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What is Geometry?
Mathematical Goals: Teachers will be able to
 Consider what geometry is and create a concept map of important geometric concepts to
consider.
 Construct geometric objects using a straightedge and compass.
Pedagogical Goals: Teachers will be able to
 Consider what topics are important for learning geometry at the high school level.
 Discuss issues students might have when constructing geometric objects with a
straightedge and compass.
Mathematical Practices:
 Construct viable arguments and critique the reasoning of others.
 Use appropriate tools strategically.
 Look for and make use of structure.
 Attend to precision.
Length of session: 90 minutes
Materials needed: Paper, markers, rulers, compasses, large paper, Pre-survey, What is
Geometry? Participant Handout
Overview:
This session will allow everyone the opportunity to get acquainted and start thinking about what they consider
geometry. Geometric constructions will also be considered.
Estimated #
of Minutes
15 minutes
Activity
Preparation
 Participants make name tents for tables.
 Assure participants are sitting in small groups.
 This will be the common set up for the week! Teachers should be
encouraged to work together for every task (unless otherwise specified). If
at all possible, teaching this institute in a computer lab or having a
computer cart would be helpful.
Getting to know you
 Who Is It? Game: Have everyone in the room write down 4 things about
themselves that no one else in the room should know. Have them put their
name on the top of the card for future reference. Collect the cards. Then as
the cards are read one at a time, have everyone write down who they think
the person on the card is. Then read off the correct results (the names from
the top of the cards) while the individuals check their lists. The person who
gets the most right is the winner.
 After the game, allow everyone around the room to provide a brief
introduction about his/herself. Maybe they can share where they are from,
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
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15 minutes
20 minutes
where they are teaching, how long they’ve been teaching, etc.
Goals for the week
 Our goal for the week is to expose you to a variety of geometric concepts
and get you thinking about how you can make geometry more engaging for
your students. Throughout the week, we will work on quite a few
problems, both with and without the use of technology.
 Explain that during the institute we will be using some materials from the
Preparing Teachers to Teach Mathematics with Technology project. Then
go over the informed consent form and ask them if they would like to
participate in our research.
 Pre-survey
What is Geometry?
 Most of you have had experience learning geometry and may have
experience teaching geometry. But what exactly is geometry?
 Questions to consider:
1. When you hear the word geometry what do you think of? Create a list
of different terms and arrange them into a concept map. Answers will
vary.
2. How would you define geometry? Answers will vary.
3. What are some important ideas for students to study when they are
learning geometry in high school? Explain why you believe those
ideas are important. Ideas for important geometry topics may
include: properties of and theorems related to triangles,
quadrilaterals and circles. Coordinate geometry, transformations,
congruence, similarity, proof, trigonometry, visualization, and
measurement. We can consider these topics in terms of objects and
processes. While particular geometrical shapes like triangles and
quadrilaterals are objects, conjecturing, reasoning, and proof are
important processes to engage students in while they are learning
geometry.
 Pause for a discussion here before moving on!
40 minutes
4. Examine the high school Geometry Common Core State Standards.
How do these compare with your concept map and ideas about what
students should study when they are learning geometry in high
school? Is there anything that surprises you? Answers will vary.
Compass and Straightedge Constructions
 Constructions: The drawing of various shapes using only a pair of
compasses and straightedge or ruler. No measurement of lengths or angles
is allowed!
 Given a compass and straightedge, complete the following constructions:
o Copy a line segment
o A perpendicular bisector
o Copy an angle
o Bisect an angle
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
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

o A square
Some participants may struggle with this if they are unfamiliar with
constructions. The facilitator may need to provide hints or help.
Questions to consider:
1. Explain how one of the constructions above works. (You cannot
choose copying a line segment!) In other words, what is (are) the
underlying geometric concept(s) that enable the construction to work?
Perpendicular bisector works because you are essentially creating
two congruent isosceles triangles by SSS.
Copying an angle works because you are creating congruent
triangles by SSS.
Bisecting an angle works because again you create two congruent
triangles by SSS.
Constructing a square works because you first construct a right angle
(this works because you generate two congruent triangles by SSS)
and then the remaining sides are drawn using the same compass
width.
2. Why is it important to teach geometric constructions? Constructions
have a close connection with axiomatic logic. In other words, the
skills you need to figure out a construction are closely related to the
skills you might use to prove theorems related to the object you’re
constructing.
3. How do you teach your students constructions? Answers will vary.
4. What are some common problems students have with constructions?
Answers will vary.
