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Learning Targets
Given a scale drawing, I can create another scale drawing that shows the same thing at a different scale.
I can use a scale drawing to find actual areas.
Notes
Notes
Sometimes we have a scale drawing of something, and we want to create another scale drawing of it that uses a different scale. We can use the original scale drawing to find the size of the actual object. Then we can use the size of the actual object to figure out the size of our new scale drawing.
For example, here is a scale drawing of a park where the scale is 1 cm to 90 m.
The rectangle is 10 cm by 4 cm, so the actual dimensions of the park are 900 m by 360 m, because 10⋅90=900 and 4⋅90=360.
Suppose we want to make another scale drawing of the park where the scale is 1 cm to 30 meters. This new scale drawing should be 30 cm by 12 cm, because 900÷30=30 and 360÷30=12.
Another way to find this answer is to think about how the two different scales are related to each other. In the first scale drawing, 1 cm represented 90 m. In the new drawing, we would need 3 cm to represent 90 m. That means each length in the new scale drawing should be 3 times as long as it was in the original drawing. The new scale drawing should be 30 cm by 12 cm, because 3⋅10=30 and 3⋅4=12.
Since the length and width are 3 times as long, the area of the new scale drawing will be 9 times as large as the area of the original scale drawing, because 32 =9.
Activity
Activity
10.2 Same Plot Different Drawings
10.2 Same Plot Different Drawings
Today, you will reproduce a map of the triangular piece of land in Philadelphia (shown left) at TWO different scales.
On CENTIMETER GRAPH PAPER, make a scale drawing of the plot of land. You will pick your scale. Make sure to label your scale on each drawing.
Answer the following questions for each drawing on the front of your graph paper.
What is the area of the triangle you drew? Explain or show your reasoning.
How many square meters are represented by 1 square centimeter in your drawing?
Scale Options:
1 cm to 5 m
1 cm to 10 m
1 cm to 15 m
1 cm to 20 m
1 cm to 30 m
1 cm to 50 m
Answer the following questions for each drawing on the back of your graph paper.
How does a change in the scale influence the size of the drawings?
How do the lengths of the scale drawing where 1 cm represents 5 m compare to the lengths of the drawing where 1 cm represents 15 m?
How do the lengths of the scale drawing where 1 cm represents 5 m compare to the lengths of the drawings where 1 cm represents 50 m?
How does the area of the scale drawing where 1 cm represents 5 m compare to the area of the drawing where 1 cm represents 15 m?
How does the area of the scale drawing where 1 cm represents 5 m compare to the area of the drawing where 1 cm represents 50 m?
Patterns your should have observed:
As the number of meters represented by one centimeter increases, the lengths in the scale drawing decrease.
As the number of meters represented by one centimeter increases, the area of the scale drawing also decreases, but it decreases by the square of the factor for the lengths (because finding the area means multiplying the length and width, both of which decrease by the same factor).
Summary
Summary
Assignment
Assignment
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