© 21st Century Math Projects
Project Title: Scale Model
Standard Focus: Geometry &
Spatial Sense, Measurement
Time Range: 5-7 Days (Can be modified)
Supplies: Cardboard, glue, Exacto knives, tape measures, basic
art supplies, glue, rulers (Optional: foam core: this is the
cheapest I can find: (http://www.dollartree.com/Readi-BoardFoam-Boards/p16450/index.pro) & hot glue)
Topics of Focus:
-
Scale Factors
-
Measurement
-
Surface Area & Volume
Benchmarks:
Ratios and
Proportional
Relationships
6.RP
1. Understand the concept of a ratio and use ratio language to describe a ratio
relationship between two quantities.
Ratios and
Proportional
Relationships
6.RP
3d. Use ratio reasoning to convert measurement units; manipulate and
transform units appropriately when multiplying or dividing quantities.
Ratios and
Proportional
Relationships
7.RP
2. Recognize and represent proportional relationships between quantities.
Ratios and
Proportional
Relationships
7.RP
3. Use proportional relationships to solve multistep ratio and percent problems.
Examples: simple interest, tax, markups and markdowns, gratuities and
commissions, fees, percent increase and decrease, percent error.
Geometry
7.G
1. Solve problems involving scale drawings of geometric figures, including
computing actual lengths and areas from a scale drawing and reproducing a
scale drawing at a different scale.
Quantities
N-Q
1. Use units as a way to understand problems and to guide the solution of
multi-step problems; choose and interpret units consistently in formulas;
choose and interpret the scale and the origin in graphs and data displays.
Geometric
Measurement and
Dimension
GGMD
4. Identify the shapes of two-dimensional cross-sections of three dimensional
objects, and identify three-dimensional objects generated by rotations of twodimensional objects.
Modeling with
Geometry
G-MG
1. Use geometric shapes, their measures, and their properties to describe objects
(e.g., modeling a tree trunk or a human torso as a cylinder).★
© 21st Century Math Projects
Procedures:
A.) Student will complete “Keeping Things in Proportion” to familiarize themselves with scale and basic
architectural concepts.
B.) Students will complete “Rescaling & Remodeling” in which they will measure drawings of famous landmarks.
There are three parts to the assignment:
First, students will use scale models of five different landmarks to compare their heights. The problem is they all
have different scale ratios. They will measure the buildings in centimeters and use the scale ratios associated
with the models to determine their real-life dimensions. They will record measurements on the “Measurement
Log Sheet”
Second, they will use their actual dimensions on the measurement log sheet and use a new standardized scale
ratio ( 1𝑐𝑚 ⁄50𝑚 ) to determine the scaled dimensions of each of the new models. This will be done on the
“Measurement Log Sheet”
Third, they will draw all five models together on the same piece of graph paper. They need to be as precise as
possible with all aspects of their drawing.
C.) “Map Your World” is an optional mini-project that asks students to create a scale drawing of a hallway in
their school. Recording sheets and graph paper is included in this file.
D.) Students will begin “Scale Model”. Pages 16-26 can be used as a student packet or handed out individually.
Step 1: RESEARCH
Websites like http://www.greatbuildings.com/ and http://www.dimensionsinfo.com
contain a lot of
information that you will find useful, but students will likely need to use multiple sources once they narrow
down their choices. The websites does include pictures taken from multiple perspectives which can be helpful
for planning. They will need to find a minimum of 5 different real life dimensions (height should be easy!). They
will choose one building and move forward.
Step 2: DETERMINE SCALE
How big of a model do they want to build? Going too small may be too difficult to detail, but going to big might
be unmanageable. Students will create a Scale Ratio using the actual dimensions and their desired size.
Step 3: SCALE DRAWINGS
In order to move forward to building, three perspectives of architectural drawings must be submitted and
approved. Once they have determined the size of your scale model, they’ll need to draw that to scale. A scale of
a scale!
Step 4: BUILDING MATERIALS
Students will be required to submit Assembly Instructions (page included). Determining what they plan to use to
assemble your model is critical. For the structure itself, cardboard or foam core usually works the best. To
connect the pieces, hot glue, super glue or craft glue can work, but they’ll likely need to test. Using small pieces
of tape may be helpful as they let the glue dry. Other materials may be useful depending on what building you
map by trying to build. Keep an open-mind and use your own creativity.
Step 5: CONSTRUCTION
Help them remember: Measure twice, cut once and be precise. This will be the difference between a great
model and a mediocre one. Then Build It! Add color and paint as appropriate.
