Lesson Overview:
In this lesson, students use calculators or pencils to predict the number of cells that result from a series of cell divisions. They then graph the results to represent their findings. Students use this investigation as a starting point for an exploration of pattern and repetition in nature, culminating with an activity in which they create a repeated or random pattern of their own. This lesson will help students gain an understanding of how patterns are reflected in nature.
Length of Lesson:
Two 45-minute periods
Notes:
This lesson is particularly suitable for students in grades 6 - 8.
Instructional Objectives:
Students will:
- identify and describe the exponential growth of a hypothetical dividing cell.
- research the phases of cell division.
- choreograph and perform a dance representing cell division.
Instructional Plan:
Introduction to Cell Reproduction
Distribute the Vocabulary Handout. Explain to students that some kinds of cells, such as bacteria cells, reproduce much faster than the cells in this experiment. Some bacteria can divide every 30 minutes. Ask students to solve the following word problem:
A cell divides every hour. Assuming no cells die during the 12-hour period, how many cells would exist after 12 hours?
Distribute the Cell Division Chart handout to students. Have students calculate cell numbers for each hour up to 12 hours, then graph the data in their science journals. One axis of the graph should represent the number of cells and the other axis should represent the hours up to the 12th hour. Allow students to compare their results with other students. Ask them if they notice any mathematical patterns.
Explain to the students that cell division involves a complex series of stages: early prophase, late prophase, metaphase, early anaphase, and telophase. (For a good digital image of these different phases, view the Mitosis resource on the National Health Museum site.)
Independent Activities: Research and Observation
Tell students that cells reproduce at different rates depending on the type of cell involved. A variety of human cells (blood, skin, etc.) divide in our bodies at all times. Have students research mitosis on the Internet, individually or in pairs. The following Internet resources could be used:
Have students look at cells under a microscope. If you do not have microscopes available in the classroom, students can look at images of cells on the Internet. As students continue to look at cells throughout the lesson, they should begin to notice patterns within, based on, or comprised of cells.
Recognizing Patterns in Nature
Tell students that artists have always recognized patterns in nature. Patterns can be random or repeated. The forest with all its trees is a random repeated pattern, as are waves in an ocean or cars lined up along the street. Tell students to look around and notice ten different patterns in their current surroundings. Ask them if they can find any repeated patterns. Can they find any random patterns?
Show students examples of patterns that artists have captured from nature. View images of patterns in nature on the Loes Modderman Microscopic ScienceArt Web site or on The University of Washington's Department of Biological Structure Web site. Explain to students that the artists were creative in their presentation of the patterns, thus creating a vibrant and original piece of art from nature.
Remind students that wallpaper designs are a great example of repeated patterns, and many of these designs are based on nature themes. Point out to students that sometimes artists and designers use only a portion of the original design. They may change the angle of vision, repeat the shapes from a variety of views, or connect the patterns together. Tell students that they will be utilizing similar techniques in the creation of their own pictures.
Tell students that there are patterns in cells. Show students the images on this National Oceanic & Atmospheric Administration site. Point out how each cell contains a series of lines, which are joined together to create a pattern, and then repeated. The lines can be wavy, thick, thin, circular, zigzag, short or long, and/or tiny or massive.
Creating a Cell Pattern
Tell students to choose a cell that they would like to make into a design pattern and copy it on a sheet of drawing paper. Have them refer to their notes from lesson one in this unit, What is Inside a Cell?, regarding the use of color. Allow them to use a microscope or magnifying glass as they copy the cell, encouraging them to use the level of accuracy and detail that a scientific illustrator would use. Remind them to be as accurate as possible with line and color.
Once students have drawn and colored their cell, they should use it as a model for the patterned picture. The students can choose to create either a simple repeated pattern or a random pattern.
Instruct students to take a 12” x 18” sheet of heavy white paper and divide it into 3” x 4” boxes. They will now have to decide how to display their cell. They may choose to complete one or more of the following activities:
- Repeat the same cell in each box. (You may wish to show how Andy Warhol used this technique in many of his designs.)
- Repeat the cell in each box but varying it by turning it upside down.
- Repeat the same cell but flipping it in each box.
Ask students to investigate how many other ways they can vary the composition. Some additional patterns can be found on the site, The Math Forum @ Drexel.
Assessment:
Assess students’ graphs using the following criteria:
- Calculations are correct for every hour calculated.
- Graph is accurate.
- Figures on the hourly and cell axes rise in equal increments.
- Graph is clean, neat and easy to read.
- All axes are correctly labeled.
- Graph includes a title.
Assess students’ pattern drawings based on the following criteria:
- Are the cells accurately drawn and colored?
- Did the student create equally-sized spaces when drawing on their 12" x 18" paper?
- Did the student create a repeated or random pattern?
- Can the student explain the pattern?
- Was the work done neatly and carefully?
Extensions:
After students research have researched mitosis and its phases on the Internet, have students answer the following questions:
- How are the results of this activity different from what would happen in nature?
- How would the data/numbers be different?
Nature has many patterns that are unique and mathematical, such as the Fibonacci Sequence. Have students explore how the pattern is replicated in shells, pine cones, and other objects in nature. For more information, see this resource on the Fibonacci Sequence on Rice University's site.
Fractals are another design element that artists have used to create patterned pictures. Students can explore these patterns through Cynthia Lanius’s Fractals site.
Sources:
Print:
- Balkwill, F., and Rolph M. Balkwill. Cell Wars. London: Harper Collins, 1999.
- Balkwill, F. and Rolph M. Balkwill. Cell are Us. Minneapolis: Carolrhoda Books, Inc., 1990.
- Berger, Melvin. Germs Make Me Sick. Revised ed. New York: Harper Collins, 1995.
- Brown, Robert J. 333 More Science Tricks and Experiments. Blue Ridge Summit, PA: Tab Books, 1984.
- Patent, Dorothy Hinshaw. Microscopic Animals and Plants. New York: Holiday House, 1974.
- Ruiz, Andre Llamas. The Life of a Cell. New York: Sterling publishing Co., Inc., 1996.
Web:
Authors:
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Susan Born-Ozment, Teacher
Oyster Bilingual Elementary
Washington, DC