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
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Preparing to Teach Mathematics with Technology: The MELT professional
development project
Pre-Survey
1. Please generate a 5-character ID number. Your ID number is the first three
letters of your mother's maiden name (if unsure use ABC) followed by the
day of the month of your birthday (Ex: if your mother's maiden name is
SMITH and your birthday is on the 3rd of a month your ID would be
SMI03).
___________________________________________________________
2. Please select all items that pertain to your teacher preparation
experiences/background.
Bachelor’s degree in Mathematics
Bachelor’s degree in Mathematics Education
Bachelor’s degree in another area (please specify):
____________________________________ with lateral entry
licensure
Master’s degree in Mathematics
Master’s degree in Mathematics Education
Master’s degree in another area (please specify):
____________________________________
National Board Certified Teacher
Other degrees/certificates (please specify):
____________________________________
3. How many years have you been a mathematics teacher?
0
1-2
3-5
6-10
11-15
16 or more
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
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4. What grade level(s) or course(s) do you teach?
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7
8
Math I
Math II
Math III
CC Algebra I
CC Geometry
CC Algebra II
Other (please specify): ____________________________________
5. What technology tools do you have available at your school?
6. What technology tools have you used in your mathematics teaching?
7. Please identify how you learned to use the technologies that you use. Select all
that are applicable.
Taking courses in my graduate program
Attending workshops at my school
Attending workshops sponsored by others
Attending regional/state/national conferences
Taking online courses
Exploring new technology on my own
Get help from others
Using online resources (YouTube, Google, software websites)
Other (please specify): ____________________________
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
6
8. Please indicate if you are comfortable using the technologies below using a scale
of 0 – 5 with 0 being not comfortable at all and 5 being extremely comfortable.
__________ Dynamic Geometry software (ex. Sketchpad, Cabri, Geogebra)
__________ Dynamic Statistics software (ex. TinkerPlots, Fathom)
__________ Non-graphing calculators (ex. four-function, fraction, scientific)
__________ Graphing calculators (ex. TI 83, TI 84)
__________ CAS (Computer Algebra Systems)
__________ Data Collectors (ex. CBL, CBR, MBL, GoMotion, Vernier Sensors)
__________ Spreadsheets
__________ Internet-based mathematical applets
__________ Mathematical applications for mobile devices (ex. apps on smart
__________ phones or tablets)
__________ Collaborative virtual bulletin boards (ex. Padlet, Corkboard.me)
__________ Collaborative online whiteboards (ex. Scribblar, Scriblink,
__________ Dabbleboard)
__________ Google Docs (ex. Forms, Spreadsheets, Documents)
__________ Wikis
__________ Social Media (ex. Twitter, Facebook, Vine, Edmodo)
__________ Video chatting software (ex. Skype, Google Hangout)
__________ Blogs
__________ Software for designing web sites (ex. Dreamweaver, WordPress)
__________ Software for creating movies, including screencasts and animations
__________ Multi-media software (ex. PowerPoint, Prezi, iBooks Author)
__________ Networked calculators (ex. TI-Navigator) or classroom
management system for networked computers
__________ Interactive White Boards (ex. SMARTboards, Promethean Board)
__________ Clickers or interactive personal response system
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html
7
What is Geometry?
Participant Handout
What is geometry?
Questions to consider:
1. When you hear the word geometry what do you think of? Create a list of different terms
and arrange them into a concept map.
2. How would you define geometry?
3. What are some important ideas for students to study when they are learning geometry in
high school? Explain why you believe those ideas are important.
Pause for a discussion here before moving on!
4. Examine the high school Geometry Common Core State Standards. How do these
compare with your concept map and ideas about what students should study when they
are learning geometry in high school? Is there anything that surprises you?
Compass and Straightedge Constructions
Constructions: The drawing of various shapes using only a pair of compasses and straightedge or
ruler. No measurement of lengths or angles is allowed! Note: Historically, a straightedge did not
have any markings!
Given a compass and straightedge, complete the following constructions:
o Copy a line segment
o A perpendicular bisector
o Copy an angle
o Bisect an angle
o A square
Questions to consider:
1. Explain how one of the constructions above works. (You cannot choose copying a line
segment!) In other words, what is (are) the underlying geometric concept(s) that enable
the construction to work?
2. Why is it important to teach geometric constructions?
3. How do you teach your students constructions?
4. What are some common problems students have with constructions?
Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Introduction to dynamic geometry environments. In Preparing to teach mathematics
with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.
For constructions used: http://www.mathopenref.com/constructions.html