Learning Activity

Taking the Shortcut to Multihybrid Genetic Probability Problems

Subject Area

Mathematics
Science

Grade(s)

7, 8, 9, 10, 11, 12

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.

Science (2015) Grade(s): 7

SC15.7.12

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

UP:SC15.7.12

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.

Scientific and Engineering Practices

Developing and Using Models

Crosscutting Concepts

Cause and Effect
Science (2015) Grade(s): 09-12 - Biology

SC15.BIO.11

Analyze and interpret data collected from probability calculations to explain the variation of expressed traits within a population.

Unpacked Content

UP:SC15.BIO.11

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.

Scientific and Engineering Practices

Developing and Using Models; Analyzing and Interpreting Data; Using Mathematics and Computational Thinking

Crosscutting Concepts

Patterns; Systems and System Models
Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.44

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams. [Algebra I with Probability, 38]

Unpacked Content

UP:MA19.8A.44

Vocabulary

  • Independent event
  • Probability
  • Dependent event
  • Event
  • Two-way table
  • Tree diagram
  • Simple event
  • Compound event

Knowledge

Students know:
  • Methods to find probability of simple and compound events.

Skills

Students are able to:
  • Interpret the given information in the problem.
  • Accurately determine the probability of simple and compound events.
  • Accurately calculate the product of the probabilities of two events.

Understanding

Students understand that:
  • Events are independent if one occurring does not affect the probability of the other occurring, and that this may be demonstrated mathematically by showing the truth of P(A & B) = P(A) x P(B).
Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.38

Explain whether two events, A and B, are independent, using two-way tables or tree diagrams.

Unpacked Content

UP:MA19.A1.38

Vocabulary

  • Independent
  • Probability
  • Tree diagram

Knowledge

Students know:
  • Methods to find probability of simple and compound events.

Skills

Students are able to:
  • Interpret the given information in the problem.
  • Accurately determine the probability of simple and compound events.
  • Accurately calculate the product of the probabilities of two events.

Understanding

Students understand that:
  • Events are independent if one occurring does not affect the probability of the other occurring, and that this may be demonstrated mathematically by showing the truth of P(A and B) = P(A) x P(B).

Phase

During/Explore/Explain
Learning Objectives

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. 

Activity Details

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

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.

Background and Preparation

Background / 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. 

Digital Tools / Resources

Punnett Square Calculator/Science Primer
http://scienceprimer.com/punnett-square-calculator

Approved Date

Owner (Author)

kmcgrady
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