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Molly Saltino
Edu 327: Teaching to the Standards
May 13, 2010
Final Learning Experience: Geometry Vocabulary
May 13, 2010
1
Table of Contents
1. Learning Context-page 3
2. Assessment Plan-page 6
3. Student Work-page 9
4. Procedure-page 20
5. Resources-page 22
6. Modification Table-page 23
7. Time Required-page 24
8. Reflection-page 24
9. Extra Attachments-page 26
May 13, 2010
2
Geometry Vocabulary
Learning Context
Purpose/Rationale for Learning Experience:
The purpose of this lesson is for the students to be able to understand geometry vocabulary and know
how to use each term properly when it comes to actual geometry problems. Using index cards for
students to write the definition as well as the illustration will help them see visually what each term is as
well as hear it when they are studying the cards. They will hopefully soon memorize and know the terms
to the point of where they won’t need to refer to their index cards anymore.
Enduring Understandings:
Students should be able to define any geometry word as well as know which each term looks
like in an illustration. The student should be able to apply these vocabulary problems to actual
geometry problems where they will need to solve for variables. If students do not understand
the vocabulary words they will struggle in the geometry unit. They will show their
understanding through quizzes, tests, graded homework, and studying their index cards with
their parents.
Essential Questions:


What words come to mind when you think of geometry?
What are important geometry concepts?
Guided Questions:
o
o
o
o
o
o
o
o
May 13, 2010
What is a transversal?
What are adjacent angles?
What are vertical angles?
What are obtuse angles?
How could you illustrate adjacent angles?
When are angles supplementary?
When are angles complementary?
When do you set an equation equal to 180?
3
New York State Standards:




Learning standard: Mathematics
Grade level: 8 intermediate.
Key Idea: Modeling/Multiple Representation
Content standard: Standard #3, Students will understand mathematics and become
mathematically confident by communicating and reasoning mathematically, by applying
mathematics in real-world settings, and by solving problems through the integrated
study of number systems, geometry, algebra, data analysis, probability, and
trigonometry.
 Performance indicators: Students use mathematical modeling/multiple representation
to provide a means of presenting, interpreting, communicating, and connecting
mathematical information and relationships.
Congruency Table:
Performance
Indicators/Core
Guide
Information
Instructional
Task (What the
standards mean
in your own
words)
Learning
Objectives
Student Work
Assessment Tool
8.CM.4
Share organized
mathematical
ideas through the
manipulation of
objects, numerical
tables, drawings,
pictures, charts,
graphs, tables,
diagrams, models,
and symbols in
written and verbal
form
8.CM.5
Answer clarifying
questions from
others
8.CM.9
Increase their use
of mathematical
vocabulary and
language when
communicating
with others
The student will
provide index
cards with
vocabulary words
and definitions as
well as diagrams
and models.
The student works
with a parent to
verbally express
what the
vocabulary means
in words.
The student will
answer what each
vocabulary word
means.
This will increase
the student’s
knowledge of
vocabulary and
they will have to
use it when
communicating to
others.
Construct two sets
of geometry index
cards. One set
consists of the
vocabulary words
and definitions.
The second set
consists of the
vocabulary words
and diagrams. The
student must
show their
understanding by
being quizzed
through the index
cards with their
parents as well as
in class.
The two sets of
index cards of 15
words.
A 20 point rubric
will be use to
assess the quality
of the index cards
as well as the
student studying
with their parents
to show their
understanding.
The parent will
sign a piece of
paper saying they
studied and then
explain how well
the student
worked.
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4
Overview of what students need to know/ be able to do in order to succeed:
Prior to Learning Experience:
Prior to this learning experience, the 8th grade students learned how to set up equalities and
inequalities. They learned how to solve equations as well as learning how to check their answers to see
if they are correct. In the geometry unit the students will have to set up equations and solve for
variables, which they previously have learned. They have also learned basic geometry such as shapes
and certain formulas before they came to 8th grade.
