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Genetics the Easy Way

By Rosie McKinney



ABSTRACT

"Genetics the Easy Way" teaches students to apply the rules of mathematics in solving genetics problems. It allows them to extend themselves beyond the textbook approach of the Punnett Square and Product-Rule Methods. Students can now calculate the probability that any particular phenotype would occur and apply this to a simulated situation (Recycle Critter) and to real life situations. By making a hypothetical critter using recyclables, one can also teach degree of biodegradability of substances and importance of recycling. One of my favorite critters has been aluminum can worms. A safety issue may be cuts, so be careful with any sharp edges. Cooperative team learning and hands-on approaches are both used. This lesson is targeted to any class teaching genetics, especially high school Biology. Have fun with your recycle critters!

INFORMATION FOR THE TEACHER

For several years I struggled early on as a student and later as teacher in genetic problem solving either using the Punnett Square or the Product Rule method and following the textbook closely without much freedom from the method. Few students succeeded in the di- or tri-hybrid problem solving. Then one year on the chalkboard in the process of explaining it to my students I saw straight through it. Realizing that all calculating probability is is multiplication, that multiplying 3X5X4 provides the same answer as multiplying 4X3X5, and that the Punnett Square is the same as the elementary school multiplication table, I have now created an alternative method to solving genetic problems quickly and accurately.

To teach the lesson a variety of strategies are used, including team and self problem solving, lecture/demonstration, and hands-on lab exemplification. First I create hypothetical critters with their own 'fun' gene pool; these have included either Marlings from Mars or Recycle Critter. Recycle Critter is created in a lab setting by students making male and female heterozygous parents with 5-8 sets of chromosomes and fertilizing them. They then build the phenotype of their Recycle Critter baby.

Next, students practice and master the six basic monohybrid problems in small groups and on the board explaining them in front of their peers. I then demonstrate solving a dihybrid problem by simply multiplying the answers of two monohybrid problems together. The preferred method is what I call the forked-line method; I prefer it since it will line up the genotypic and phenotypic ratios in a nice order, saving the time of counting through all the squares.

To do this method, one simply writes the ratio of the first cross one on top of another with some space inbetween, then draws n lines out from each one (n=equal to the number of possibilities in the ratio of the second cross) and writes the ratio of the second cross by each possibility of the first cross. Then one simply multiples along the forked-line to get the final ratio. This can be done with genotypic ratios which can be converted to phenotypic ratios or can be done with just phenotypic ratios. To double check the problem, make sure the sum of the ratio is equal to 4n. Furthermore, if the problem just asks for the possibility of one particular phenotype, then all one would have to multiply together are the predicted probabilities for that phenotypic combination.

Another method is to multiply the answers of the two squares together by creating a third Punnett Square; however this time instead of gametes on the sides, the ratio of one monohybrid cross goes on one side and the ratio of the other cross goes on the other side. As I have explained in the first paragraph, I usually also tell my students how I derived these methods; this lets them see how the math they have already learned can be applied. Since the 16-square Punnett Square is in the text and especially since my methods do not allow for one to find gamete possibilities, I also teach the textbook method. Students receive a "How-To" step by step hand-out on all methods and practice several problems.

Students quickly mastered dihybrid problems and then were challenged onto trihybrid problems, using the forked-line method. For the Recycle Critter (which had 5-8 traits), my honors students were able to calculate the percent probability of the particular phenotype they created, an octahybrid problem! Did they shine after this accomplishment!

Learning was evaluated both by success with problems done as homework or teamwork and by a test. Tests were given on two levels, based on ability. The general test had monohybrid and dihybrid problems; the advanced test had mono-, di-, tri- , and tetra-hybrid problems. Students were turned on by the challenge of the work and their capability.

What made this successful can be attributed to four things: the hypothetical "fun" critter created, the mastery of monohybrid problems, the team-teaching, and the simplicity and ease of solving more complex genetic problems by the forked-line method, i.e., applying the rules of mathematics!

Even though this method seems so obvious and simple, it is amazing how many people do not see it. I know that such an explanation of genetic problem solving would have greatly helped me in college genetics and that many science teachers have been very thankful for it.

RECYCLE CRITTER

OBJECTIVE

The student will use recyclable trash to construct a Recycle Critter family. The student will calculate the probability of the phenotype of the offspring that two heterozygous parents produced.