Step 6: PRESENT IT
Once they have something that they are proud of share it. It’s Presentation time!
© 21st Century Math Projects
Keeping things
in Proportion
When considering the areas where math and the real world intersect, architecture
is often one of the first answers. Architecture is math. Whether it is building a hotel
or a new bedroom, every square inch matters -- literally. We don’t regularly walk
into rooms with lopsided floors or walls that aren’t near perfect 90 degree angles.
While these are the more tangible ways we can see and feel the math, the guts of
an architecture project are in the blueprints.
Proportional thinking with scale is a fundamental attribute of architectural planning. Whether this
is sketching designs or building scale models, architects need to understand scale to prepare
appropriately. Below, you will encounter problems where you need to either determine the scale
or apply a given scale. The following proportion serves as a reminder.
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
𝑚𝑜𝑑𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
𝑚𝑜𝑑𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
Determine the Scale in each of the three situations (watch the units!)
A Vegas based real estate developer plans to recreate a Sydney Opera House. Determine the
scale that the developer is using.
Scale
Actual
Souvenir
A souvenir manufacturer is creating models of the Taj Mahal. Determine the scale of the model.
Scale
Actual
Model
A photographer has blown-up a picture of the St. Louis Arch. Is the picture to scale?
Original
Enlargement
Scale
© 21st Century Math Projects
Apply the Scale in each of the three situations
In the Nashville archives, a researcher found a scale drawing that was used to build their replica of
the Greek Parthenon. If the scale was 1:128, what are the actual dimensions of the structure?
Scale
Drawing
Actual
1:128
The floor plan for a home was measured in inches. If the scale was 2.5 ft : 1 in, how much larger is
the area of the actual master bedroom than the actual guest bedroom?
Scale
Plans
𝟐. 𝟓 𝒇𝒕
𝟏 𝒊𝒏
A 3-D replica of the Great Pyramid of Giza was built at a 10 meter : 1 inch scale. If the volume of a
1
pyramid can be calculated with the formula v = 3 𝑙𝑤ℎ, what is the volume of the replica pyramid?
Scale
Actual
Replica
𝟏𝟎 𝒎
𝟏 𝒊𝒏
© 21st Century Math Projects
Sketch a diagram for each situation using the given scale. Be Precise!
Redraw the COTTAGE with a scale of (2:1)
Redraw the HOUSE with a scale of (4:1)
Redraw the SKYSCRAPER with a scale of (1: 2)
© 21st Century Math Projects
Rescaling &
Remodeling
Tourist will travel half-way around the world just to set their eyes on
a piece of architecture. Whether it’s the ancient work of the Mayans
or the modern work of the Emiratis, people have long had a
fascination with beautiful (and humongous) structures.
In this assignment, there are three parts. First, you will use drawings of five different landmarks to
compare their actual heights. The problem is they all have different scale ratios. You will measure
the buildings in centimeters and use the scale ratios associated with the models to determine their
real-life dimensions. Be sure to measure many aspects of the models so you can make a perfectly
proportionate copy. Record measurements on the Measurement Log Sheet.
Second, you will use the actual dimensions from the Measurement Log Sheet and use a new
standardized scale ratio ( 1𝑐𝑚 ⁄50𝑚 ) to determine the “re”scaled dimensions of each of the new
models. This will be recorded on the Measurement Log Sheet.
Third, you will draw all five models together on the same piece of graph paper. Be as precise as
possible with all aspects of your drawing. Don’t put too much space between your drawings.
