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Lesson and Activity on Coordinate Planes
Adriana Magallanes
This is a lesson, which introduces the Cartesian coordinate plane, its parts, and �its origin,� and
historical practical uses.� The parts of the coordinate plane that are
introduced will be the axes, the origin, the quadrants, and the concept of ordered pairs.� We will also discuss the French mathematician Ren� Descartes development in the creation and documentation of
the coordinate plane, as stated by many.� In contrast, the way this has
been used by Native Americans will also be introduced and explored.� Next, students will create their own Cartesian plane, label all parts, and create their own �bead� design as
discussed in uses of the coordinate plane by Native Americans.� In
conclusion, after all points plotted have been recorded correctly they will reproduce their creations using a
�virtual beadloom� website.
����������� The anticipatory set for this lesson, the attention grabber
as it�s known, is an easy but fun warm-up activity (see appendix A).� The students must be partnered up another and each has a piece of paper and a small sticker of writing
utensil of some sort.� Have the students stand back-to-back, one facing
the front of the room.� Instruct the students who are facing you to put
their stick, or make a dot on their paper.� Meanwhile those who are no
doing this remain looking to the back wall.� Now, have the students
with the dot on their paper attempt to instruct their partner where to put their dot without looking at one
another.� They will find that this is a difficult task to do because a
plain sheet of white paper does not have any reference points; it is all based on the judgment and
interpretation of the individual.� Finally, have the students discover
this through discussion.�
����������� Following the warm-up the history of Rene Descartes, the
French mathematician is introduced (see appendix A).� The students will
come to find out that it has been documented in history that he thought up the idea of a coordinate plane
while lying sick in bed� and so forth.� The students will be interested
if the delivery is good.� This will also demonstrate that good ideas do
not always come to scholars in a classroom, or lab setting, it�s really quite the contrary.���
����������� A transparency of �� graphing paper should be shown now,
students should also have their own sheet on which they will mimic what is being modeled (notes).� On here, we will make a Cartesian coordinate plane.� First, the axes
should be introduced along with the terms horizontal and vertical, and the (0,0)
coordinate called the origin.� Next, name and number the sections
created by the axes called quadrants. Following this, discuss the concept of ordered pairs, including the
order (x,y) and how they are determined.� This can then be followed by
discussion of analogies such as an intersection, and how much easier the opening activity would have been
using this tool, the coordinate plane.�
����������� While asking the students what other uses that there may be
for this idea that was thought up so long ago, pose this question, �Do you think that no one else had ever
thought of this concept or used it until Descartes came up with it one day?
If so, why?�� My students often struggle
when I ask questions of this nature because they have been taught to listen and write, rather than listen,
question, and learn.� Let the silence continue until there is a
response, this may take a few minutes.� Then, present them with
pictures.
����������� The pictures I presented were from the website of Dr.
Eglash of RPI.� There were four pictures, consisting of Native American
embroidery, a sand painting, a buffalo hide drum, and beadwork.� I
enlarged the images and put one on transparency and asked if anyone could see a coordinate plane being used in
the picture.� The first student to raise their hand was asked to come
up and draw in on the picture.� This leads into the historical
discussion of the coordinate plane and it use by the Native Americans, before Descartes had �thought of
it.�� Though the Native American had not named it and shared it with
the rest of the world,
����������� The activity portion of this lesson is based on the
historical, Native American use of the coordinate plane within their culture and characteristics of the
drawings and designs that were used.� There were samples of student
works passed around, from elaborate and time consuming designs to simple ones.� Each student is then given a piece of white construction paper, 11 �� by 18� to make their coordinate plane
on.� This is done as a class with a ruler so that everyone has 1�X1�
squares (or close to that) on their paper.� Students then have the
option to use the paper vertically or horizontal and to create a labeled coordinate plane, on which they will
be creating their beadwork.��
����������� Putting their design together has no boundaries, using
their imagination, individuality, and being creative is encouraged.� The only requirement is that it had to be symmetrical or on four fold symmetry.� I provided four different colors of paper, and gave each student a template to cut out 1� circles.� Also, it should be explained that the circles need to be placed on a coordinate where two lines were
intersecting, not inside the squares to make determining the ordered pairs easier.�� Now, any last questions should be answered and at that point the activity should begin.