MATERIALS

Recyclables: aluminum cans, tin cans, newspaper, plastic bottles, glass bottles/jars. Something to hold them together with: string, tape, or glue. Blue and pink construction paper, scissors, pen

INSTRUCTIONS FOR STUDENTS

    PART I. THE PLAN

  1. In your teams, discuss what possible critter you could design with the above materials.
  2. On a sheet of paper, plan out your design by sketching it.
  3. List the physical characteristics (traits) of your critter. Your teacher will tell you how many traits (different kinds of genes) your critter is required to have.
  4. For each trait, list a dominant and a recessive phenotype.
  5. Create a genotype symbol for each phenotype.
  6. Have your teacher sign your critter plan sheet.

    PART II. CONSTRUCTING THE PARENT CRITTERS

  7. Both parents will be heterozygous for all traits. Sketch what your parents will look like.
  8. Construct the two parent critters: mom and dad.

    PART III. MAKING THE CHROMOSOMES

  9. Use pink construction paper to make mom's chromosomes.
  10. Cut ___ strips of equal size (approx. 1 cm X 8 cm). Since chromosomes come in sets of two (diploid), the number of strips or chromosomes will equal two times the number of traits your critter has. (See step #3). We will pretend that the last trait is on the X sex chromosome.
  11. Label your chromosomes with the appropriate allele, using the genotype symbols you designed in step #4.
  12. Repeat steps #9 - 11, using blue construction paper for dad's chromosomes, with one modification. For the last trait, make one of the chromosome strips half the length of the rest. This is the Y sex chromosome and it does not get a genotype symbol (allele) written on it, since the Y chromosome is a blank. To decide whether its sister chromosome (homolog) is dominant or recessive, toss a coin and decide randomly.

    PART IV. EGG, SPERM, AND FERTILIZATION

  13. Turn over your chromosome sets, so that the genotype symbol does not show. Do this for both mom's and dad's chromosomes.
  14. Have another team member, who did not see which chromosome is which, to randomly (with eyes shut) pick from mom's chromosomes one from each diploid set. This is the egg cell, which is haploid or half of the chromosomes of the diploid cell.
  15. Repeat, picking one of each set of dad's chromosomes. This is the _____ cell.
  16. FERTILIZE the egg and sperm. Unite the egg and sperm cells by pairing up the chromosomes so their alleles/genotypes match. (Blue "A" or "a" matches to either pink "a" or "A".) When an egg and a sperm fertilize, a single cell called a __________ forms which grows into an embryo, then a fetus, and then a new baby. CONGRATULATIONS! You are now the proud expectant parents a new baby Recycle Critter.
  17. You went in to have an amniocentesis done, where doctors draw amniotic fluid to obtain some of the baby's cells. They then can predict the baby's chromosomes and genotype. Record the new baby's genotype (What were your results in step #16).
    Will you have a boy or girl? _________
  18. Record the new baby's phenotype. Sketch the new baby (Baby's first photo!)
  19. Have your teacher sign for approval.

    PART V. THE BIRTH!

  20. Construct the new recycle critter baby.
  21. CONGRATULATIONS! YOU ARE NOW THE PROUD PARENTS OF A HEALTHY WEE ONE! SHOW HIM/HER OFF! BE PROUD.
  22. Now calculate the percent probability that it took for the two parents to produce that baby. Remember, follow the genetic problem solving rules you used in class. Multiply.

TEACHER TIPS FOR RECYCLE CRITTERS

Adjust the number of traits / genes studied based on the learning level of the class. I base this on their response to the practice mono- and di-hybrid problems we work on in class. My honors class caught onto the method and so I challenged them to 8 genes, whereas my general biology class did 5 genes. You may even want to do 3 genes for slower students. I like the Recycle Critter to challenge them somewhat, so I usually do at least a trihybrid cross.

Work in cooperative teams of 3 or 4 students. Assign students a position as A,B,C, D. Assign a specific task for A, another task for B, etc. For example:
A constructs Mom
B constructs Dad
C constructs the chromosomes for Mom
D constructs the chromosomes for Dad
A makes her egg by picking with eyes shut the haploid egg set of chromosomes
B makes his sperm by picking with eyes shut the haploid sperm set of chromosomes
C constructs the baby
D You may want this student to construct a recycle critter too. A pure homozygous recessive critter would be interesting to see. This could be the older sister.
ALL students should do the calculation of the percent probability of the new baby.

