Lesson Title: Scale Drawing
Creator: Mary McClung
Grade Level:
5
Big Idea: Geometry
Essential Question: Why do we need scale drawings?
CSO –
 M.O.5.3.5
draw a similar figure using a scale, given a real world situation
LS –
 21C.O.5-8.2.LS.1 Student engages in a critical thinking process that supports
synthesis and conducts evaluations by applying comprehensive criteria.
 21C.O.5-8.2.LS.2 Student draws conclusions from a variety of data sources to
analyze and interpret systems.
 21C.O.5-8.2.LS.3 Student engages in a problem solving process that divides
complex problems into simple parts in order to devise solutions.
Launch/Introduction:
(suggested time: 15 – 25 minutes)
Activating Prior Knowledge
1. Launch the lesson by reading Cut Down to Size at High Noon, a Math Adventure,
by Scott Sundby aloud to students.
2. As you read the book, display the illustrations of scale drawings used throughout
the story using a document camera.
3. After completing the story, review the scaled-down drawing of the Jersey Cow on
page 7. Ask students the following questions:
 What scale was used? (4 inches = 1 square)
 How long is the tail? (48 inches) How many squares did it take to draw
the tail? (12 squares) How did you find your answer? (48 ÷ 4 = 12) Did
anyone find the answer another way?
 How many squares did it take to draw the face? (5 squares) Why?
(Because the face is 20 inches long.)
4. Repeat the same process with the scaled-up drawing of the grasshopper on
page 27.
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Specialized Vocabulary Development:
Note: Students should begin working on the specific vocabulary necessary for
this lesson two days prior to the lesson.
1. Give students a set of four 3 by 5 inch note cards.
2. Working together as a class, put the vocabulary word on the front of the note
card. Discuss possible meanings of the word. Use a dictionary if necessary.
3. After agreeing upon a definition, write it beneath the word on the front of the note
card.
4. On their own, students are to use the word in context. Have them use the word
in a sentence on the back of the card. (Check to see that all students write an
appropriate sentence in context. Provide help as needed.)
Vocabulary Words
ratio
Definition: A ratio is a comparison of two numbers.
Possible example used in context: Since we have twice as many boys as girls in our
class, the ratio of boys to girls is 2 to 1.
proportion
Definition: A proportion is a statement that two ratios are equal.
Possible example used in context: 1 to 2 and 3 to 6 are equal ratios; therefore, they
form a proportion.
equivalent
Definition: Being the same or equal.
Possible example used in context: The width of our classroom windows are equivalent
to the width of our classroom door.
scale
Definition: The ratio of the size of a model to the actual size of the object.
Possible example used in context: By looking at the scale, we could tell that one inch
was equal to twenty miles on our map.
Investigate/Explore:
(suggested time: varies from 30 – 40 minutes)
1. Explain to students that they are going to make a scale drawing of their
classroom. They will use the scale 2 cm:1 foot (2 cm = 1 foot).
2. Divide students into pairs, and provide each pair with a ruler and sheets of 1 cm
graph paper.
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3. Follow these steps:
 Step 1: Explain to students that in order to complete a scale drawing, we
will be using equal ratios, or a proportion, for the dimensions. The scale
they are to use is 2 cm = 1 foot.
Example 1: if 2 cm = 1 foot, what does 4 cm equal? Answer: 2 feet
2 = 4
1
?
Example 2: if 2 cm = 1 foot, what does 6 cm equal? Answer: 3 feet
2 = 6
1
?
 Have students share strategies for finding the missing numbers. Be sure
everyone is clear on how to do this.

Have students complete the table of equal ratios (located below) to find
the length of the corresponding sides to be used in the scale drawing.
2
1
drawing (cm)
actual (ft)
32 34 36 38 40 42 44 46 48 50 52 54 56 58 60




4
2
6
8
Table of Equal Ratios
10 12 14 16 18 20 22 24 26 28 30
drawing (cm)
actual (ft)
Step 2: Measure the length of each side of your classroom to the nearest
foot. Record the measurements for your scale drawing.
Step 3: Additionally, measure all doors and windows to the nearest foot
and record the measurements. These objects are to be included in your
scale drawing.
Step 4: Construct the scale drawing. Tape together sheets of the
centimeter graph paper as needed.
Step 5: Write the scale on the drawing and label each object, including
doors and windows, in the drawing so that others understand.
4. Walk around and help students as needed. Check students’ work.
Summarize/Debrief the Lesson:
(suggested time varies from 30- 40 minutes)
Summarize the lesson by asking students the following questions verbally:
1. What scale might you have used if you wanted the scale drawing to be larger?
Smaller? (Sample answers: 1 cm = 1 foot; 3 cm = 1 foot)
2. Could you make a scale drawing of your classroom that would fit on one sheet of
centimeter graph paper? Explain. (Yes; by changing the scale, you could make
your drawing fit on one sheet of graph paper.)
3. Return to the essential question: Why do we need scale drawings? Allow
students to respond. A possible answer might be: We need scale drawings
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because some things are too large (or too small) to be drawn to actual size. If
you know the actual length of an object and you know the scale, you can
make a scale model.
4. What are some examples of scale drawings that we often use in everyday life?
(Maps, blueprints, model airplanes, model trains, cars, etc.) Is accuracy
important? Why or why not?
Writing in Math
Have students answer this question in writing in their own words:
1. Suppose you want to use the scale 3 cm =1 foot to make a drawing of your room.
How could you use a table of equal ratios to decide what length and width the
drawing should be?
Answers may be similar to this: Make a table using the scale 3 cm = 1 ft. Continue
the table until you have included the actual length and width of your room. Then the
number of centimeters that corresponds with the actual length and width is the
length and width that the drawing should be.
Materials:
A copy of the book, Cut Down to Size at High Noon, a Math Adventure, by Scott
Sundby.
Document Camera
LCD Projector
1 cm graph paper, tape
Rulers
Duration: 90 minutes
Teacher Discussion:
Students often have difficulty determining the actual measurement when given the
distance on the scale drawing or vice versa. Encourage them to write the scale as a
ratio, and then write the known and missing information in a ratio, for example:
1 inch and 4 inches
3 feet
? feet
Scale drawing units offer a good opportunity for cooperative learning.
Note: *This lesson has been adapted from Pearson/Scott Foresman Mathematics.
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