Probability and Punnett Squares

Transcription

1 Performance Task Probability and Punnett Squares Essential Knowledge 3.A.3 Challenge Area 3.14 Building Block A The chromosomal basis of inheritance provides an understanding of the pattern of passage (transmission) of genes from parent to offspring. The student is able to apply mathematical routines to determine Mendelian patterns of inheritance provided by data sets. Probability and Punnett Squares Setting the stage Building Block A concept: Although fundamental to further understanding of the study of genetics, probability and Punnett squares can sometimes be a stumbling block for students. This building block provides a foundation for developing an understanding of inheritance and applying mathematical routines to traits inherited through Mendelian genetics patterns. Rationale: To grasp additional genetics concepts, students must first have a basic understanding of possibility, probability and the means of predicting the expected results of a cross. Command of genetic terms such as genotype, phenotype, homozygous and heterozygous is also necessary. Goal: Build students understanding of the relationship to Enduring Understanding 3.A: Heritable information provides for continuity of life. The use of a Punnett square is fundamental in developing a student s understanding of EU 3.A. As a tool in genetics, the Punnett square provides a mechanism for predicting genotypic probabilities, allowing students to see how genetic information may be passed from one generation to the next. Overview of student task Background: The Punnett square is a graphical method proposed by the British geneticist Reginald C. Punnett in 1906 to visualize all the possible combinations of different types of gametes in particular crosses or breeding experiments (each gamete is a combination of one maternal allele with one paternal allele for each gene being studied in the cross). The Punnett square is a table in which the gametes of one parent fit horizontally and the gametes of the other parent fit vertically. The genotypes that are created from the gametes combinations are shown where the rows and columns intersect. The completed Punnett square allows us to determine the probability of each genotype in a particular cross. Task rationale: Though your students may have a basic understanding of Mendelian genetics, you may find they need further practice calculating genotypic frequencies and predicting possible offspring and gametes. This task will help you evaluate your students ability to compare the concepts of possibility and probability as well as calculate the probability of specific genotypes in given genetic crosses through the use of a Punnett square. Use or distribution of these materials beyond participation in this program is prohibited. Page 1 of 6

2 Teacher materials: Each pair of students will need access to the website used in Task 1: Task 1: Possibility or probability? (Group) 1. Working with a partner, go to Toss the coin a few times, increasing your flips by 1, 10 or 100 as you choose. Record your results. Be sure to note how your results change as the number of flips increases. Then answer the following: a. What are the possible outcomes? List all. Heads, Tails b. What is the probability of each of the possible outcomes? Heads = 50%, Tails = 50% c. How is possibility related to probability? Possibility lists all the possible outcomes without defining how probable it is for each to occur. Probability assigns a quantitative likelihood for each outcome to occur. d. What happens to your probability of getting the heads side of the coin the more you toss the coin? The probability stays the same for each flip of the coin. It doesn t change as the number of coin flips increases. 2. Consider the representations of genetic traits below: E_ = unattached earlobes ee = attached earlobes W_ = widow s peak ww = straight hairline a. If a woman has attached earlobes, what are the possible alleles she can give to her offspring? e b. If a man is heterozygous for unattached earlobes, what are the possible alleles he can give to his offspring? E or e c. Draw a Punnett square to show the possible offspring genotypes in a cross between an Ee male and an ee female. Use or distribution of these materials beyond participation in this program is prohibited. Page 2 of 6

3 d. List all possible phenotypes and the probability for each. Unattached earlobes = 50%, attached earlobes = 50% 3. Determine the possible genotypes that can be formed in a cross between a man with a widow s peak and unattached earlobes and a woman with a widow s peak and attached earlobes. Both are heterozygous for the traits. Calculate the probability for each possible phenotype. 9/16: widow s peak, unattached earlobes 3/16: widow s peak, attached earlobes 3/16: straight hairline, unattached earlobes 1/16: straight hairline, attached earlobes Use or distribution of these materials beyond participation in this program is prohibited. Page 3 of 6

