Polygons and Algebraic Relationships

Lesson 12

Math

Unit 5

10th Grade

Lesson 12 of 15

Objective


Describe how the area changes when a figure is scaled.

Common Core Standards


Core Standards

  • G.GPE.B.7 — Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.EE.A.2
  • 7.G.B.6

Criteria for Success


  1. Scale dimensions of polygons and determine area off the coordinate plane.
  2. Compare the area of the original figure and the area of the scaled figure. Establish generalizations comparing the scale factor of the dimension to the scale factor of the area. 
  3. Describe why the repeated reasoning established through numerical practice of squaring the scale factor to find the scale for the area makes sense for any general polygon. 
  4. Identify scale factors from the relationship between the side lengths and/or area.

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Anchor Problems

25-30 minutes


Problem 1

a.  Triangle $${ABC}$$ is dilated by a factor of $$3$$ about point $$A$$. How does the area of triangle $${ABC}$$ compare to the area of triangle $$A'B'C'$$?

b.  The parallelogram shown below is dilated by a factor of $${{1\over2}}$$. How do the areas of the original and the scaled parallelograms compare?

 

Guiding Questions

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References

EngageNY Mathematics Geometry > Module 3 > Topic A > Lesson 3Exploratory Challenge

Geometry > Module 3 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

The dimensions of rectangle $$A$$ are $$3$$ units and $$4$$  units, and the area of rectangle $$B$$ is $${75\space \mathrm{units}^2}$$. What are the dimensions of rectangle $$B$$?

Guiding Questions

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Target Task

5-10 minutes


In the following figure, $${\overline{AE}}$$ and $${\overline{BD}}$$ are segments. 

a) Show that $${{{{\triangle ABC}}}}$$ and $${{{{\triangle CDE}}}}$$ are similar. 
b) What is the scale factor of similarity transformation that takes $${{{{\triangle ABC}}}}$$ to $${{{{\triangle CDE}}}}$$?
c) What is the value of the ratio of the area of $${{{{\triangle ABC}}}}$$ to the area of $${{{{\triangle CDE}}}}$$? Explain how you know.
d) If the area of $${{{{\triangle ABC}}}}$$ is $${30\space \mathrm{cm^2}}$$, what is the area of $${{{{\triangle CDE}}}}$$?

References

EngageNY Mathematics Geometry > Module 3 > Topic A > Lesson 3Exit Ticket

Geometry > Module 3 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include probelms with polygons on the coordinate plane.

Next

Solve area applications by creating and solving quadratic equations.

Lesson 13
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Distance on the Coordinate Plane

Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments

Topic C: Area and Perimeter On and Off the Coordinate Plane

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