National Agricultural Literacy Curriculum Matrix


Double the Muscle: Probabilities and Pedigrees

Grade Level(s)

9 - 12

Estimated Time

Two 1-hour class periods


This lesson allows students to apply the concept of Mendelian genetics and learn about the double muscling trait found in cattle. Students will apply their knowledge of genetics and Punnett squares to calculate the probability of genotypes and use a pedigree chart.


  • Double the Muscle: Genotype and Probability worksheet, 1 per student
  • Double the Muscle: Using Pedigrees worksheet, 1 per student
  • Teacher worksheet keys
  • For each group of 2-3 students:
    • 2 coins
    • 1 calculator

Essential Files (maps, charts, pictures, or documents)

Essential Links


Punnet square: a visual depiction of all the possible ways the alleles from two parents could combine

allele: an alternative version of a gene

chromosome: DNA is found in large molecules in the nucleus known as chromosomes.  Each chromosome is composed of thousands of genes. During cell division, chromosomes duplicate and divide, maintaining the genetic integrity of the organism

diploid: cells that have two complete sets of chromosomes, one from each parent

dominant allele: whenever this allele is present, the dominant trait is expressed (ie:T)

gamete: a mature male or female reproductive cell (sperm /pollen or egg/ ovum) containing half of the total number of chromosomes in a cell

genotype: the genetic constitution of an individual organism

haploid: having a single set of unpaired chromosomes

heterozygous: a pair of genes where one is dominant and one is recessive (ie: Tt)

homozygous: a diploid organism that has two identical alleles at a gene pair (ie: TT or tt)

hyperplasia: the enlargement of an organ or tissue caused by an increase in the reproduction of its cells

hypertrophy: an enlargement of an organ or tissue caused by an a increase in the size of individual cells within the organ or tissue

phenotype: the physical appearance of an organism determined by the genotype

recessive allele: two copies of this allele must present for the recessive trait to be expressed

segregation: the behavior of the genes at a gene pair during gamete formation where the paired genes separate

somatic cell: diploid cells that are specialized and make up the body of a multicellular organism

Did you know? (Ag Facts)

  • Belgian Blue, Piedmontese, and Parthenais cattle are common breeds affected by double-muscling.
  • Double-muscled cattle tend to have 10% less bone mass than normal cattle. This is because their bones are shorter, more slender, and of lower density.1
  • Double-muscling, when at a phenotypic extreme, is associated with problems such as calving difficulty, inability to fatten, and reduced heat tolerance.1
  • Moderate double-muscling in cattle can produce a higher proportion of desirable lean-cut meats with greater efficiency than comparable conventional cattle.1

Background Agricultural Connections

Prior to this lesson students should be familiar with how genes are related to DNA and inheritance. Students should be knowledgeable of Mendelian genetics and using Punnett squares to calculate genotype and phenotype probabilities. Students should also be familiar with the terms heterozygous, homozygous, dominant, and recessive. Students will learn that pedigrees are used to map and predict the genotype and phenotype of of specific animal or plant crosses. Students will apply their knowledge of Punnett squares and probabilities to help a farmer decide which cattle should be mated to maximize the probability of getting offspring with the desirable phenotype.

Key STEM Ideas:

Pedigrees are a way of tracking genetic and inheritance information to visualize parental crosses and their resulting offspring’s genotype. Probabilities are calculated to predict the likelihood of crosses resulting in offspring with particular genotypes or phenotypes. Scientists and breeders use pedigrees to make a plan for selecting for certain traits or qualities that they feel are desirable or undesirable.

Connections to Agriculture:

Gregor Mendel originated the science of modern genetics. He conducted careful and detailed studies with garden pea plants and generated large numbers of different families from crossing two parents that differed in obvious traits. By generating large numbers of pea seeds and plants, he could look for mathematical regularities in the inheritance data in these families of peas across several generations. Mendel observed repeatable patterns of ratios in his experiments and proposed a biological model to explain the ratios. Mendel proposed traits that vary and are inherited are controlled by variation in “particles” that were inside the somatic cells and traveled in the gametes.  These particles were later called genes by other biologists. Mendel called his explanation or model the principle of segregation. This model explains how genes are passed from generation to generation with predictable outcomes.

Cattle breeders and producers use the principles of inheritance uncovered by Mendel to predict and breed cattle for desirable traits while avoiding undesirable characteristics. Breeders use their knowledge of inherited genetic traits to select for traits such as muscle, milk production, and even coat color.