During the Implementation of the Learning Experience:
During the implementation of this learning experience students should start to learn their geometry
vocabulary, which is extremely important to be successful in this unit. They will be able to apply the
vocabulary to solve problems on complementary angles, supplementary angles, vertical angles, etc.
These problems involve setting up equalities and their own problems to find values of angles.
After the Implementation of the Learning Experience:
After the learning experience, the students should know all of their vocabulary. The students should be
able to apply this vocabulary too all of the different word problems and general problems that are done
in geometry. The students should be able to identify relationships between angles and be able to explain
those relationships.
Key Subject-Specific Vocabulary:














Acute angle-an angle that measures less than 90
Obtuse angle-an angle that measure greater than 90, but less than 180
Complementary angle-two angles whose measure have a sum of 90
Right angle-an angle that measures 90
Supplementary angle-two angles whose measures have a sum of 180
Straight angle-an angle that measures 180
Alternate interior angles-two angles inside the parallel lines that are on opposite sides
of the transversal
Vertical angles- two nonadjacent angles formed when two lines intersect. The angles in
a vertical angle pair are congruent.
Line-a straight path that continues infinitely in both directions
Line segment-a line with definite endpoints
Ray-a part of a line starting at a particular point and extending infinitely in one direction
Parallel lines-lines in the same plane that do not intersect
Perpendicular lines-lines that intersect to form a 90 angle
Transversal-is a line that intersects two or more other lines at different points
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5






Corresponding angle-a pair of angles that have the same relative position at each
intersection where the transversal crosses the other two
Adjacent angles-angles that have a common side but no interior points in common
Alternate exterior angles-two angles outside of the parallel lines that are on opposite
sides of the transversal
Congruent angle- an angle that has the same measure as another angle
Intersecting lines-lines that cross at one point
Vertex-is the common endpoint of the rays forming the angle
Assessment Plan
Pre-Assessment
This learning experience will take place towards the end of the unit, before a couple of quizzes
and the final test. The students did homework the day previous to receiving the flashcard
assignment. This was their pre-assessment, so the teacher can see the level at which they are at
when it comes to geometry. The students must understand previous information in order to do
geometry. It is extremely important to test their previous knowledge.
Formative-Assessment
Students are formally assessed through observation, student participation, and homework
assignments. Homework is usually collected and graded. If it is not collected it still gets a 5, 2, or
0. A grade of 5 is if the student fully attempted and completed the homework, a 2 if they only
did half of it and a 0 if they didn’t do it at all. We always go over every homework and I asked
questions to check for understanding as well.
Summative Assessment
Many different topics are assessed on the two quizzes at the end of the unit that were
used as the summative assessment. All of the quizzes consist of most vocabulary words as well
as the process of setting up equations. They will have to explain and identify what type of
relationships and terms they must use for each problem. Most of the quizzes were based on
NYS math grading for the final state assessment. We want the students to get used to the
grading style of the state, so we usually used the 2, 3, 4 point rubric. Certain questions we made
5 points because they were so much work.
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Scoring Rubric related to other semester grades
The scoring rubric is similar to other semester grades because most grades in the 8 th grade class
are usually worth 40-55 points. I had a rubric for the flashcards that was worth 20 points and
doubled it, so it was equivalent to most grades in the class. This way a student is willing to do all
work instead of the piece of work that is worth the most points. The work in this class is mainly
equivalent in points so they are more willing to do all of it. I also used a 4 point rubric because
in a math exam most of the problems are based on a 4 point rubric, which is based on NYS
standards. Each section is worth 4 points. The students role in the assessment process is that
they will learn how they are graded. They will be able to clearly see where they need work.
They can argue for a better grade if necessary. It is nice for them to see where their points are
coming from.