Empire State Building (USA)
Scale
1 cm = 29.5333 m
Burj Khalifa (UAE)
Scale
1 cm = 53.3333 m
© 21st Century Math Projects
Big Ben (United Kingdom)
Canton Tower (China)
Eiffel Tower (France)
Scale
Scale
Scale
1 cm = 6.4 m
1 cm = 40.6667 m
1 cm = 21.60 m
© 21st Century Math Projects
Measurement Log Sheet
Building:
Description of
Dimension
Given Drawing
(in centimeters)
(what is being measured)
Actual
Measurement
Rescaled Drawing
(include units)
(include units)
Scale Used
(Drawing to Actual)
Scale Used
(Actual to Rescaled)
50 m = 1 cm
Height
Base Length
Building:
Description of
Dimension
(what is being measured)
Given Drawing
(in centimeters)
Actual
Measurement
Rescaled Drawing
(include units)
(include units)
Scale Used
(Drawing to Actual)
Scale Used
(Actual to Rescaled)
50 m = 1 cm
Height
Base Length
© 21st Century Math Projects
Measurement Log Sheet
(cont’d)
Building:
Description of
Dimension
Given Drawing
(in centimeters)
(what is being measured)
Actual
Measurement
Rescaled Drawing
(include units)
(include units)
Scale Used
(Drawing to Actual)
Scale Used
(Actual to Rescaled)
50 m = 1 cm
Height
Base Length
Building:
Description of
Dimension
(what is being measured)
Given Drawing
(in centimeters)
Actual
Measurement
Rescaled Drawing
(include units)
(include units)
Scale Used
(Drawing to Actual)
Scale Used
(Actual to Rescaled)
50 m = 1 cm
Height
Base Length
© 21st Century Math Projects
Measurement Log Sheet
(cont’d)
Building:
Description of
Dimension
(what is being measured)
Given Drawing
(in centimeters)
Actual
Measurement
Rescaled Drawing
(include units)
(include units)
Scale Used
(Drawing to Actual)
Scale Used
(Actual to Rescaled)
50 m = 1 cm
Height
Base Length
© 21st Century Math Projects
© 21st Century Math Projects
Rescaled Models (each unit in the grid is 1 centimeter)
Map Your
World
Grab a tape measure because you’re about to see
your world from an all new dimension -- the second
dimension. In teams of 3 or 4 you will choose a
hallway in your school to create a scale drawing. To complete this task you will need to…
-
Grab a tape measure and remember how to use it,
-
Make a rough “reference sketch” of the area that you can use to mark the
measurements.
o
-
-
This sketch does not need to be to scale.
Label your “reference sketch with notable areas including:
o
All rooms labeled with Teacher’s Names
o
Restrooms
o
Drinking Fountains
o
Lockers
o
Stairs
o
Other Noteworthy Spaces
Using a piece of 8.5 x 11 graph paper you must sketch your area. You will need to:
o
Choose a Scale (perhaps 10 meters will equal 1 cm, perhaps 20 feet will equal 1
inch)
o
Create a Key
o
Use a Straightedge to construct your model. Measure twice. Draw once.
*** Remember, in the world of architecture, precision is key, details are essential and
perfection is expected. After all, we do not want a lopsided house.
© 21st Century Math Projects
Reference Sketch
In this space, make a rough sketch of the area you will be modeling.
Notes
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Scale Drawing
© 21st Century Math Projects
Scale Model
Once blueprints are finalized, an architect will need to turn their 2-D imaginings into
3-D reality. Computer software like Google Sketchup help architects and industrial
designers do this, but nothing beats a tangible scale model. For abstract architects,
like the famous Frank Gehry, there’s no other way to visualize a structure. In this
project, you will research three architectural works, choose one, determine a scale
factor, construct a blue print of a scale model (from three views) and… build it!
Process & Materials
Step 1: RESEARCH
Websites like http://www.greatbuildings.com/ and http://www.dimensionsinfo.com
contain a lot of information that you may find useful for your project, but you will likely
need to use multiple sources once you narrow down your choices. The websites do
include pictures taken from multiple perspectives which can be helpful for planning.
You will need to find a minimum of 5 different real-life dimensions (height should be
easy!). You will choose one building and move forward.
Step 2: DETERMINE SCALE
How big of a model do you want to build? Going too small may be too difficult to detail,
but going to big might be unmanageable. Create a Scale Ratio using the actual
dimensions of the structure and your desired size.
Step 3: SCALE DRAWINGS
Once you have determined the size of your scale model, you’ll need to draw that to scale. A
scale of a scale! In order to move forward to building, three perspectives of architectural
drawings must be submitted and approved (at least two sides and from above).
Step 4: BUILDING MATERIALS
You will be required to submit Assembly Instructions. The major pieces
need to be drawn and labeled as parts (just as if you were putting
together a TV Stand). Determining what materials you plan to use to
assemble your model is critical. For the structure itself, cardboard or
foam core usually works the best. To connect the pieces, hot glue,
super glue or craft glue can work, but you’ll likely need to test to see
what works for you. Using small pieces of tape may be helpful as your let the glue dry. Other
materials may be useful depending on what building you map by trying to build. Keep an openmind and use your creativity.
Step 5: CONSTRUCTION
Use straightedges. Measure twice, cut once and be precise. This will be the difference between
a great model and a mediocre one. Once everything is cut… Build It!
Add color and paint as appropriate.
Step 6: PRESENT IT
Once you have something that you are proud of… share it! You’ve
accomplished something pretty cool!
