Aaron Hamann
Oct. 4, 1999
LA Lesson Plan
Grade Level: 10th
A. Learning Objective:
After doing some research and creating a presentation using any media that they choose, 10th graders will have learned to write a research paper, how to write a thesis statement, and present this formal presentation to the class in a creative manner. The
y will also increase their ability to ask questions that broaden the discussion after the presentation as well as develop the ability to respond to these questions as they pertain to their own presentation, including defending ideas and using logical argu
ments.
B. Instructional Context:
This lesson can be used in a high school Geometry class (9th, 10th, and 11th graders) after students have worked with theorem proofs. It requires that students have been introduced to proofs and have been required to do some of them on their own. It does
not require extensive knowledge of complex proofs, but does require
basic knowledge of proof structure and Geometrical reasoning.
This lesson would take time to be completed, as the research and preparing of the presentation can only take place after the assignment is initially given. But the actual presentation unit can be done in a single computer classroom with projection capabi
lities. This lesson lends itself well to the use of group presentations
when a large class size is a problem. This will also add another element
of presenting as a group rather than as an individual.
C. Materials Needed:
•Student access to a computer (for project development)
•Computer in classroom with projection capabilities
•Screen or board to project onto
•Handout about thesis statement writing and using
analogies/examples
*Optional
•Presentation software(Powerpoint, Hyperstudio, etc.)
•Teacher created example
D. Description of the Lesson and Procedures:
What the Lesson Involves The lesson begins after some discussion
of proofs in Geometry has already taken place. The teacher will introduce the project by explaining that each student is expected to be able to present a proof and defend it. This sh
ould not be a big surprise since students have already done proofs in
their homework. However, the concept of presenting a proof to the whole
class may be a new concept to most.
The teacher will explain that the class will have a presentation day where each student, or group of students, will present a proof to the class using whatever media they choose.The proofs to be used will be designated by the instructor with lots of poss
ibilities so that the students have a wide range of choices. The presentation should include a thesis statement and show a creative use of visual aids. There should be examples and any analogies that support the proof. Information should be gathered from
a variety of credible sources and should be defendable using logical
statements. The students should also be able to intelligently field any
questions from the rest of the class.
Next, the instructor will, if available, show an example of what they expect from the students. However, since this activity is also trying to stimulate creative methods of presenting the information, the instructor should be careful not to insinuate a s
pecific form of presentation media.The instructor may also want to
suggest some web sites or magazines to reference when preparing a formal
presentation.
During the discussion of the example, the instructor will go through a lesson on writing thesis statements and provide examples on a handout for students to use as examples when writing their own thesis statements. The instructor will also give the stude
nts a list of references that discuss analogies and examples that may be useful for the students to use within their presentations. Emphasis will be placed on the analogy being relevant and beneficial when it comes to defending or adding to their presenta
tion of the proof. Analogies are not required, but are suggested if it
adds to the understanding and explanation on the day of presentation.
After this is done, the students are provided with some in-class research time. This would allow students to go to the library/media center, computer lab, or to discuss in small groups. The amount of time allowed in-class is up to the discretion of the i
nstructor, but ample time should be allowed as to provide for equitable
computer use.
On the day of presentations, each group is allotted a certain amount of time to present, a standard for each group that is pre-decided, and then a few minutes for a question and answer session. Students not presenting should be preparing any questions th
at they may have about the proof being presented so they can provide
feedback to their classmates. The students will also hand in anything
that they have presented for the instructor to look over, whether it is a disk, overheads, or paper print-outs.
What the Teacher Does The teacher acts as a guide to the students
as they prepare their presentations. The teacher will give feedback as to whether or not things will work or are feasible. The teacher will introduce the project and answer any ques
tions pertaining to it and will give them some basic information about thesis statements and relevant analogies or examples. He will then observe the groups progress so the students don’t get too far off task. If he feels that students are getting lo
st, he will interject and help them get back on track working on their projects. Specific achievement milestones during the research phase will also be required of the students so the instructor‘s expectations are not a surprise. He will also control
the formation of groups so stronger students and weaker students get
mixed together allowing more learning within the groups.
What the Students Do The students are expected to prepare a
presentation as described above. They are also expected to work collectively in their groups with every member contributing. Midway milestones will be required to be met by each group and
will be included in their grading. Finally, their main responsibility is they must present in front of the class and field questions from other students. When not presenting, students are expected to ask questions and help create discussion about the pro
of. All students are allowed to discuss, but each group will be assigned
to lead the discussion and ask questions about another presenting group
Role of Computer The computer will be utilized by students and
used as a tool to aid them in gathering information and presenting their findings. In the Thomas & Boyson taxonomy, this would be classified as utilizing. According to Bloom’s
taxonomy, this activity would be classified as Synthesis and Analysis when it comes to the proof, and Comprehension when it comes to the actual presentation. The students can take what they’ve learned in this lesson and use it to become more logical
in their Geometrical proofs. It also helps them to better understand the
proofs used in the presentations and have another way of seeing the proof
in action.
E. Evaluation Tool:
Students will be evaluated on the creativeness of their presentation and the formality in which it is presented. The instructor will be specifically looking for a thesis type statement and actual content within the proof itself in the research material t
hat is handed in and will be looking for citing of where this is proven or why certain statements were used. If analogies were used that added to the understanding of the proof being presented, the group has done a very successful job of creatively presen
ting and should be graded favorable in that sense. If a group cannot
successful convey their proof and thus produce lots of student questions,
then they have not achieved creative and effective presenting.
