ALEX Learning Activity

  

Taking the Shortcut to Multihybrid Genetic Probability Problems

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  This learning activity provided by:  
Author: Katrina McGrady
System:Talladega County
School:Talladega County Board Of Education
  General Activity Information  
Activity ID: 2129
Title:
Taking the Shortcut to Multihybrid Genetic Probability Problems
Digital Tool/Resource:
Punnett Square Calculator/Science Primer
Web Address – URL:
Overview:

In this lesson, students will use the concept of finding the probability of an offspring having more than one genetic trait simultaneously. They will use a shortcut method to find the probability and they will use a Punnett square calculator to check their answers. This lesson can be used to teach genetics in a science classroom or a practical "real world" application of probability calculations in a math classroom.

This activity was created as a result of the GAP Resource Summit.

  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra I
47 ) Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. [S-CP2]

Science
SC2015 (2015)
Grade: 7
Life Science
12 ) Construct and use models (e.g., monohybrid crosses using Punnett squares, diagrams, simulations) to explain that genetic variations between parent and offspring (e.g., different alleles, mutations) occur as a result of genetic differences in randomly inherited genes located on chromosomes and that additional variations may arise from alteration of genetic information.

Unpacked Content
Scientific And Engineering Practices:
Developing and Using Models
Crosscutting Concepts: Cause and Effect
Disciplinary Core Idea: Heredity: Inheritance and Variation of Traits
Evidence Of Student Attainment:
Students:
  • Identify and describe the relevant components of the model.
  • Develop a model for a given phenomenon involving the variations that arise between parent and offspring as a result of randomly inherited genes and alteration of genetic material.
  • Use a model to explain a given phenomenon involving the variations that arise between parent and offspring as a result of randomly inherited genes and alteration of genetic material.
Teacher Vocabulary:
  • Punnett square - monohybrid cross
  • Homozygous and Pure
  • Heterozygous and
  • Hybrid
  • Homologous
  • Dominant
  • Recessive
  • Models
  • Genetic variation
  • Parent
  • Offspring
  • DNA
  • Genes
  • Inheritance
  • Allele
  • Variation
  • Mitosis (introduced in Standard 2; use here for comparison to Meiosis)
  • Meiosis
  • Chromosome
  • Mutation
  • Probability
  • Gregor Mendel
  • Mendel's laws
  • Sexual reproduction
  • Asexual reproduction
  • Sperm
  • Egg
  • Zygote
Knowledge:
Students know:
  • Chromosomes are the source of genetic information.
  • Organisms reproduce, either sexually or asexually, and transfer their genetic information to offspring.
  • Variations of inherited traits from parent to offspring arise from the genetic differences of chromosomes inherited.
  • In sexual reproduction, each parent contributes half of the genes acquired (at random) by the offspring.
  • Individuals have two of each chromosome, one acquired from each parent; therefore individuals have two alleles (versions) for each gene. The alleles (versions) may be identical or may differ from each other.
Skills:
Students are able to:
  • Construct a model for a given phenomenon involving the differences in genetic variation that arise from genetic differences in genes and chromosomes and that additional variations may arise from alteration of genetic information.
  • Identify and describe the relevant components of the model.
  • Describe the relationships between components of the model.
  • Use the model to describe a causal account for why genetic variations occur between parents and offspring.
  • Use the model to describe a causal account for why genetic variations may occur from alteration of genetic information.
Understanding:
Students understand that:
  • During reproduction (both sexual and asexual) parents transfer genetic information in the form of genes to their offspring.
  • Under normal conditions, offspring have the same number of chromosomes (and genes) as their parents.
  • In asexual reproduction: Offspring have a single source of genetic information and their chromosomes are complete copies of each single parent pair of chromosomes. Offspring chromosomes are identical to parent chromosomes.
  • In sexual reproduction: Offspring have two sources of genetic information that contribute to each final pair of chromosomes in the offspring because both parents are likely to contribute different genetic information, offspring chromosomes reflect a combination of genetic material from two sources and therefore contain new combinations of genes that make offspring chromosomes distinct from those of either parent.
AMSTI Resources:
AMSTI Module:
Studying the Development and Reproduction of Organisms

Alabama Alternate Achievement Standards
AAS Standard:
SCI.AAS.7.12- Compare and contrast traits of animal parents and their offspring (e.g., eye color, hair/fur color, size); recognize that variations between parents and offspring are the result of randomly inherited genes; recognize that genes are located on chromosomes which are found in the cells of living things.