© 21st Century Math Projects
Requirements
Individual or team grades for the project will be
broken into the following components:
300 pts
Research & Design
scale was chosen & solved correctly
three different perspectives
diagrams drawn to scale
400 pts
Product
The final product is precisely to scale and built
with great craftsmanship and attention to detail.
The final product is mostly to scale and
assembled nicely with some attention to detail.
The final product is inconsistently to scale or
craftsmanship shows uneven effort.
The final product is not to scale or assembled in
a careless way.
400 pts
350 pts
300 pts
___ pts
0 pts
The final product is not complete.
300 pts
____/100 pts
____/100 pts
____/100 pts
Presentation
describe your building and why you
chose it
explain the geometric components of
the design (i.e. what shapes are present?)
expound on the design process (i.e.
what was challenging? interesting?)
reflect on the results (i.e. what could have
gone better? what would you do differently?)
presentation delivery & writing
mechanics (i.e. content command, spelling)
____/50 pts
____/50 pts
____/50 pts
____/50 pts
____/100 pts
Total _____/1000
© 21st Century Math Projects
Building 1
Building Name
Location
Quick Sketch of Building
Geometric Shapes Included
Dimensions
Height
Base Dimensions
Notes (Reminders, Design Challenges, Etc.)
© 21st Century Math Projects
Building 2
Building Name
Location
Quick Sketch of Building
Geometric Shapes Included
Dimensions
Height
Base Dimensions
Notes (Reminders, Design Challenges, Etc.)
© 21st Century Math Projects
Building 3
Building Name
Location
Quick Sketch of Building
Geometric Shapes Included
Dimensions
Height
Base Dimensions
Notes (Reminders, Design Challenges, Etc.)
© 21st Century Math Projects
Scale Calculations
Building Name:
Description of Dimension Measurement
(what is being measured)
(include units)
Scale Model
(include units)
Scale Used
(Actual to Model)
Scale Drawing
(include units)
Scale Used
(Model to Drawing)
© 21st Century Math Projects
Perspective 1 (Side A)
© 21st Century Math Projects
Perspective 2 (Side B)
© 21st Century Math Projects
Perspective 3 (From Top)
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Perspective 4
© 21st Century Math Projects
Assembly
Instructions
In this space, sketch the parts that need to be built and the material you will use to make it.
Materials List
© 21st Century Math Projects
Thank you for being my Math Friend!
If you liked this
21st Century Math Project
You might like others.
(Click the logo)
Math it Up.
Boomdiggy.
© 21st Century Math Projects
Keeping things
in Proportion
When considering the areas where math and the real world intersect, architecture is
often one of the first answers. Architecture is math. Whether it is building a hotel or
a new bedroom, every square inch matters -- literally. We don’t regularly walk into
rooms with lopsided floors or walls that aren’t near perfect 90 degree angles. While
these are the more tangible ways we can see and feel the math, the guts of an
architecture project are in the blueprints.
Proportional thinking with scale is a fundamental attribute of architectural planning.
Whether this is sketching designs or building scale models, architects need to understand scale to
prepare appropriately. Below, you will encounter problems where you need to either determine
the scale or apply a given scale. The following proportion serves as a reminder.
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
𝑚𝑜𝑑𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
𝑚𝑜𝑑𝑒𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
Determine the Scale in each of the three situations (watch the units!)
A Vegas based real estate developer plans to recreate a Sydney Opera House. Determine the scale
that the developer is using.
Scale
Actual
Souvenir
1 ft : 64 ft
A souvenir manufacturer is creating models of the Taj Mahal. Determine the scale of the model.
Scale
Actual
Model
1 cm :
1140cm
A photographer has blown-up a picture of the St. Louis Arch. Is the picture to scale?
Original
Enlargement
Scale
4 in : 1 in
Yes it is to
scale
© 21st Century Math Projects
Apply the Scale in each of the three situations
In the Nashville archives, a researcher found a scale drawing that was used to build their replica of
the Greek Parthenon. If the scale was 1:128, what are the actual dimensions of the structure?
Scale
Drawing
Actual
Length: 30.848m, Column: 10.4m, Tri
1:128
Top: 3.67m
The floor plan for a home was measured in inches. If the scale was 2.5 ft : 1 in, how much larger is
the area of the actual master bedroom than the actual guest bedroom?
Scale
Plans
6.25ft x 9.5 ft
𝟐. 𝟓 𝒇𝒕
Guest
𝟏 𝒊𝒏
9ft x 6.875ft
Master
Guest Area 59.375ft2
Master Area
61.875ft2
2.5ft2 difference
A 3-D replica of the Great Pyramid of Giza was built at a 10 meter : 1 inch scale. If the volume of a
1
pyramid can be calculated with the formula v = 3 𝑙𝑤ℎ, what is the volume of the replica pyramid?