����������� As students finish, they will be instructed to write down
the coordinates for each point they have plotted with a colored dot and group them either by color or by color
and quadrant, on a separate sheet of paper.� Once they have documented
all ordered pair, students will go to the virtual beadloom (http://www.rpi.edu/~eglash/csdt.html) webpage and recreate their beadwork there.� During this last stage
of the lesson/activity, the ability to properly write down the ordered pairs and reproduce it on the website
will demonstrate understanding of the coordinate plane.� Those students
who have not identified the correct ordered pair will be deliberated with one-on-one to determine where the
misunderstanding has taken place.� Lastly, after the entire lesson was
completed, students were given a short quiz to demonstrate cognizance and comprehension of the coordinate
plane.
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����������� I, Adriana Magallanes, gave
this lesson to a seventh grade pre-algebra class.� Students were
excited to learn a concept without the book but seemed to feel awkward with the posing of questions.�� However, it was expected because this is the typical reaction when this practice is employed.� This exercise offered another point of view to the student frame of mind and they were able to relate to
it.� They also came up with their own examples of where they thought
the idea of the coordinate plane could have been used such as the Aztec calendar,
serap�s, and even pottery designs they have seen.� Although not all of the examples were correct, it was enlightening to see students attempting to make their
own connection to the curriculum.� There were many who became highly
engaged in making their �beadwork,� as well as those who did not want to go to too much trouble.� However, on the whole this was a successful lesson for another outlook on the �Cartesian� coordinate plane,
not dominated by Eurocentrism.� This was a
lesson that addressed the standards, but was adapted for the student population that it is serving.� At no time was it ever watered down but rather enriched.�
Appendix A
Introduction
Anticipatory Set- Activity with a partner, related to ambiguity without the use of a coordinate plane.
Objective- Represent quantitative relationships graphically, interpret meaning of specific parts of a graph, understand
the use of graphs to plot simple figures, and understand how to graph and read ordered pairs.
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CA Standards:
Algebra and Functions 1.5, represent quantitative relationships graphically and
interpret the meaning of a specific part of a graph in the situation represented by the graph and Measurement
and Geometry 3.2, understand and use coordinate planes to plot simple figures, determine lengths and areas
related to them, and determine their image under translations and reflections.
Objective- students will be able to identify specific parts of a coordinate plane and is origin, as well as plot point
and identify ordered pairs of specific points that have been plotted.�
Activity- Each student will be creating his or her own Cartesian coordinate plane and points to be plotted, as related
to historical lecture.�
Strategy- Begin with partner activity followed by explanation of Rene Descartes creation of the Cartesian coordinate
plane, as he named it.� Next, question to students, �Do you think he was the first to come
up with the idea just because it has been written down that way?� discussion.� Introduction of Native American works that used this same idea but also incorporated symmetry, show
examples.
Title 1-
This population will be able to create a meaningful application and related to the subject.� They will also be required to label all parts of the plane, list all coordinates by quadrant, and reproduce
this on the �virtual beadloom� to show success of documentation.�
GATE-
These students will be expected to develop intricate designs and also label the plane correctly, and provide
guidance at their table as necessary.�
RSP and LEP- This activity will provide a hands-on application and connection to the concepts presented.� In addition, allowing them to develop their own design and name it will also encourage �ownership� of the
concept.�
Modeling- Show a sample of what a finished product could look like.� Encourage
creativity and individuality.�
Guided Practice- This will essentially be taking place during the entire activity, as students demonstrate acquired
knowledge.��
����������� Do you now agree that Native Americans have used the Cartesian coordinate plain effectively?� Should they be given credit for the idea even though it was not formally document as such?� Small quiz on parts of a Cartesian coordinate plane, plotting points, and identifying ordered pairs of points
that have been plotted previously.�
Warm Up Activity
Have the students get into pairs with their backs to each other.� Give
one of the students of each pair a sheet of plain paper with a dot, a sticker, or some other kind of mark on
it, (you may decide to have the student mark the paper on their own).� Have one student describe to the other one the location of the mark, dot, or sticker while the second student
tries to put a mark on the location on the plain sheet of paper from the description given.� Repeat the activity with the other student doing the describing (optional).� When completed discuss how easy or difficult the task was.� Point out
that a way of doing it with more success and accuracy would be to use some kind of mapping system, such as the
one developed by Descartes.
Brief History of Descartes
����������� Ren� Descartes was a French mathematician and philosopher
who lived from 1596-1650.� A story goes that once, while sick in bed,
he noticed a fly on the ceiling.� It came to him that there should be a
way to accurately describe the location of the fly to someone else, like his nurse.� Supposedly, from this thought he developed the Cartesian coordinate plane with coordinates to determine the
exact location of points on a plane.