May 13, 2010
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Math - Problem Solving : Geometry Flashcards
Teacher Name: Ms. Saltino
Student Name:
CATEGORY
Mathematical
Terminology and
Notation
Diagrams and
Sketches
Neatness and
Organization
Working with
Others
Completion
________________________________________
4
Correct
terminology and
notation are
always used,
making it easy to
understand what
was done.
Diagrams and/or
sketches are clear
and greatly add to
the reader's
understanding of
the procedure(s).
The work is
presented in a
neat, clear,
organized fashion
that is easy to
read.
Student was
engaged, listening
to suggestions of
and working
cooperatively with
parent.
All problems are
completed.
3
Correct
terminology and
notation are
usually used,
making it fairly
easy to understand
what was done.
Diagrams and/or
sketches are clear
and easy to
understand.
2
Correct
terminology and
notation are used,
but it is sometimes
not easy to
understand what
was done.
Diagrams and/or
sketches are
somewhat difficult
to understand.
1
There is little use,
or a lot of
inappropriate use,
of terminology and
notation.
The work is
presented in a neat
and organized
fashion that is
usually easy to
read.
Student was
engaged but had
trouble working
cooperatively.
The work is
presented in an
organized fashion
but may be hard to
read at times.
Student
cooperated, but
needed prompting
to stay on-task.
The work appears
sloppy and
unorganized. It is
hard to know what
information goes
together.
Student did not
work effectively
during quizzing of
the flashcards.
All but three of the
vocabulary words
are completed.
All but seven of the
vocabulary words
are completed.
Several of the
vocabulary words
are not completed.
Diagrams and/or
sketches are
difficult to
understand or are
not used.
Date Created: Feb 22, 2010 02:24 am (UTC)
Comments and Suggestions:
May 13, 2010
8
Student Work
The three students work in this learning experience are 8th grade students. Each of these
students had about the same ability to learn and do well in class.
Pre-Assessment
Class scores on a homework assignment before the flashcard assignment (91 students)
This was out of 28 points
This was based on only a couple of vocabulary words and previous knowledge in order for the
students to complete this worksheet.
Scores out of 28 points in percentage form
0-20%
21-40%
41-60%
61-80%
81-100%
Numbers of students that got that score
8
20
7
45
11
50
40
0-20%
30
21-40%
20
41-60%
10
61-80%
0
Number of
Students that got
that score
81-100%
Post-Assessment
I gave two quizzes as post assessments both out of 36 points.
These two quizzes were after all the definitions and vocabulary words were given and plenty of
worksheets and reviews were done as well as the flashcards.
Quiz 1
Scores out of 36 points in percentage form
Numbers of students that got that score
0-20%
2
21-40%
0
41-60%
5
61-80%
62
81-100%
22
May 13, 2010
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70
60
50
0-20%
40
21-40%
30
41-60%
20
61-80%
10
81=100%
0
Studnets that got that score
Quiz 2
Scores out of 36 points in percentage form
Numbers of students that got that score
0-20%
1
21-40%
0
41-60%
4
61-80%
33
81-100%
43
50
40
0-20%
30
21-40%
41-60%
20
61-80%
10
81-100%
0
Students that got that score
Distinguished Work
I have an example of distinguished work of four vocabulary words from the flashcard project.
Most of the students that had distinguished work, you could tell really took their time and
concentrated. They were clear with their writing as well as with their illustrations. They used
rulers and colored pencils.
Proficient Work
I have an example of proficient work. They were neat, but made a couple of mistakes with their
spelling or not being specific in their illustrations. You could still tell that they understood their
definitions and what they were doing.
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10
Developing Work
I also have an example of the developing work. You could tell rushed through their work. This
affected their post assessment as well as their grade for this assignment. They made mistakes,
weren’t specific, and did not use rulers and were unclear with their writing.
Class Work as a Whole
The class for the most part all did pretty well. I had a lot of distinguished work. There were only
about 4 students to fail this project. The students got really into this assignment and were
excited. They took it very seriously and tried their best to make the flashcards perfect. My main
focus for the learning experience was the grading of the flashcards. I included the preassessment and post-assessments to help you better understand the order of my class work
and how it all flowed together.
