Integrate Math and Science with the Vision Unit
By Lynne Kepler

See how they go together with these activities about eye color and vision! You're probably aware of the call to integrate math and science. The "Benchmarks for Science Literacy: Project 2061" report, published last year by the American Association for the Advancement of Science, even said that the ideas and practice of science and mathematics are so closely linked that they can't really be taught well when separated.

### The Skills Math and Science Share

A comforting word about integrating math and science: It's easier than you think. After all, the two subjects are close cousins, sharing such skills as:
• Collecting, Recording, and Organizing Data
• Recognizing Space/Time Relationships
• Classifying/Grouping
• Communicating
• Interpreting Data
• Graphing
• Observing
• Predicting
• Estimating

### Three Golden Rules for Integrating Science and Math

As you think about ways to integrate science and math, keep these three ideas in mind:
1. Plan lessons that use two or more of the skills listed above. Work from the basic principle that both math and science are about problem-solving.

2. Make hands-on activities a priority. When kids work with manipulatives, they gain the concrete experience that is so important to concept development.

3. Make science and math personal for kids by introducing activities with anecdotes, questions, or demonstrations that involve kids' local environments, whether it's their homes or the lake on the edge of town.

### Activity 1: What Color Are Your Eyes?

Concept: Individuals have varying eye color.

Skills: predicting, collecting data, counting, graphing, computing and interpreting data.

Materials: 2-inch-square pieces of white paper, assorted crayons, chart paper, a glue stick, masking tape

Procedure

1. Get personal. I like to begin science activities with a question, demonstration, or anecdote that connects to my students' lives. For this activity I tell them that when I was pregnant with my first baby, I predicted he or she would have brown eyes –– just like Mom and Dad. Was I ever surprised to meet my blue-eyed son! Then I pass around a snapshot of my husband and me and our three blue-eyed children. I confide that people often ask, "Where did those blue eyes come from?" I tell the class we're going to explore that question.

2. Make predictions. Next, I invite students to create hypotheses to answer two questions. First, "Which eye colors are represented in our class?" It's important that kids establish the eye colors they think will be found, because this prompts them to make observations of one another's eyes. The second question is: "Which eye color will we find most frequently among this group?"

3. Form a living graph. I give each student crayons and a 2-inch-square piece of paper, and ask them to draw a picture of their eyes. I put a line of tape on the floor and invite the whole class to form a series of single-file lines according to eye color. Students note the length of each line and compare their predictions with the actual results.

4. Create an eye-catching chart. Now we convert our living graph into a bar graph. Along the bottom of a piece of chart paper, we list the eye colors found in our group. Students use a glue stick to post their drawings in the appropriate columns. I ask students how the results compare with their predictions and challenge them to state something they have learned from the graph.

5. Develop story problems. I invite students to write (or dictate) a story problem based on the data, and then compile the problems into a booklet for students to swap. Children are highly motivated to solve story problems that involve information they collected themselves. One first grader dictated: "Which eye color has the most?" A third grader posed: "We have 24 kids in our room. Eight of us have hazel eyes. How many of us don't have hazel eyes?"

6. Graph it again. Now I help students make a more abstract version of their graph by asking such questions as: What symbol could you use instead of your drawings? How could you convert the bar graph into a line graph? (Mark a dot at the top of each column of drawings and then connect the dots.)

7. Widen the net. I ask students what would happen if they collected more data on eye color, increasing the sample size. Would their results change? How could they find out? One teacher I know, Ted Smith of Liberty Valley Elementary in Danville, Pennsylvania, had his second graders survey the entire student body! They compiled their data on a hallway graph for all to see. Whether you poll a few grades or your entire school, this activity will get across the concept that increasing the sample size of any survey will give you a truer representation of the population.

### Activity 2: Does Brown Always Rule?

Concepts: A person's eye color is determined by each parent's eye-color genes. Brown and hazel are dominant over blue.

Skills: observing; predicting; comparing; collecting, recording, and organizing data; probability

Procedure:

1. Focus on family matters. As a take-home activity, I have students list or illustrate the eye colors of family members. Then I ask them such questions as: Does your eye color match your parents' eye color? Your grandparents'? Your siblings'? When students bring in their data, I again show them the snapshot of my family and ask, "Where did those kids get their blue eyes?" I then give them a simple lesson in genetics, as follows.