Science
SC2015 (2015)
Grade: 9-12
Biology
11 ) Analyze and interpret data collected from probability calculations to explain the variation of expressed traits within a population.

a. Use mathematics and computation to predict phenotypic and genotypic ratios and percentages by constructing Punnett squares, including using both homozygous and heterozygous allele pairs.

b. Develop and use models to demonstrate codominance, incomplete dominance, and Mendel's laws of segregation and independent assortment.

c. Analyze and interpret data (e.g., pedigree charts, family and population studies) regarding Mendelian and complex genetic disorders (e.g., sickle-cell anemia, cystic fibrosis, type 2 diabetes) to determine patterns of genetic inheritance and disease risks from both genetic and environmental factors.


NAEP Framework
NAEP Statement::
L12.10: Sorting and recombination of genes in sexual reproduction results in a great variety of possible gene combinations from the offspring of any two parents.

NAEP Statement::
L12.8: Hereditary information is contained in genes, which are located in the chromosomes of each cell. A human cell contains many thousands of different genes. One or many genes can determine an inherited trait of an individual, and a single gene can influence more than one trait.

NAEP Statement::
L12.9: The genetic information encoded in DNA molecules provides instructions for assembling protein molecules. Genes are segments of DNA molecules. Inserting, deleting, or substituting DNA segments can alter genes. An altered gene may be passed on to every cell that develops from it. The resulting features may help, harm, or have little or no effect on the offspring's success in its environment.


Unpacked Content
Scientific And Engineering Practices:
Developing and Using Models; Analyzing and Interpreting Data; Using Mathematics and Computational Thinking
Crosscutting Concepts: Patterns; Systems and System Models
Disciplinary Core Idea: Heredity: Inheritance and Variation of Traits
Evidence Of Student Attainment:
Students:
  • Collect and analyze data on traits within a population to identify patterns within expressed traits in a population.
  • Mathematically calculate the probability of expressed traits of offspring, given parental traits and an understanding of inheritance patterns.
  • Use a model to determine potential gametes from parental genotype and develop a Punnett square to predict inheritance outcomes.
  • Annotate a Punnett square, identifying maternal and paternal gametes, and use mathematics to explain the predicted outcomes.
  • Observe traits in offspring and use knowledge of inheritance patterns and Punnett squares to infer parental genotypes.
  • Use probability to predict the likelihood of specific offspring given parent traits and inheritance pattern.
  • Distinguish between homozygous and heterozygous allele pairs and relate these to phenotype.
  • Analyze data to find inheritance patterns and explain those patterns in terms of incomplete dominance, codominance and Mendel's laws of segregation and independent assortment.
  • Use models, diagrams, and/or text to connect Mendel's laws of inheritance to the biological processes of meiosis.
  • Differentiate genetic disorders in humans in terms of errors of meiosis, either large scale (chromosomal) or small scale (point mutations).
  • Apply concepts of inheritance to explain patterns seen in pedigrees, offspring ratios, and trait prevalence in a population.
  • Identify non-genetic factors that may impact expressed traits.
Teacher Vocabulary:
  • Genetics
  • Allele
  • Dominant
  • Recessive
  • Homozygous
  • Heterozygous
  • Genotype
  • Phenotype
  • Law of segregation
  • Hybrid
  • Law of independent assortment
  • F1 and F2 generations
  • Monohybrid
  • Dihybrid
  • Punnet square
  • Probability
  • Crossing over
  • Genetic recombination
  • Carrier
  • Pedigree
  • Incomplete dominance
  • Codominance
  • Multiple alleles
  • Epistasis
  • Sex chromosome
  • Autosome
  • Sex-linked trait
  • Polygenic trait
Knowledge:
Students know:
  • Inheritable genetic variations may result from: new genetic combinations through meiosis, viable errors occurring during replication, and mutations caused by environmental factors.
  • Variations in genetic material naturally result during meiosis when corresponding sections of chromosome pairs exchange places.
  • Genetic material is inheritable.
  • Genetic variations produced by mutations and meiosis are inheritable.
  • The difference between genotypic and phenotypic ratios and percentages.
  • Examples of genetic crosses that do not fit traditional inheritance patterns (e.g., incomplete dominance, co-dominance, multi-allelic, polygenic) and explanations as to how the observed phenotypes are produced.
  • Mendel's laws of segregation and independent assortment.
  • Pedigrees can be used to infer genotypes from the observation of genotypes.
  • By analyzing a person's family history or a population study, disorders in future offspring can be predicted.
Skills:
Students are able to:
  • Perform and use appropriate statistical analysis of data, including probability measures to determine the relationship between a trait's occurrence within a population and environmental factors.
  • Differentiate between homozygous and heterozygous allele pairings.
  • Create Punnett squares to predict offspring genotypic and phenotypic ratios.
  • Explain the relationship between the inherited genotype and the visible trait phenotype.
  • Examine genetic crosses that do not fit traditional inheritance patterns (incomplete dominance and co-dominance).
  • Use chromosome models to physically demonstrate the points in meiosis where Mendel's laws of segregation and independent assortment are observed.
  • Analyze pedigrees to identify the patterns of inheritance for specific traits/ disorders including autosomal dominant/ recessive as well as sex-linked and mitochondrial patterns.
Understanding:
Students understand that:
  • In sexual reproduction, chromosomes can sometimes swap sections during the process of meiosis, thereby creating new genetic combinations and thus more genetic variation.
  • Although DNA replication is tightly regulated and remarkably accurate, errors do occur and result in mutations, which are also a source of genetic variation.
  • Environmental factors can also cause mutations in genes, and viable mutations are inherited.
  • Environmental factors also affect expression of traits, and hence affect the probability of occurrences of traits in a population.
  • The variation and distribution of traits observed depends on both genetic and environmental factors.
AMSTI Resources:
ASIM Module:
Dragon Genetics; Alkaptonuria; Blood Typing; Corn Lab; HNPCC; Chromosocks; Collecting Cancer Causing Changes (C4)

