Western Connecticut State University
Lesson Plan
Student Teacher: Sean Kerton
Title: Geometry – Performing Dilations
Grade Level: 9 – 10
Date of lesson: April 8, 2014
Length of lesson: 45 minutes
Content Standards:
Common Core State Standards
 8.G.3: Describe the effect of dilations, translations, rotations, and reflections, on twodimensional figures using coordinates.
 G-SRT.1b: Verify experimentally the properties of dilations given by a center and scale factor.
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Common Core Mathematical Practices
 Model with mathematics
 Attend to precision
 Reason abstractly and quantitatively
AHS School-side Expectations
 Apply critical thinking skills to solve problems
 Work independently, reflectively, and/or collaboratively to accomplish goals
Learner Background:
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This unit: Students have defined and experimented with translations and reflections of figures in
the coordinate plane.
Topics directly related to this lesson: plotting points, solving equations, transformation of
geometric figures
General topics that students have learned this year: polygons, similarity, right triangles and
Pythagorean Theorem, properties of quadrilaterals, finding area of triangles, trapezoids,
rhombuses, kites, and circles, volume and surface area of 3d shapes including polyhedrons, sphere,
and cones
Student Learning Objective(s):
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
Students will identify the scale factor of the given dilation and determine if that scale factor will
result in an enlargement or reduction
Students will use maps and known distances to mathematically verify the scale on each map.
Assessment:
Formative Assessment
 Socrative multiple choice checks
o In groups, students will use a smartphone to connect to socrative.com. There, they will be
able to answer a multiple choice question. This data can then be used to view how many
students are on task and understanding the material
 Socrative Exit Ticket
 Guided practice with active monitoring
Summative
 Quiz #1: Translations, vectors, reflections and symmetry (4/9)
 Quiz #2: Rotations and dilations (4/11)
 CFA (4/22 – 4/25)
Materials/Resources:
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Smartboard powerpoint
Socrative exit ticket
Guided practice worksheets
Group assignments
Extra pencils and paper
Learning Activities:
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Prep:
Students will be group in threes ahead of class. These groups will be heterogeneous based on
ability. Desks will also be prearranged.
Remind students of make-up work: Jay, Eric, Tyrell, David
Initiation:
The Hook – Architecture (Whole class 5 minutes) Engage
o “One of my buddies from high school, Steven Kear, is studying to become an architect. He
is currently in a Master’s program at Wentworth Institute of Technology in Boston, MA.
He loves his program and he is very happy he has chosen this particular career. He sent
me a picture of one of his models that we will discuss about in a few minutes.”
o Before huge sky scrapers can be built, architects build scale models of their designs. These
models are much smaller than the actual building. What are some advantages of doing
this? This allows architects and engineers to test for design flaws. It also allows architects
to make presentations and improve their creative process.
o Architects also use computer programs to design models and experiment with new ideas.
Which geometric concepts do you think they need to know to carry out this process?
Coordinate plane, plotting points, properties of similar figures, properties of congruent
figures, geometric transformations (translations, rotations, reflections, dilations).
Lesson Development:
Instruction – Intro to Dilations (Whole Class 15 minutes) Explain
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
What is dilation? Dilation is a stretching or shrinking of a figure. We call a stretch an
enlargement and we call a shrink a reduction.
What is a scale factor? The scale factor is the magnitude of the dilation. In other words, how much
are we changing the preimage of the figure? A scale factor greater than one will result in an
enlargement. A scale factor greater than zero and less than one will result in a reduction.
Enlargement or reduction?
o Use Socrative to do a formative assessment.
o “What is the approximate scale factor for the following dilation?”
o Complete the statement…
Guided practice with active monitoring (Group 15 minutes) Explore
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Students will calculate the image of a point after a dilation of a given scale factor
Ask students to write their work on the board
Use the timer. 7 minutes per page
Application (Group 10 minutes) Explore
 Last problem of the guided practice handout
 Students will verify the scale factor of a map’s scale by measuring a distance and then comparing
that distance to known distances
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Closure:
Have students turn in their packets for participation points
Review the answer to the application question
Today we discussed dilations. This is the third transformation we have covered. We learned that
architects use dilations to construct scale models of their designs. We also learned that a scale
factor of a number greater than one will result in an enlargement and a scale factor of a number
greater than zero and less than one will result in a reduction. Lastly, we tried some dilations of
our own and verified a scale factor on a map.
Individuals Needing Differentiated Instruction:
Which students do you anticipate may struggle with the content/learning objectives of this lesson?
ELLs & Special
Evidence that the student needs
How will you differentiate instruction in this lesson to support student
Needs
differentiated instruction
learning?
Tugce - ELL
Tyrell, Steven
Tugce is from Turkey and
English is not her native
language. She normally
does not have a hard time
understanding English
instruction during class.
These two students are
distracted easily. They also
have difficulty starting
tasks when asked.
Use freetranslation.com to translate guided practice worksheet
and instructional notes into Turkish.
Inquire if she has any questions during guided practice.
Teacher should help these students start assignments and guided
practice. Printing guided notes may also help
Which students will need opportunities for enrichment/higher level of challenge?
TAG
Evidence that the student needs
differentiated instruction
How will you differentiate instruction in this lesson to support student
learning?
Jacob
Jacob consistently scores
well on quizzes and test, he
is always eager to answer
questions during
instruction. He normally
completes his work before
others.
Encourage these students to help their group. Ask these students
to show other students how they arrived at their answer. If he
calls out an answer, ask another student to confirm it.
Name:
Geometry - 9.7 Perform Dilations
Worksheet A
Date:
Calculate and graph the image of the given figure after the given transformation
1. Dilation: Scale factor of 2
Preimage: A(1, 1), B(3,4), C(4,1)
Image: A’(
, ), B’( , ), C’(
,
)
Preimage: A(-6, 6), B(-4, 2), C(-1, 6)
Image: A’(
, ), B’( , ), C’( ,
)
1
2. Dilation: scale factor of 2
1
3. Dilation: scale factor of 3
Preimage: A(3,6), B(6,6), C(3,3), D(6,3)
Image: A’(
, ), B’( , ), C’( ,
), D’(
4. Dilation: scale factor of 3
Preimage: A(-2,1), B(2,0), C(0,-1)
Image: A’(
, ), B’( , ), C’(
,
)
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
,
)
Above is a map of the wind power classifications for Long Island Sound. This data is provided by the
U.S. Department of Energy.
5. Using the ruler provided measure the distance between New Haven and Hartford in inches.
Distance between New Haven and Hartford: ___________ inches
6. Use the scale on the bottom of the map to calculate how many miles is between New Haven and
Hartford. (Hint: set up a ratio)
7. The distance between New Haven and Hartford is approximately 40 miles. Does this provide
evidence that our map is accurate?
8. Is this map an example of an enlargement or reduction dilation? Explain why