Name:
Jennifer L. Sundstrom Email: jensundstrom@hotmail.com

School: Houghton High School School Phone: 906-482-0450

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**Title***: **Symmetry of
Diatoms*

**Subject(s) in which unit
will be taught: **Geometry
** **

** **

**Target Grade: **9^{th}
and 10^{th} ** **

Unit Overview: Students in Geometry study symmetry. In order to incorporate Great Lakes Ecology into my math classroom I have decided to have the students study the symmetry of fresh water diatoms. After the normal lesson(s) on reflection and rotation symmetry, students will have the opportunity to apply these concepts to a real life situation. The students will be scientists. They will be in charge of collecting water samples from ponds, streams, rivers, lakes, swamps, or ditches, which will then be examined under a microscope. They will identify, examine and discuss the symmetry of diatoms and diatom clusters in each sample. They will then make posters displaying their findings. These posters may include the following: location of water sample, drawings of diatoms and clusters observed and their names, data on numbers of different species found, charts or graphs, discussion of symmetry of each (or lack of), drawn in symmetry lines, hypotheses about the water quality, and anything else they find interesting and want to share.

**Sources Consulted:**

** **

1. Usiskin, Z., Hirschhorn, D., Coxford, Al,
Highstone, V., Lewellen, H., Oppong, N., DiBianca,

Maeir,
M. (1997). *The University of Chicago
School Mathematics Project: Geometry*.

Glenview, IL: Scott, Foresman and
Co.

2. Pappas, J.L. (April 19, 2002). Great Lakes
Diatoms [online]. Available

http://www.umich.edu/~phytolab/GreatLakesDiatomHomePage/top.html

3. Michigan
Department of Education. (1996). *Michigan Curriculum Framework*. Lansing,
MI: State of Michigan

**Objectives**

** **

After this presentation, students will be able to:

1. discuss
diatom basics

2. determine if a figure has reflection and/or
rotation symmetry

3. identify different species of diatoms

4. analyze and discuss the symmetries of the
various diatoms

Michigan Content Standards Addressed:

1. Mathematics, Geometry Strand, Content
Standard 1

2. Mathematics, Geometry Strand, Content
Standard 2

3. Mathematics, Data Analysis and Statistics
Strand, Content Standard 1

4. Science, Using Scientific Knowledge in Life
Science Strand, Content Standard 2 and 5

** DAY 1** Describe
classroom or field activities

On the first day of the unit, we will be discussing
reflection and bilateral symmetry. A
figure is said to be reflection symmetric when the figure can be reflected over
a straight line such that the reflection image coincides with the original
figure (or preimage). Below is a very
basic example of a figure that is reflection symmetric. The line of symmetry is shown in red.

Students
will be reading the lesson in their textbook on reflection symmetry and doing
exercises, short activities, and problems to help solidify their understanding
of the concept. Exercises will include
having to determine if figures are reflection symmetric, drawing lines of symmetry,
and drawing figures that have a certain number of symmetry lines. The amount of symmetry that occurs in nature
is amazing. The basic shapes (outlines)
of many diatoms have reflection symmetry, as the students will see when they
look under the microscope at their water samples that they will be
collecting. Students will be told that
they are to collect and bring in a water sample for use on Day 4 of the
unit. They can collect the water
samples from ditches, rivers, streams, ponds, swamps, lakes, etc.

** DAY 2** Describe classroom or field activities

On the second day of the unit, we will be discussing
rotation symmetry. A figure is said to
have rotation symmetry if it can be rotated some number of degrees, *n*,
about a fixed point (called the center of rotation), such that the rotated
image coincides with the original figure. The number, *n,* must be less
than or equal to 180 degrees. The
rotation image must coincide with the original figure for any integer multiple
of *n* as well. Below are some figures
that have rotation symmetry.

**a g**

**e **

**h k**

**b** **d**

**c** **f i j**

The first figure has what we call 4-fold rotation
symmetry. The figure can be rotated 4
times, 90 degrees each time, and the rotated images will coincide with the
original figure. When the figure is
rotated 90 degrees counterclockwise about the center of the figure: **a**
will end up where **b** is, **b** will end up where **c** is, **c**
will end up where **d** is, and **d** will end up where **a** is. If it is rotated 90 degrees again, then **a**
will be where **c** is in the original figure, **b** will end up where **d**
is in the original figure, and so on.
The fourth 90-degree rotation will bring **a** back to where it
started.

The second figure has 2-fold rotation symmetry. That is, the figure can be rotated 2 times,
180 degrees each time, such that the rotated images will coincide with the
original figure. When the figure is
rotated 180 degrees about the center of the figure, **e** will end up where **f**
is and **f** will end up where **e** is.
Another 180-degree rotation in the same direction will bring the figure
back to its original position. The
third figure has 5-fold rotation symmetry.
It can be rotated 5 times about its center, 72 degrees each time, such
that the rotated images will coincide with the original figure.

The students will do exercises, short activities and
problems to help them understand this concept. Many diatoms have rotation symmetry. The students will examine this when they look at their water
samples under the microscope.

__ __

__ __

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** DAY 3 ** Describe
classroom or field activities

On the third day of the unit we will discuss
diatoms. Some topics/questions I intend
to lecture on are the following: a
description of diatoms, their role in the food chain, their habitat, uses for
diatoms, and diatoms as possible indicators of water quality. I will show the students some pictures of
diatoms on the projector that I will connect to my laptop. I intend on showing
them pictures from the “Great Lakes Diatoms” Web site. We will be using this Web site to help
identify the types of diatoms the students find in their water samples. I will show them how to use the website for
that purpose. We will also look at the
slide of a water sample that was taken and prepared aboard the Lake Guardian.
This should get the students interested in viewing their own water
samples. Students will be reminded that
they need to have their water samples for the next day.

Students will have water samples with them today. In groups, students will prepare slides from
their water samples and begin looking at them under the microscopes. The students will take notes on what they
see.

__ __

** DAY 5** Describe classroom or field activities

Today, students will spend the class period viewing and classifying diatoms from their sample. The Great Lakes Diatoms page, and handouts created from that page, will be the primary source for identification. The students will keep a tally of how many of each type of diatom there are on their slides. Students will examine diatoms for symmetry and start working on their posters. Work on their posters will continue for several more days. When complete, the posters will be on display in my classroom and/or in the hallway.

Overall Unit Assessment:

I think developing this unit will be a good way to
incorporate Great Lakes Ecology into my math classroom without straying too far
from the normal math curriculum. It
fits in with topics we already cover.
Standards from both the math and science content areas will be
addressed. And most importantly it will
help associate math with “real world” applications, and possibly spark an
interest in an ecological career.