Future City Learning Block
Model Building Concepts
Activity 1: Proportions, Ratios, and Scale Drawings
Objective
Students will learn about proportions, ratios and scale and apply that knowledge to create
a scale drawing of an actual room.
Questions
•
•
•
What is the appropriate scale to map the object(s) being drawn given the size of
paper being used?
Is the scale appropriate in relationship with other items in the drawing?
Is the scale consistent throughout the drawing?
Explorations
1. Supplement 1: Proportions Worksheet
2. Map scales and Supplements 2-3.
3. Students will complete a home assignment (Supplement 4: Scale Drawing of a
Room)
• They should choose a room in their home.
• All large furniture/appliances should be measured and recorded.
• Using graph paper, students will decide on an appropriate scale and transfer
their dimensions.
• Similar to a map, students will identify their scale.
• All representations should be drawn to scale.
4. Extended Activity: Students work in groups of three to develop a scale map drawing
of the classroom/school.
Analyze Results
Students will exchange room drawings and work on labeling the dimensions of items in
the drawing. Students will use the designated scale to do so.
Assessment
Students will complete Supplement 5: Reflection Worksheet about the challenges of
creating a scale room map.
Activity 1
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Future City Learning Block
Model Building Concepts
Supplement 1: Proportions Worksheet
Create a proportion from each set of numbers.
This will help students learn proportional reasoning.
Miles
45
Hours
1
Dollars
3.30
Pounds
1
2
3
4
5
2
3
4
5
Dollars
Hours
45
1
2
3
4
Dollars
Hours
42
1
2
3
4
Dollars
Meters
5
5
15.50
0.10
0.20
0.30
0.40
0.50
Utilizing the information from the tables above:
1. How many miles will someone travel in 11 hours?
2. If you are working for 9 dollars per hour, how much would you make for an 8 hour
shift minus a one hour lunch period?
3. How much would 1 meter of fabric cost?
Supplement 1
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Future City Learning Block
Model Building Concepts
Supplement 2: Map Scale
In a scale drawing or a scale model, all the dimensions of the actual object are reduced or
enlarged proportionally.
A map is a scale drawing in which actual distance is reduced.
The towns of Ardon and Bacton are on a map with a scale
1 cm = 15km.
If the map distance between Ardon and Bacton is 4.5 cm, what is the actual distance?
Actual Distance
Actual Distance
=
Map Distance
Map Distance
15 km
X km
=
1 cm
4.5 cm
1 (x)
=
15 (4.5)
X
=
67.5 km Actual distance between Ardon and Bacton
Supplement 2
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Future City Learning Block
Model Building Concepts
Complete to find each unknown measurement.
1. A map scale is 1 in. = 75 mi.
The map distance between Lewiston and Portage is 3.5 in. Find the actual distance x
between the towns.
Actual Distance
Actual Distance
=
Map Distance
Map Distance
2. The actual distance between two towns is 175 km. If the distance between them on a
map is 7 cm, what is the map scale?
3. An archway in a ½ in. scale drawing is 4.5 in. tall. Find the actual height x.
4. Under a 7:1 magnification, this letter F appears to be 84 points high. Find the actual
height x.
Supplement 2
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Future City Learning Block
Model Building Concepts
Supplement 3: Exercises in Scale
The scale of a drawing is ¼ in. = 15 ft. Find the actual measurement.
1.
9 in.
2.
12 in.
3.
14 in.
4.
15 in.
The scale is 2 cm = 25 m. Find the length each measurement would be on a scale
drawing.
5.
150 m.
6.
475 m.
7.
350 m.
8.
500 m.
Tell whether each scale reduces, enlarges, or preserves the size of an actual object.
9.
1 m : 25 cm
10.
8 in : 1 ft
11.
12 in : 1 ft
12. On a map the distance between Atlanta, Georgia, and Nashville, Tennessee, is 12.5
in. The actual distance between cities is 250 miles. What is the scale?
13. Blueprints of a house are drawn to the scale of ¼ in. 1 ft. A kitchen measures 3.5 in.
by 5 in. on the blueprints. What is the actual size of the kitchen?
14. A scale model of a house is 1 ft long. The actual house is 50 ft long. In the model,
the window is 1 1/5 in. high. How many feet height is the actual window?
15. A model of a skyscraper is 1.6 in. long, 2.8 in. wide, and 11.2 in. high. The scale
factor is 8 in. :250 ft. What the actual dimensions of the skyscraper?
Supplement 3
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Future City Learning Block
Model Building Concepts
Supplement 4: Scale Drawing of a Room
Create a list of large items/furniture in your chosen room. This activity will involve
horizontal scaling to create a room blueprint. Items should be measured by width as well
as length. Dimensions of each item should be labeled on the table below, not on the
actual drawing. Remember to include the actual wall dimensions minus any doors.
ITEM
Example: Dresser
Supplement 4
LENGTH
WIDTH
42 in.
18 in.
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Future City Learning Block
Model Building Concepts
1. Using the graph paper, decide how much area 1 square will represent.
Example: 1 = 6 inches
2. Once the scale has been determined, map the layout of your room on the graph paper.
Make sure dimensions and scale are appropriate.
ROOM SCALE: 1 unit/square = _________ inches
Supplement 4
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Future City Learning Block
Model Building Concepts
Supplement 5: Reflection Worksheet
Utilizing your experiences with ratios/scale and proportions, answer the following prompts
below:
What are some examples of how scale and/or proportions are used in everyday life?
In what careers would the understanding of ratios and scale be the most helpful?
What was the most challenging part of mapping out your room to scale?
In what other ways could you practice understanding scale and proportions?
Why is scale important?
Supplement 5
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