Double muscling is a naturally occurring homozygous recessive genetic defect. Double muscling in cattle is a result of the loss of function of a gene coding for myostatin. Myostatin is a hormone that controls the growth of muscles. Cattle that do not have functional myostatin will display an increase in the number of muscle fibers (hyperplasia) and, to a lesser extent, an enlargement (or hypertrophy) of muscle fibers.

Breeders are interested in double-muscled cattle because studies have shown that the meat quality (assessed by tenderness, ease of fragmentation, and amount of connective tissue) was better in carcasses with at least one defective myostatin gene than in carcasses with two normal myostatin genes. The meat on double muscled cattle is more valuable to consumers and producers, which may drive producers to breed for double muscling.

Under normal conditions, probability calculations can help us to predict what will result from potential genetic combinations of two parents. This concept is illustrated using Punnett squares and the outcomes can be mapped on pedigree charts. A pedigree can be used to determine trends in desirable traits (such as more muscle or higher milk production) or undesirable traits (such as susceptibility to disease). In addition, pedigrees can help breeders plan for crosses that will maximize the likelihood of desirable traits and minimizing the risk of undesirable traits.

Interest Approach – Engagement

  1. Project slide 2 of the Double the Muscle: Probabilities and Pedigrees PowerPoint. Ask the students to study the pictures and list the differences and similarities of the meat cuts. (Students should notice a difference in the external fat as well as the amount of fat within the muscle. This is commonly known as "marbling." There is a also a difference in the overall size of the muscle and the meat to fat ratio.)
  2. Ask students to discuss what might cause these differences in the meat. Guide the discussion to first determine if the characteristics are determined strictly by genetics or if they are determined by environmental factors such as the amount and type of feed the cattle ate. After discussion inform the students that although feed quality does affect the meat (tenderness, lean to fat ratio, and flavor), in this case the differences in the cuts of meat are due to the genetics of the cattle that they originated from.
  3. Review with students the vocabulary on slides 3-4 to recall their prior knowledge about traits and genetic inheritance. Be sure students have a solid understanding of genetics and inheritance before continuing with the rest of the lesson.
  4. Use slide 5 to explain the role of the gene which produces myostatin. Explain that this gene expresses itself in a trait (phenotype) known as double muscling.
  5. Ask students why it might be a good or bad trait for (1) the cattle, (2) a consumer, and (3) a farmer/producer.
  6. After discussion explain to students that they will conduct a series of activities demonstrating that math can be applied to predict the outcome of random events such as a coin toss (or the segregating of allele during gamete formation). This lesson will illustrate how knowledge of statistics and probability allows breeders to predict the ratios of resulting possible genotypes and phenotypes.


Activity 1: Calculating the probability of genotypes

  1. Hand out the Double the Muscle: Genotype and Probability worksheets, coins, and calculators to each group of 2-3 students. Discuss the procedures and expectations of the lab. (Use books as a back stop for coin flips if needed.)
  2. Read page 1, Introduction to the Double Muscle Trait with students to explain that they will be using their coins to represent the random chance of a parent contributing 1 of 2 alleles (represented by heads and tails of the coin).
  3. Use a coin to illustrate the following as the steps of the activity.
    • Step 1: Calculate gametes for the bull.
    • Step 2: Calculate gametes for the cow.
    • Step 3: Compare the bull and cow results.
    • Step 4: Predict offspring genotypes from a mating of a heterozygous bull and cow.
    • Step 5: Calculate the probability of each offspring type.
    • Step 6: Reflect on the coin tossing results.
  4. As students begin step 1, draw blank tables on the board for students to fill in their coin toss data from steps 1 and 2 on the worksheet. 
  5. Assist students as needed to calculate the percentage of head and tail flips for the entire class. It is recommended that you work through an example calculation.
  6. Have students share and compare their findings from steps 1 and 2 in step 3. Help students connect the idea that their equal chance of getting heads or tails in a coin toss is the same probability that happens when gametes are formed and receive one of two alleles. In step 1, the heterozygous bull is just as likely to give the dominant allele as the recessive allele. The same is true for the heterozygous cow in step 2.
  7. In step 4, students will determine the four possible combinations when 1 allele is contributed from each parent and understand that these combinations represent the potential genotypes of the offspring (DD, Dd, and dd).
  8. Discuss whether Dd and dD are phenotypically distinct from each other. They are not distinct from each other and the probability of getting heads and tails in any order would be found by adding the 2 separate probabilities (¼ and ¼). Phenotype and genotype probabilities can be illustrated using a sample Punnett square on slide 6.
  9. Before step 5, assign students to work in pairs (if they aren’t already doing so) and provide each group with two different coins. This will make it easier for students to keep track of coin flips simulating the bull gametes and the cow gametes.
  10. For step 5, encourage students to predict how often the DD, Dd, dD, and dd genotypes will be flipped (as a percentage) and decide how many coin tosses should be done as a class to adequately test their prediction.
  11. Pairs of students will conduct as many coin tosses as needed to feel confident in the genotype probabilities. Have students contribute their data to a class data table on the board.
  12. Have students calculate the total number of coin tosses completed for the whole class.
  13. Assist students as needed in calculating the percent coin tosses in Step 5, #5.
  14. Assuming students conducted a reasonable number of trials, all allele combinations (or genotypes) should have approximately a ¼ chance of being tossed.
  15. For evaluation, have students complete step 6 on their own. The answer to Step 6, #1 is ¼ and uses the product rule. The product rule states that the probability of independent events occurring together is equal to the product of the probabilities of these events occurring separately. For example, if you tossed 2 different coins simultaneously, the probability of both turning up heads is as follows:      