2. Discuss basic genetics. I explain that for every characteristic –– from our eye color to the shape of our big toe –– each parent contributes one gene. The gene may be strong (dominant) or weak (recessive). For example, with eye color, brown and hazel are dominant over blue, which is recessive. If even one of the two eye-color genes a person receives is brown or hazel, then his eye color is brown or hazel. But if a person receives a recessive gene (blue) from each parent –– which was the case with my children –– then that person will have blue eyes.

3. Chart those baby blues. On the chalkboard, I draw the matrix shown below and then plug in the Kepler family eye colors. (Since we have blue-eyed kids, my husband and I obviously both have a recessive gene.) As you can see, there was a one in four chance that each Kepler child would have blue eyes. How could students express that as a fraction? As a ratio?

### Activity 3: How Can We See in the Dark?

Children love to learn about the peepers of creatures –– from a spider's set of eight to glow-in-the-dark cat eyes. In this activity, kids learn about their own night vision and compare it to nocturnal animals' keen eyesight.

Concept: Animals possess varying abilities to see at night.

Skills: observing, predicting, counting, classifying, making a table, computing,finding averages.

Materials: 12 pairs of socks, including a variety of dark colors (black, navy, brown) and light colors (white, tan, pink).

Procedure:

1. Present the challenge. I tell kids that their task is going to be to sort socks –– long pause –– in the dark! I ask students to write in the sock colors on a chart.

2. Gather students in a circle. I place the mixed-up socks in the center of the group and then have the kids establish where we will place the socks once the lights are out.

3. Lights out. Students go to work! I make sure each child has a chance to place a sock in what he or she thinks is the correct color pile.

4. Find out the score. When all the socks are sorted, I turn on the lights just long enough to tally the number of socks correctly placed in each pile. Students record the number on the chart.

5. Lights out again. Sitting in the dark, I tell kids we're going to try the sock sort again and ask them to predict the results. Some students may predict they will do better this time, noting prior experience in the dark. I deliberately spend ten minutes or so talking with the kids, so their eyes have time to adjust.

6. Sort the socks. When children are finished, I turn on the lights and we record the results. We compare the two scores. Did the length of time spent in the dark improve their ability to see in the dark? Why? Were some colors easier to sort than others? Why is this so? (The lighter colors –– which reflect more light –– are easier to see than the darker ones.)

7. Talk about nocturnal animals. Now that children have a sense of their own night vision, they can appreciate the eyesight of nighttime creatures. I have students list animals that they know have good night vision. Why might it be advantageous for these animals to see at night? I ask students to discuss their ideas and then explain that nocturnal animals' eyes reflect much more light than ours. Their eyes contain many more tiny cells called rods than the eyes of day animals. These rods allow them to see well at night. I ask kids: Thinking back to the socks, who do you think would do a better job of sorting in the dark –– an owl or us?

8. Launch a study of night animals. At this point kids are all set to investigate animal vision. There are many good resource books available: click here for a few of my favorites. Use the principles you've learned here to develop math and science-linked vision activities of your own.

### Great Science and Math Resources

For Teachers
AIMS (Activities Integrating Math and Science) Education Foundation offers 32 different publications, including a monthly magazine. Call (209) 255-4094 or write P.O. Box 8120, Fresno, CA 93747-8120.

GEMS (Great Explorations in Math and Science) is a hands-on math and science curriculum for PreK-10. Write to GEMS, Lawrence Hall of Science, University of California, Berkeley, CA 94720, or call (510) 642-7771.

Science Place and Math Place (Scholastic) are new K-6 hands-on curricula designed for easy integration. For information, call (800) 325-6149.

Better Vision Institute offers a free teachers' guide and poster about eye health and vision. Call (800) 424-8422.

Benchmarks for Science Literacy: Project 2061 (American Association for the Advancement of Science, Oxford University Press, 1993). To order, call (800) 451-7556.

For Students
Eyes by Judith Worthy (Doubleday, 1988)

One Eye, Two Eyes, Three Eyes, Four . . . The Many Ways Animals See by Dorothy Leon (Messner, 1980).

Seeing Things by Allan Fowler (Children's Press, 1991).

Lynn Kepler (Science), a science writer and consultant based in Pennsylvania, also works in the classroom as an elementary-school teacher.