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Teach Exemplar
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Distinguished Work
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Distinguished
Work
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Proficient Work
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Proficient Work
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Developing Work
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Developing Work
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Procedure
Task One: Anticipatory Set
1. Students will come into class and take out their homework
2. We will go over the homework together and grade it together as well. (pre-assessment)
3. In pairs students will come up to the elmo and explain one of the problems that was
done for homework
4. Through explaining the problem that the students are presenting, the teacher can check
for understanding
5. Engage the students in a discussion on some of the terms that are used in the
homework for example, congruent angles.
Task Two: Modeling
6. I will model the geometry flashcards by using my teacher exemplars to show the
students was it expected of them.
7. I will put the flashcard on the elmo(technology) so students can see it on the overhead.
8. I will explain to them how they need to use colors and rulers for their diagrams, clear
and neat definitions.
Task Three: Guided Practice
9. The students were supposed to bring in index cards a week ahead of time.
10. I will pass out the index cards
11. I will do one of the pairs of index cards together with the student
12. I will have the students write the word vertical angles on two of the index cards
13. I will guide them on how to write the definition
14. On the second vertical angle index card I will show them how to draw vertical angles
using the ruler. The students all must use two colors to represent the two sets of vertical
angles.
15. Give students feedback on what they are doing correct and what needs to be fixed. Be
positive while giving the student feedback.
Task Four: Independent Practice
16. The students will then get the rest of the class time to work on the rest of the
flashcards.
17. The teacher will walk around to check for students understanding.
18. The teacher will help any students that need help.
Task Five: Closure
19. Students will summarize the lesson by answering the following questions:
a. How will the flashcards help you to study?
b. What terms do you now understand that you didn’t understand before?
May 13, 2010
20
c. Depending on the word the student chooses, ask them about that term and
what it looks like and what the term actually means.
20. Have students pass up all colored pencils and rulers to the front of the class and let
them know that they have a week to finish the assignment.
Classroom Procedures
1. Upon entering the classroom, take out your homework from the previous
night and work on the problem of the day to prepare yourself and get yourself
thinking about you will be learning for the day.
2. Ask to get up or leave the classroom for any reason, take the hallway pass.
3. If you missed a day of class, make sure to come to see me to make up any
missed work.
Classroom Rules
1. Come to class prepared with proper materials
2. Raise your hand and wait to be called on in order to speak
3. One person talks at a time
May 13, 2010
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4. Use school appropriate language
Resources
There are good sources for geometry angles. These sources helped me research information on
geometry as well as be more creative with me lessons during the geometry unit.
 This brainpop website below explains angles and the parts of angles
http://www.brainpop.com/math/geometryandmeasurement/angles/


There is an Angelside School Adventure game
The Prentice Hall Brief Review for New York Grade 8 Book

Also in the Appendices there are:
 Pairs of Angles Homework
 Geometry Quiz #1
Complementary and Supplementary Quiz
Classroom Supplies:

May 13, 2010
 Index Cards
Colored pencils/markers
 Ruler
22
Modification Table
th
8 Grade Modifications in Geometry
The students were note classified as having any disabilities, but some of the students still struggled.
I felt that these modifications would best help students with their weaknesses and struggles.
Assigned seats allow them to become less distracted. Another main concern was the amount of
time given to the students and the neatness of their cards. I felt that providing them with type
words and giving them more time if they needed it was necessary because the importance of these
flashcards was for the students to learn. The students were using these to study and understand
the geometry unit.