Alabama Alternate Achievement Standards
AAS Standard:
SCI.AAS.B.HS.11- Recognize that parents and offspring may have different traits.


Learning Objectives:

The students will calculate the probability of more than one genetic trait occurring at the same time using probability rules and a Punnett square simulator. 

  Strategies, Preparations and Variations  
Phase:
During/Explore/Explain
Activity:

The teacher will explain that the students are genetic engineers and that they have been tasked to breed certain plants to get certain traits. In order to determine which crosses will produce the most offspring with the desired traits, the students will be calculating the probability that two parents will produce offspring with the desired traits by using Punnett squares for multiple traits. The teacher will explain that they will be working the problems using a shortcut method and check their answers with a Punnett square simulation that completes each problem using the longer, more complicated method. 

The teacher will then use explicit teaching to show the students the shortcut method by working the first problem on the handout. Then, the teacher will show the students how to check their answer using the Punnett Square Calculator. (The students will count the total number of squares that have the desired genotype and count the total number of squares to determine the probability. It should be the same as their calculation.) Then, the teacher will have the class lead her through the next problem together using the same format. Finally, the students will work the third problem alone and check their work. After taking questions, the teacher will explain that if the probability of individual traits occurring at the same time is the same as their product, that the traits are inherited independently of each other, which is Mendel's Law of Independent Assortment. The teacher can then ask if this has been true for all of the problems that have been completed so far. After some discussion of the law of independent assortment and rules of probability in Algebra, the teacher will let the students complete the rest of the handout on their own. 

Assessment Strategies:

Give each student an exit problem where they will have to calculate the probability of two or three traits occurring at once WITHOUT using the simulator. They may choose to use the shortcut method OR the longer method.


Advanced Preparation:

Before this lesson, the students should know how to complete a monohybrid Punnett square and how to determine the probability of one trait using a monohybrid Punnett square. 

The teacher should be familiar with the shortcut method of calculating the probability of more than one trait occurring at once. Here is a YouTube video that demonstrates the shortcut.

Any copies of the handout should be made prior to the start of class. 

Variation Tips (optional):
 
Notes or Recommendations (optional):
 
  Keywords and Search Tags  
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