Some interesting critters that my students have made include...

  • aluminum can worms (Traits include color of can, number of cans, number of ring pull eyes, legs, tail or proboscis, bumps on skin).
  • plastic bottle critters (Traits include arms, legs, hair color, eye color, type of nose, tail, etc.)
  • newspaper monsters (Papers are cut, twisted and tied to form various traits)
  • You may want to restrict them solely to what we recycle, or you may want to allow them to use other miscellaneous items to create more traits.

    Throw in a quick lesson about how fast things biodegrade or the benefits of recycling and the world's garbage crisis. Newspaper is a wood product and may eventually decay. Tin cans will rust and decay eventually. Aluminum will be next and will weaken and decay (but as an unmineable source in a landfill) Plastic bottles will last forever and not decay. If it is photo-sensitive, it may break down in the presence of light, but will remain as small plastic beads in the soil (What harm will this do?) Glass will not decay.

    If anyone has any stats as to the length of time of decay, please send them to me. email AERMcKinne@AOL.com

    PUNNETT SQUARE METHOD

    1. Create a "key box"
      Write down the inherited traits and their dominant and recessive genotypes and phenotypes. Use a different letter of the alphabet or symbol for each trait.

    2. Write the phenotypic parental cross.
      (ie, verbally write what the problem said is to be crossed.)

    3. Write the genotypic parental cross Translate the parents phenotypes into the respective genotypes. (ie, write the symbols that fit the phenotype given, remembering that the organism is diploid and has 2 alleles/letters for each inherited trait.)

    4. On the side, calculate the number of squares needed in the Punnett Square by the formula 4n, where n = number of traits in the problem (number of different letters of the alphabet).

    5. Figure out all possible gametes (egg or sperm) that could be formed by meiosis for that parent. What are all the possible ways you could combine the alleles and in each case have the haploid combination, such that you have 1 allele/letter for each inherited trait? The number of possibilities will equal to the number of squares down one side. Note: Some problems just ask for gamete possibilities and not for final ratios of the offspring, in which case, this would be the last step.

    6. Draw the squares and write in the gametes by putting the female gametes (eggs) on one side (the top, say) and the male gametes (sperm) on the other side (the left, say). <

    7. Fertilize the egg and sperm by combining the gametes where the row and column intersect to form the diploid offspring. Remember these are predicted possible offspring.

    8. Complete the problem by writing out the genotypic ratio of the offspring. Count how many of each genotypic combination that there is.

    9. Translate the offspring's genotypic ratio into the phenotypic ratio and write it down too.

    10. If the problem asked for the percent chance that a particular phenotype or genotype could occur, calculate it as you would any percent: Number X 100%. Total

    11. To double check, make sure your final ratio adds up to the total number of squares in the punnett square (4n).

    FORKED LINE METHOD

    1. Create a "key box". Write down the inherited traits and their dominant and recessive genotypes and phenotypes. Use a different letter of the alphabet or symbol for each trait.

    2. Write the phenotypic parental cross. (ie, verbally write what the problem said is to be crossed.)

    3. Write the genotypic parental cross by translating the parents phenotypes into the respective genotypes. (ie, write the symbols that fit the phenotype given, remembering that the organism is diploid and has 2 alleles/letters for each inherited trait.)

    4. From the genotypic parental cross, take each trait separately and cross it using a four-square punnett square. (Follow the Punnett Square Method Steps 4-9.)

    5. Multiply all the ratios of the traits together using the forked line method. If the problem asks for genotypic ratios of the offspring (or genotypic and phenotypic ratios), you will want to multiply your genotypes together using the forked line and then translate them into phenotypes, if necessary. If it just asks for the offspring's phenotypic ratio, just multiply the phenotypes in the forked line. If the problem asks only for the percent chance for a particular phenotypic combination, then you need only to multiply that combination together and divide by the total number of squares in the punnett square (4n) times 100%.

      To do the forked line, write the first ratio vertically (on top of each other with some space inbetween). Draw forked lines (the number of lines is equal to the number of possibilities in the second ratio). Write the second ratio by each line. Repeat until all forks are filled. If there is a third, fourth, etc. trait crossed, draw forked lines, write the next ratio, and repeat to the bottom. When finished multiply along the forked lines to create your overall ratio.

    6. To double check, make sure your final ratio adds up to the total number of squares in the punnett square (4n).


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