Modification Type:
Specific Modification
Rational
Benefits
Environmental/Management
Assigned Seats
Students are placed
There will be less
close to the teacher distractions for all of
the students and it
will be easier for the
teacher to control
the classroom
Instructional
Students will study
Students will have
Through repetition
their flashcards in
repetition to visually
students are more
class and at home
see the terms and
likely to remember
with parents
verbally hear the
all of the terms and
terms
understand the
terms better
Material
Words and
It will be neat and
The student will not
definitions typed up easier to read and it
be deducted for
will help students
neatness if they use
who struggle with
the typed terms and
writing
definitions.
It will also be easier
for the student to
read their index
cards
Tasks
Time
More time if
Even though no
necessary
students were
identified, some
students who
struggle do need the
extra time to finish
their flashcards
They won’t be as
stressed and
overwhelmed.
May 13, 2010
23
Time Required
Preparation
The planning of this lesson took approximately 2 and a half hours. The first part of the planning
was involved in making the worksheets and the teacher exemplar. I wanted the students to be
engaged and for that to work it took time to have extra index cards ready, colored pencils,
rulers, and any other needed material. The last part was pulling all of the worksheets and
materials together, laying it out to make sure the lesson flowed together in a good and
understanding way.
Implementation
The implementation of this lesson takes one class period. This class period is 45 minutes long.
Any unfinished work on the flashcards needed to be finished within a week, unless otherwise
advised differently.
Assessment
Scoring of the flashcards will take approximately 1-2 hours because you have to go through
every single set of index cards for each student. You must check for neatness and read every
single definition.
Schedule
This lesson is taught towards the end of the geometry unit to check for students understanding
and help them study for the test as well as the final state assessment.
Reflection
I developed this learning experience because I felt that it was something any teacher
could use. This can be used for any subject area and in any grade levels. This activity gets the
students involved. It also keeps the parents involved so they know what is going on in their
classroom. One student said: “I am really starting to understand this, the index cards really
help.”
I also felt that I did meet my teaching objectives. The students should have been able to
use geometry terms towards word problems and equality problems and I felt that through my
post-assessments they were able to do so. The students also should have been able to identify
terms within larger pictures of angles through the study of the flashcards and after the
flashcards they did understand larger pictures of angles better.
The students also met the performance indicators. One performance indicator was where
the students needed to share organized mathematical ideas through the manipulation of drawings,
pictures, and diagrams visually and verbally. They succeeded in this performance indicator by making
the flashcards and studying the flashcards with a parent or partner. Another performance indicator was
for the student to increase their use of mathematical vocabulary and language when communicating
May 13, 2010
24
with others. This was also done through the students studying the flashcards as well as explaining their
answers in post assessments.
It prepares students for life outside of school because they need to be organized and neat. They
also need to finish projects on time. In real life they will be told to do things by their bosses that need to
be done in a considerable time period.
The peer review was also extremely helpful. My peer review was on March 25th at
Daemen College, room 336 in Duns Scotus. The main questions that were focused on during my
peer review was how I would be able to teach this to students with learning disabilities. They
also asked if I could maybe point out things in the classroom that involved angles. Lastly,
another question was on my technology and if I could have used more technology. One person
from my peer review group said: “the lesson used many different learning styles and that is
something that can be great for students that learn through different styles.”
Through the advice of my peers I modified my learning experience by adding more
technology. I added a brainpop video as well as allowing students to go online to work on
practice problems. I included the New York State Standards, which I originally forgot to include.
I also felt that I added more modifications to my lesson that would cater to students with
disabilities.
Criteria
Relation to Learning Standards
Intellectual Challenge
Assessment Plan
Engagement
Adaptability
Technology
May 13, 2010
Warm Comments
 N/A

Great lesson for students
to learn the vocabulary
dealing with geometry
 (Pre & Post Assessment)
Saw the learning that
took place throughout
the lesson.
 Involved the parents
with the flashcards
 Motivation with the
extra credit points
 Having the students
create their own angles
and pictures was a great
idea to get them
involved
 Used many learning
styles that were great for
the students
 N/A
Cool Comments
NYS Standards were not
given
 How can you teach this
students with a learning
disability?
