Lesson Title: Verifying Dilation
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 1
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.SRT.1.b Verify experimentally the properties of dilations given by a center and a scale factor. The dilation of a
line segment is longer or shorter in the ratio given by the scale factor.
MP2: Reason abstractly and quantitatively.
MP5: Use appropriate tools strategically.
MP6: Attend to precision.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Have students work in small groups to discuss what
they know about dilations. Have them formulate a
working definition of dilation. Finally have the groups
create a list of where they can find dilations in the realworld.
Conduct a brief class discussion on the concept of
dilation, its use, and properties.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
3-2-1
List 3 criteria that you could use to show that an image is
a dilation of a pre-image?
List 2 Standards for Mathematics Practice that you used
during today’s lesson. How did using these practices
support learning the criteria for determining when an
image is dilation?
List 1 Working definition of dilation or your
understanding of the concept of dilation.
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students are working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
Divide the class into pairs. Pairs will work together to verify the properties of dilation. Have the pairs follow the
steps below for the verification.
Using dot paper or graph paper, rulers and protractors, Geoboards, or dynamic geometry software program:
(Look for evidence of MP5)
1. Draw a line segment.
2. Select a point not on the line for the center of dilation.
3. Extend a ray from the center of dilation through each endpoint of the segment.
4. Choose a scale factor that will double the size of the segment (k = 2).
5. Determine the lengths of the segments from the center to each endpoint along each ray.
6. Multiply the lengths by the scale factor to determine the dilated distance.
7. Measure the dilated distance along the appropriate ray from the center to the new endpoint.
8. Connect the dilated endpoints.
9. Determine the length of the original and dilated segments.
(Look for evidence of MP6)
10. Measure the corresponding angles formed by the intersection of the ray, original segment, and dilated
segment.
11. Verify the following properties associated with similar figures:
a. The dilated distance is twice as large as the original distance.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Verifying Dilation
Course: Common Core Geometry, Unit 1
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
b. Corresponding angles are congruent.
c. The distance along the ray from the center to the dilated endpoint is twice as large as the distance
from the center to the original endpoint.
12. Without creating a dilation describe the how the properties of dilation would effect a size change with a
scale factor less than 1 (k = 0.75).
(Look for evidence of MP2)
The screen capture below illustrates the process of verifying the properties of dilation.
Discuss with the class the results of their investigations.
1. How would the properties of dilation be affected with a size change with a scale factor less than 1 (k =
0.75)?
2. The properties of dilation have been verified for a segment. Can the properties also be verified when
dilating a figure like a triangle or a parallelogram?
3. How is dilation a transformation?
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student success? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened and conceptual understanding.
Students will be able to accurately identify and verify images that are the product of dilation. This understanding
will be used to examine similarity and transformation in greater depth.
Student success will be measured by the teacher circulating between the student groups to determine the level of
understanding. Groups that have created representations that preserve angle measure and double all lengths
demonstrate mastery of the standard.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Verifying Dilation
Course: Common Core Geometry, Unit 1
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Transformation
Similarity
Dilation
Transformations are change in the location and/or size of a figure. Transformations must create a similar figure to
the figure that was transformed. Transformations that only change the location of a figure and create congruent
figures include reflections, rotations, translations, and glides. A dilation is an example of a transformation that
creates a similar figure that is a different size and in a different location.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Dot or graph paper
Rulers, compasses, and protractors
Geoboards
Dynamic Geometry Software (such as Geometer’s
Sketchpad or GeoGebra)
Homework should involve problems that require students
to perform the dilation on an image and verify they have
dilation according to the properties. Problems should also
focus on verifying dilation of images in real-world
situations such as a photo enlargement/reduction, sets of
blue prints, and scale models.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Do my students know the properties of dilation? Can my students verify that an image is a dilation? Can my
students apply the properties of dilation in a variety of real world situations?
Looking forward to the next day’s lesson, will my students be able to use the properties of dilation in the context of
similarity and similarity transformations?
Did my students demonstrate an understanding of the 3 SFMPs that I tried to elicit in the lesson? To what extent did
they demonstrate proficiency in using and applying the 3 SFMPs elicited in the lesson?
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.