Overview

Summary

In this lesson, students use calculation 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.

Learning Objectives

Students will:

• Identify and describe the exponential growth of a hypothetical dividing cell
• Create a graph showing their results
• Examine examples of patterns in nature
• Create a patterned drawing

Teaching Approach

Arts Integration

Teaching Methods

• Discussion
• Visual Instruction
• Lab Procedures

Assessment Type

Informal Assessment

Preparation

Lesson Setup

Teacher Background

Teachers should

• Understand cell reproduction
• Be familiar with the Fibonacci sequence, tessellation, and other mathematical patterning found in nature
  

Prior Student Knowledge

• This lesson builds on prior lessons in the 'The Magic Universe of Cells' unit, so students should understand basic cell anatomy and function, including mitosis.
• Students should have some experience with exponents.
• Students should have experience with drawing and interpreting graphs.
• Students should be familiar with the use of microscopes.

Physical Space

Classroom

Grouping

• Large Group Instruction
• Small Group Instruction
• Individualized Instruction

Staging

If microscopes are used, slides with live cells should be prepared.

Instruction

Engage

1. Remind students that living things, including cells, reproduce, and review the process of mitosis if necessary. (See the 'Vocabulary' handout located within the Resource Carousel if students need to refresh their memories.) Point out that different plants and animals take different lengths of time to reproduce and explain to students that different cells also reproduce at different rates, even within the same organism. Some cells take 20 minutes to reproduce, while others may take 24 hours. Some, like skin cells, continually reproduce, while others, like those in the liver, don’t usually reproduce in adult humans at all.

2. Ask students to calculate the number of cells produced in a hypothetical scenario. Have them imagine a cell that divides into two cells every hour for 12 hours. Assuming no cells die during the 12-hour period, how many cells would exist after 12 hours? While students will probably not have an immediate answer to the question, encourage discussion of possible approaches to the problem.

3. Distribute the 'Cell Division Chart' handout located within the Resource Carousel 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.

4. Have students look at cells under a microscope in small groups. If you do not have microscopes available in the classroom, students can look at images of cells at the Nanoworld gallery. As students continue to look at cells throughout the lesson, they should begin to notice patterns within, based on, or comprised of cells.

Build Knowledge

1. Discuss 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. Have students find ten different patterns in their current surroundings. Compare results and list some examples of both random and repeated patterns.

2. Show students examples of patterns that artists have captured from nature. View artists’ images of patterns in nature on these websites:

• Nikon’s Small World Competition Gallery
• Zeiss Gallery
• National Geographic’s Patterns in Nature (7 galleries)
• Bill Graham’s Patterns in Nature

3. Discuss the patterns as works of art. The galleries above show works of photography or microscopy (photography using an electron microscope). These patterns existed in nature but were captured and presented in intentional ways by artists. Ask students to compare the range of images and approaches, noticing the style and creativity of the artists. 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.

4. As a class, list some of the choices the artists made in their representation of the patterns of nature. Some characteristics that should be included on the list:

• Using only a portion of the original design
• Changing the angle of vision
• Repeating the shapes from a variety of views
• Connecting patterns together

5. Look more closely at the natural patterns in cells. As a class, focus on the cells viewed in the microscopes, or on images of cells (such as those in the Nanoworld Gallery). 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, tiny or massive.

Apply

1. 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.

2. Have students create a patterned picture based on their completed cell drawing. Have students take a 12” x 18” sheet of heavy white paper and divide it into 24 equal boxes. They will now have to decide how to display their cell. Discuss some possible approaches:

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 vary it by turning it upside down
• Repeat the same cell but flip it in each box
• Repeat the cell but rotate it in a random or regular pattern
• Show different parts of the cell in each box
• Offset the cell images by showing both the top and bottom of the image in a box, but reversing the order in neighboring boxes

3. Encourage students to be creative in their patterning. Display the finished artworks.

Reflect

1. Have students discuss the following questions about their calculations and their patterned picture:

• How are the results of this activity different from what would happen in nature?
• How would the data/numbers be different?

Some points to introduce:

• Cells die as well as dividing.
• New cells have to reach a certain size before they’ll divide.
• Cells reach a point at which the rate of death is equal to the rate of division, so the population of cells doesn’t normally keep dividing indefinitely.
• Cells are less tidy than the boxes on the paper.
• Animal cells have membranes, but plant and some other cells also have cell walls. The patterns created by cells with and without walls differ.

Standards

The National Standards For Arts Education:

Visual Art

Grade 5-8 Visual Arts Standard 2 : Using knowledge of structures and functions

Grade 5-8 Visual Arts Standard 5 : Reflecting upon and assessing the characteristics and merits of their work and the work of others

Mathematics

Math Standard 6 :
Understands and applies basic and advanced concepts of statistics and data analysis

Science

Science Standard 5 :
Understands the structure and function of cells and organisms

Common Core/State Standards

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