 N/A


Vocabulary pair up with
the students and get
them engages and
maybe find things in the
room with the angles
that you are discussing

N/A
 No technology integration
 Have the students use a
camera and take pictures
of angles in objects that
have learned about in
class
25
Name___________________
Date_____________
Homework #____
Pairs of Angles
Directions: Solve every problem and explain your answer.
1. x and y are congruent angles. If x is 26 what is the measure of y?
y = ______
x
Explanation: ____________________________
y
_____________________________________.
2. Find the measures of x and y.
45
x
y
x =________
Explanation:________________________________________________
y =________
Explanation:________________________________________________
May 13, 2010
26
3. Find the measure of x.
21
x
x =_______
Explanation:________________________________________________
4. Find the measure of x.
x
47
x =_______
Explanation:________________________________________________
5. Find the measures of x and y.
x
32
May 13, 2010
y
27
x =________
Explanation:________________________________________________
y =________
Explanation:________________________________________________
May 13, 2010
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Name_____________________
Date __________________
Group # ____
Geometry Quiz #1
1. In the diagram below, which pair of angles are supplementary?
1
3
4
A. 1 and 3
B. 1 and 2
C. 2 and 4
D. 3 and 1
2
2. Name the highlighted angle.
A
D
C
B
3. Draw an acute angle and explain why the angle is acute.
Explanation: ____________________________________________________
4. In the diagram below, which pair of angles is complementary?
A. 1 and 2
B. 2 and 3
C. 2 and 4
D. 4 and 5
1
5
3
2
4
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29
5. Find the measures of x and y. Explain your answer.
x
y
73
x =_________
Explanation: _________________________________________________
y =_________
Explanation: __________________________________________________
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30
Name________________________
Date______________
Group #_____
Complementary and Supplementary Quiz
Directions: Find the measures of the angles specified, show your work and explain
your answer.
1. Find ACB and BCD
B
50 + 2x
A
40 + x
C
D
ACB_______
BCD_______
Explanation _____________________________________________________
2. Find ACB and BCD
A
B
3x + 20
x + 10
D
C
ACB_______
BCD_______
Explanation _____________________________________________________
May 13, 2010
31
Dear parent/guardian,
First of all, I would like to welcome you and your child to my classroom. Your child will be
involved in a lot of partner work, group work, as well as solo work. It is more important than ever that
your child attends and participates in class every day. It tends to be very difficult for students to make
up work that is missed and they will often miss a great deal of understanding because they will be
learning new information, but also reviewing 6th and 7th grade information. The students will be given
participation points during each class. I would like to ask you to encourage your child to attend and
participate in class every day.
If your child is sick or needs to miss a day of class they have a week to make up their work. They
can make up the work after school from 2:45-3:30. If your child is in class, assignments will only be
accepted at the beginning of class on the day they are due. This not only helps the students to review
the material at an appropriate time, it also ensures that they will be prepared for the test. Students will
receive half off if they hand in their homework late. After a week they will receive no credit. If there are
extreme circumstances for which your child was not able to complete an assignment, I would appreciate
a note or an email.
The supplies needed for this class include a binder with 5 dividers, paper, pens, pencils and a
highlighter. We provide the students with calculators, however if your child has a calculator I would
recommend they bring them in. Students cannot take home a school calculator from the school. We
only need a basic calculator for 8th grade. Any loss or damage caused to the school calculator while in
the possession of the student will be charged to them.
Thank you very much for your cooperation and understanding. Please contact me with any
questions or concerns that you have. The best way to contact me is e-mail ([email protected]). I
am looking forward to a wonderful year. Please sign the bottom of this letter along with your child so
that I know that you have read this letter. This is the first assignment of the year and will count as a
grade. Thank you.
Sincerely,
Miss Saltino
_____________________ Return bottom portion only _________________________
_____________________
Student’s Signature
May 13, 2010
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Parent/Guardian’s Signature
32