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The Scale Factor as a Percent for a Scale Drawing




 

Video solutions to help Grade 7 students understand scale factor to be the constant of proportionality and make scale drawings in which the horizontal and vertical scales are different.


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Common Core For Grade 7

New York State Common Core Math Grade 7, Module 4, Lesson 12


Lesson 12 Student Outcomes


• Given a scale factor as a percent, students make a scale drawing of a picture or geometric figure using that scale, recognizing that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distances in the original picture.
• Students understand scale factor to be the constant of proportionality.
• Students make scale drawings in which the horizontal and vertical scales are different.

Lesson 12 Summary

The scale factor is the number that determines whether the new drawing is an enlargement or a reduction of the original. If the scale factor is greater than then the resulting drawing will be an enlargement of the original drawing. If the scale factor is less than then the resulting drawing will be a reduction of the original drawing.
When a scale factor is mentioned, assume that it refers to both vertical and horizontal factors. It will be noted if the horizontal and vertical factors are intended to be different.
To create a scale drawing with both the same vertical and horizontal factors, determine the horizontal and vertical distances of the original drawing. Using the given scale factor, determine the new corresponding lengths in the scale drawing by writing a numerical equation that requires the scale factor to be multiplied by the original length. Draw new segments based on the calculations from the original segments. If the scale factors are different, determine the new corresponding lengths the same way but use the unique given scale factor for both the horizontal length and vertical length.

Lesson 12 Classwork

Opening
Review the definitions of scale drawing, reduction, enlargement, and scale factor from Module 1, Lessons 16–17.
Compare the corresponding lengths of Figure A to the original octagon in the middle. This is an example of a particular type of scale drawing called a reduction. Explain why it is called that.
Compare the corresponding lengths of Figure B to the original octagon in the middle. This is an example of a particular type of scale drawing called an enlargement. Explain why it is called that.
The scale factor is the quotient of any length in the scale drawing and its corresponding length in the original drawing. Use what you recall from Module 1 to determine the scale factors between the original figure and Figure A and the original figure and Figure B.
Using the diagram, complete the chart to determine the horizontal and vertical scale factors. Write answers as a percent and as a concluding statement using the previously learned reduction and enlargement vocabulary.

Example 1
Create a snowman on the accompanying grid. Use the octagon given as the middle of the snowman with the following conditions:
a. Calculate the width, neck, and height for the figure at the right.
b. To create the head of the snowman, make a scale drawing of the middle of the snowman with a scale factor of 75%. Calculate the new lengths for the width, neck, and height.
c. To create the bottom of the snowman, make a scale drawing of the middle of the snowman with a scale factor of 125%. Calculate the new lengths for the width, neck, and height.
d. Is the head a reduction or enlargement of the middle?
e. Is the bottom a reduction or enlargement of the middle?
f. What is the significance of the scale factor as it relates to 100%? What happens when such scale factors are applied?




Example 2
Create a scale drawing of the arrow below using a scale factor of 150%.
Example 3: Scale Drawings where the Horizontal and Vertical Scale Factors are Different
Sometimes it is helpful to make a scale drawing where the horizontal and vertical scale factors are different, such as when creating diagrams in the field of engineering. Having differing scale factors may distort some drawings. For example, when you are working with a very large horizontal scale, you sometimes must exaggerate the vertical scale in order to make it readable. This can be accomplished by creating a drawing with two scales. Unlike the scale drawings with just one scale factor, these types of scale drawings may look distorted. Next to the drawing below is a scale drawing with a horizontal scale factor of 50% and vertical scale factor of 25% (given in two steps). Explain how each drawing is created.

Exercise 1
Create a scale drawing of the following drawing using a horizontal scale factor of 183 1/3% and a vertical scale factor of 25%.
Exercise 2
Chris is building a rectangular pen for his dog. The dimensions are 12 units long and 5 units wide.
Chris is building a second pen that is 60% the length of the original and 125% the width of the original. Write equations to determine the length and width of the second pen.


 

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