Scale
Actual
Replica
23.04 in x 23.04 in x 14.65 in * 1/3=
𝟏𝟎 𝒎
2592.28in3
𝟏 𝒊𝒏
© 21st Century Math Projects
Sketch a diagram for each situation using the given scale. Be Precise!
Redraw the COTTAGE with a scale of (2:1)
Redraw the HOUSE with a scale of (4:1)
Redraw the SKYSCRAPER with a scale of (1: 2)
© 21st Century Math Projects
Rescaling &
Remodeling
Tourist will travel half-way around the world just to set their eyes on
a piece of architecture. Whether it’s the ancient work of the Mayans
or the modern work of the Emiratis, people have long had a
fascination with beautiful (and humongous) structures.
In this assignment, there are three parts. First, you will use drawings of five different landmarks to
compare their actual heights. The problem is they all have different scale ratios. You will measure
the buildings in centimeters and use the scale ratios associated with the models to determine their
real-life dimensions. Be sure to measure many aspects of the models so you can make a perfectly
proportionate copy. Record measurements on the Measurement Log Sheet.
Second, you will use the actual dimensions from the Measurement Log Sheet and use a new
standardized scale ratio ( 1𝑐𝑚 ⁄50𝑚 ) to determine the “re”scaled dimensions of each of the new
models. This will be recorded on the Measurement Log Sheet.
Third, you will draw all five models together on the same piece of graph paper. Be as precise as
possible with all aspects of your drawing. Don’t put too much space between your drawings.
Empire State Building (USA)
Scale
1 cm = 29.5333 m
Burj Khalifa (UAE)
Scale
1 cm = 53.3333 m
© 21st Century Math Projects
Big Ben (United Kingdom)
Canton Tower (China)
Eiffel Tower (France)
Scale
Scale
Scale
1 cm = 6.4 m
1 cm = 40.6667 m
1 cm = 21.60 m
© 21st Century Math Projects
Measurement Log Sheet
Building: Empire State Building
Description of
Dimension
Given Drawing
(in centimeters)
(what is being measured)
Actual
Measurement
Base Length
(include units)
(include units)
Scale Used
Height
Rescaled Drawing
Scale Used
(Drawing to Actual)
(Actual to Rescaled)
1cm=29.533m
50 m = 1 cm
15 cm
443M
8.86 cm
4.06 CM
119.9 m
2.398 cm
Given Drawing
Actual
Measurement
Rescaled Drawing
Building: Burj Khalifa
Description of
Dimension
(in centimeters)
(what is being measured)
(include units)
Scale Used
Height
Base Length
(include units)
Scale Used
(Drawing to Actual)
(Actual to Rescaled)
1 cm = 40.667 m
50 m = 1 cm
15 cm
830 m
16.6 cm
2.929 cm
119.11 m
2.3833 cm
© 21st Century Math Projects
Measurement Log Sheet
(cont’d)
Building: Big Ben
Description of
Dimension
Given Drawing
(in centimeters)
(what is being measured)
Actual
Measurement
Base Length
(include units)
(include units)
Scale Used
Height
Rescaled Drawing
Scale Used
(Drawing to Actual)
(Actual to Rescaled)
1 cm = 6.4m
50 m = 1 cm
15 cm
96 m
1.92 cm
2.6 cm
16.64 m
0.33 cm
Given Drawing
Actual
Measurement
Rescaled Drawing
Building: Canton
Description of
Dimension
(in centimeters)
(what is being measured)
(include units)
Scale Used
Height
Base Length
(include units)
Scale Used
(Drawing to Actual)
(Actual to Rescaled)
1 cm = 40.6667 m
50 m = 1 cm
15 cm
610 m
12.2 cm
2.51 cm
102.0 m
2.04 cm
© 21st Century Math Projects
Measurement Log Sheet
(cont’d)
Building: Eiffel Tower
Description of
Dimension
Given Drawing
(in centimeters)
(what is being measured)
Actual
Measurement
Base Length
(include units)
(include units)
Scale Used
Height
Rescaled Drawing
Scale Used
(Drawing to Actual)
(Actual to Rescaled)
1 cm = 21.6 m
50 m = 1 cm
15 cm
324 m
6.48 cm
7.023 cm
151.70 m
3.034 cm
© 21st Century Math Projects
© 21st Century Math Projects
Rescaled Models (each unit in the grid is 1 centimeter)