4 Check your understanding Are you confident in your ability to: Distinguish between probability and possibility? Demonstrate possible offspring genotypes for monohybrid and dihybrid crosses using a Punnett square? Predict the probability of occurrence for specific genotypes? Task 2: Check your understanding (Individual) For the next two questions, consider the key to genetic traits below: D_ = dimples dd = no dimples F_ = freckles ff = no freckles 1. If a woman is homozygous for dimples, what are the possible alleles she can give to her offspring? D 2. If a man is homozygous for no dimples, what are the possible alleles he can give to his offspring? d 3. Draw a Punnett square to show the possible offspring genotypes in a cross between the male and the female. 4. List all possible phenotypes and the probability for each. Dimples = 100% Use or distribution of these materials beyond participation in this program is prohibited. Page 4 of 6

5 5. Determine the possible genotypes that can be formed in a cross between a dimpled man with freckles who is homozygous for both traits and a woman who is heterozygous freckled and dimpled. Calculate the probability for each possible phenotype. Dimple Freckled = 100% Check your understanding Are you confident in your ability to work alone to: Distinguish between genetic possibility and genetic probability? Calculate the probability of specific genotypes in given genetic crosses? Apply your understanding (if time allows) If you see a 3:1 ratio in the offspring from a genetic cross, predict the genotypes of the parents. Your justification should incorporate both probability and possibility of each genotype. A 3:1 ratio in the offspring indicates that both parents must be heterozygous assuming the trait shows complete dominance (G dominant over g). With two heterozygous parents there is a possibility for GG, Gg, and gg offspring. The probability of each genotype is GG = 25%, Gg = 25%, gg=25%, and gg=25%. Since the G allele is dominant over g, then the phenotypic ratio would be 75% to 25% or 3:1. Use or distribution of these materials beyond participation in this program is prohibited. Page 5 of 6

6 Interpretive framework Evaluation of student work: Student responses to open-ended questions may differ in phrasing from the provided answers, but should be similar at a conceptual level. Variation is not expected on calculated responses. Rubric: Criteria Beginning Approaching Target Does the student correctly distinguish between genetic possibility and genetic probability? The student uses the terms possibility and probability interchangeably and does not distinguish between the two or recognize the relationship of the two terms. The student recognizes that genetic probabilities are mathematical calculations indicating the likelihood that certain genotypes may occur, but the student cannot distinguish between genetic possibility and probability. The student recognizes that genetic possibilities represent all of the possible combinations of parental alleles in the formation of offspring genotypes, while genetic probabilities represent the likelihood of the occurrence of specific possible combinations. Are Punnett squares used to accurately calculate the probability of specific genotypes in given genetic crosses? Punnett squares inaccurately reflect the possible parental gamete allelic composition, resulting in inaccurate offspring genotypes. Punnett squares reflect impossible gamete combinations while offspring genotypes are placed in the squares by adding the male gamete to the female gamete alleles. Punnett squares are set up to accurately reflect the various combinations that can occur in parental gametes. Offspring genotypes accurately reflect the combination produced by the union of the male and female gametes. Closing the gap through instruction: How do I help students close the gap? Closing gaps may require development of concepts and science practices through the use of activities such as: 1. Provide students several genetic cross descriptions and allow students to practice applying the terms genotype, phenotype, heterozygous and homozygous as they read genetic problems. Have them circle the genotypes, underline the phenotypes, draw a box around the heterozygotes and highlight and describe any homozygous organisms in each problem. 2. Students who are struggling to set up the Punnett square will benefit from revisiting the laws of independent assortment and segregation. Work with individuals to practice writing out all of the possible allelic combinations that can occur from genotypes such as TtRr, TTRR, TTrr and ttrr. Ask students to explain how the Punnett square represents the possible combinations. Use or distribution of these materials beyond participation in this program is prohibited. Page 6 of 6