imaginary child...and other probabilities, The

Teaching Pre K-8, Jan 1999 by Davies, Cathy H, Anderson, Sara

A seventh grade math unit that focuses on genotypes, phenotypes and Punnett squares

At the middle school where I teach, we are encouraged to teach content through an interdisciplinary, thematic approach. Too often, mathematics is force fit.

One natural fit, however, is genetics. While seventh graders study probability in math, they work on genetics in science class and write about the ethics of genetic engineering in language arts. The study of world cultures in social studies prompts a family tree project that crosses over into art and technology, both core subjects within our team structure.

Guessing games. An integral part of the genetics unit I teach is the use of manipulatives in experiments. Students guess at the outcome of a situation, then test their guesses by experimenting - for example, playing a game like the following:

Two cubes of one color and two cubes of another color are placed in a bag. Player A takes out two cubes without looking. If they are the same color, a match, Player A wins; if they are a mismatch, Player B wins. The players take turns drawing. They then discuss whether the game is fair or unfair and adjust it accordingly. This is followed by analytically comparing the experimental and theoretical results.

Probability on rye. The unit on genetics can be thought of as an extension of my unit on probability, permutations and combinations. Students explore problems that ask for choices for a sandwich at a local deli if they have whole wheat and rye bread; American, Swiss and mozzarella cheese; salami and turkey. An item must be selected from each category.

Listing, drawing pictures (or arrows) and using other strategies to solve such problems can become cumbersome (and even tedious), which may force students to look for a more efficient strategy.

However, before students have had experience with such problems, the visual/concrete methods are more effective. For example, the state and regional lotteries provide a great source of material for problems and discussions because students are able to personalize their study of permutations.

Pam and Jerry. To provide an early "tie-in" to genetics, I use a wonderful problem from the NCTM Standards ("Patterns and Functions," Grades 5-8, p. 31). It's about a couple, Pam and Jerry, who plan to have four children. They currently have two daughters. Jerry thinks they'll end up with two girls and two boys, but Pam thinks they'll have three girls and one boy. Both provide data to "prove" their hypotheses.

Students are asked to try several methods that will show four-child families. Actually, when discussing the problem in class, the seventh graders often come up with a myriad of methods. Some even go so far as to make a list of every four-child family they know to prove their answer.

Invaluable resources. I use resources from many math and science programs (some of them slightly altered to fit the activities). "Ask Marilyn," a syndicated weekly newspaper column that frequently deals with probability problems, has provided me with both questions and answers which I've found invaluable over the years.

As the unit progresses, we focus more on science than on math. We use Punnett squares to look at the physical characteristics of plants, animals and ourselves. The first time the students' math homework comes from their science book generates surprise.

Tracking the traits. The culmination of our study of probability is a project called "The Imaginary Child." Students are given an extended time (usually a school recess when family members might be together) to find as much information as they can about their own specific traits - both genotypes (genetic) and phenotypes (obvious physical characteristics).

After the students have been able to narrow down their personal genotypes for the traits, I provide each student with an "imaginary spouse." The students are each given a "genetic calling card" for the spouse, at the top of which is the first name of the spouse. For obvious reasons, I use unusual names so that none of my current students' names are listed.

The card shows the spouse's genotypes for a number of visible physical traits - for example, hair color, eye color, widow's peak, dimples, tongue rolling and handedness. I've revised and/or simplified some of the fundamental parts because more than one gene may be involved - for example, eye color.

Next, each student creates a Punnett square of all options for each trait for his or her imaginary child. Through the Punnett square, they can understand (and show) the probability of any given trait to be dominant or recessive in the imaginary child. From the options presented in the square, they select the trait they wish their child to possess.

Finally, the students write a story (and draw a picture, if they wish), interweaving as much information as they can about the physical characteristics of their imaginary child and spouse. Since the child is created from half of their personal genetic make-up, even the most reluctant writers enjoy this activity. As might be expected, students really love to share their stories aloud in class.