED
AMBER GREEN
I understand all the key terms.
I can describe contexts in which
scaled representations are used.
I can use a scale drawing or model
to determine the dimensions of a
3-D object.
I can draw scaled views and the
component parts of a 3-D object.
I can construct a scale model of
a 3-D object.
I can draw a 3-D object using
isometric dot paper.
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Apprenticeship and workplace Math 11
St.John Brebeuf
I can draw a one-point perspective
drawing of a 3-D object.
I can draw an exploded diagram
of a 3-D object and explain how
the pieces fit together.
I have completed all
homework assignments.
I have attended tutorials
for extra help.
I am ready to sit my
unit 5 test.
Target:
In my Unit Test I hope to achieve
%
Student’s Signature ____________________
Date__________
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