The groups will also be evaluated on their ability to field questions related to their research and defend their positions using logical arguments. If the question is not specifically related to their proof, they will not be expected to have the correct
answer. Each student will also be graded on their ability to ask questions of other groups when they are assigned to do so and they are required to participate in any class discussion on the ideas they have presented or suggested. Effective use of the med
ia chosen will be evaluated by the instructor, not simply the choice of media itself. If the ideas were presented illogically or if a technical flaw is noted by the instructor, then the effective use of the media chosen will be deemed as unsuccessful.. If
the ideas presented were solid and undisputable, then no questions on
this presentation by the class is acceptable. However, those assigned to
ask questions should be able to develop a tangent or similar idea that can be discussed.
F. Examples of Student Product:
A student sample of this magnitude and the various possibilities of media to be used is difficult to portray within a text document. I feel as though this project allows much creativity and can be utilized in many different types of media. As I stated ea
rlier, too many specific examples will limit the expansion of use by the
students and may restrict what they see as possible.
Pythagorean
Theorem(Example)
Thesis Statement: The length of the longest side of a
right triangle, known as the hypotenuse, is equal to the square root of
the sum of the squares of the two remaining sides.
c = Ã ( a2 + b2 )
This statement is used to find the lengths of sides of right triangles. It is known that this is true and accepted ever since the day of Pythagoras, for whom the theorem is named. By using basic algebra, each side of the triangle can be solved for, thus p
roving that each side of a triangle is directly affected by the lengths
of its other two sides. By changing one side, the other two must
compensate. The two other equations that can be derived are as follows:
a = Ã ( c2 - b2 )
b = Ã ( c2 - a2 )
To see how this can be used in our school, be went out to the baseball field and drew lines from home to first, home to third, and third to first. These three lines form a right triangle and are measurable distances. By measuring from home to each base, w
e revealed that the distance is 90 feet for both. We then applied our theorem to these distances and calculated the distance from third to first, the hypotenuse, as being about 127.3 feet. We then measured our hypotenuse and revealed that we were in fact
correct. By applying this idea to other triangles, the outcomes can be
consistently predicted.
Possible Student Questions/Discussion: Does this equation
hold for triangles that are not right? Are there any possible reasons as
to why this idea can’t be used in squares by breaking them into two
adjacent triangles?
Defense: Refer to the baseball field and the fact that the
bases do in fact form a square that is measurable. Also, by knowing any two of the three sides, can you determine the third? This was not specifically noted by the presenters and sho
uld be brought up by the class. This is the basis for many theorems that
are to be discussed following Pythagoras.
SCOPE & SEQUENCE
http://198.17.205.11/standards-benchmarks/standardslib/langarts.html
Language Arts Standards
1.Demonstrates competence in the general skills and strategies of the
writing process
2.Demonstrates competence in the stylistic and rhetorical aspects of
writing
3.Uses grammatical and mechanical conventions in written compositions
4.Gathers and uses information for research purposes
5.Demonstrates competence in the general skills and strategies of the
reading process
6.Demonstrates competence in the general skills and strategies for
reading a variety of literary texts
7.Demonstrates competence in the general skills and strategies for
reading a variety of informational texts
8.Demonstrates competence in speaking and listening as tools for learning
Language Arts Standard 4
•http://198.17.205.11/standards-benchmarks/standards/langarts/S4.html
Level IV: High School (Grades 9-12)
Uses government publications to gather information for research
topics
Uses microfiche to gather information for research topics
Uses a variety of news sources to gather information for research
topics (e.g., newspapers,
news magazines, television, radio, videotapes,artifacts)
Uses telephone information services found in public libraries to
gather information for
research topics
Synthesizes a variety of types of visual information, including
pictures and symbols, for
research topics
Uses a variety of primary sources to gather information for
research topics
Considers the motives, credibility, and perspectives of the
authors of primary sources
Determines the validity and reliability of primary and secondary
source information and uses
information accordingly in reporting on a research topic
Synthesizes information from multiple research studies to draw
conclusions that go beyond
those found in any of the individual studies
Identifies and defends research questions and topics that may be
important in the future
Writes research papers (e.g., includes a thesis statement;
synthesizes information into a logical
sequence)
Creates bibliographies for research topics (e.g., uses a style
sheet format, such as the Modern
Language Association or the American Psychological Association)
Language Arts Standard 8
•http://198.17.205.11/standards-benchmarks/standards/langarts/S8.html
Level IV: High School (Grades 9-12)
Evaluates own and others' effectiveness in group discussions and in formal presentations
(e.g., evaluates accuracy, relevance, and organization of information; evaluates clarity of
delivery; evaluates relationships among purpose, audience, and content; identifies types of
arguments used)
Asks questions as a way to broaden and enrich classroom discussions
Adjusts message wording and delivery to particular audiences and for particular purposes
(e.g., to defend a position, to entertain, to inform, to persuade)
Makes formal presentations to the class (e.g., includes definitions for clarity; supports main
ideas using anecdotes, examples, statistics, analogies, and other evidence; uses visual aids
or technology)
Uses a variety of explicit techniques for presentations (e.g., modulation of voice, inflection,
tempo, enunciation, physical gestures) and demonstrates poise and self-control while
presenting
Responds to questions and feedback about own presentations (e.g., defends ideas, expands
on a topic, uses logical arguments)
Makes informed judgments about non print media (e.g., detects elements of persuasion and
appeal in advertisements; recognizes the impact of pace, volume, tone, and images on
media consumers)
Compares form, meaning, and usefulness of different kinds of language
Understands influences on language use (e.g., political beliefs, positions of social power,
culture)