Coin 1 


Coin 2


Turning up heads


Turning up heads





= ¼ or .25 or 25%

Activity 2: Using a Pedigree

  1. Explain to students that you are going to further explore Mendelian genetics by applying their knowledge to a pedigree.
  2. Discuss how a knowledge of inheritance and probabilities can help make predictions that, when used in conjunction with pedigrees, can help breeders select for desirable traits or select against undesirable traits.
  3. Distribute the Double the Muscle: Using Pedigrees worksheet to each student and read page 1, Introduction to Pedigrees which tells about the beef rancher, Walter, and his cattle herd.
  4. Following the reading, help students recall their prior knowledge of pedigrees. Using the pedigree from the student worksheet, discuss the basics of how pedigrees work. Remind students that:
    • Circles represent females
    • Squares represent males
    • Shading  indicates that an animal or plant has a specific trait.
    • The horizontal lines that connect circles to squares indicate a mating (or a marriage in humans).
    • The vertical lines coming from a “marriage” line indicates that the individuals had offspring.
    • Multiple offspring are shown with a vertical line connecting to a horizontal line where several vertical lines can be drawn and connected to offspring.
  5. Discuss the purpose of pedigrees. In genetics, pedigrees help breeders keep track of the genotype and phenotype of related individuals. In humans, pedigrees are often used to show relationships between family members, but can also be used to make predictions about genetic disease inheritance in families.
  6. Once students are comfortable with how a pedigree works and its purpose, have students add the information from Activity 2 (top of page 2) to Walter’s cattle herd pedigree.
  7. As students work through updating the pedigree, encourage them to write the suspected genotypes of the animals in the pedigree shown. If students need guidance, indicate that working up from the bottom can be helpful and that we may not be able to identify the genotype for every animal in the pedigree.
  8. Once students have determined the updated pedigree and the associated genotypes, have students compare their pedigrees to the answers on slides 7 & 8 in the Double the Muscle: Probabilities and Pedigrees PowerPoint presentation. Alternatively, students can collectively build an updated pedigree on the board and fill in genotype information.
  9. Have students work independently to show their understanding on questions 7-10 of the worksheet.

Concept Elaboration and Evaluation

Student worksheets can be gathered as a means of assessing student understanding. In addition, review and summarize the following key concepts:

  • Farmers and ranchers use their knowledge of genetics to select plants and animals that have ideal characteristics.
  • Variation is found in populations of plants and animals according to the distribution of various traits within a gene pool.
  • Using basic Mendelian genetics, the probability of an offspring inheriting a specific trait can be calculated.
  • Pedigrees can be used as a visual representation of the occurence of specific traits through multiple generations of parents and offspring.

We welcome your feedback! Please take a minute to tell us how to make this lesson better or to give us a few gold stars!


Suggested Companion Resources

Agricultural Literacy Outcomes

Culture, Society, Economy & Geography

  • Discuss how agricultural practices have increased agricultural productivity and have impacted (pro and con) the development of the global economy, population, and sustainability (T5.9-12.e)

Science, Technology, Engineering & Math

  • Identify current and emerging scientific discoveries and technologies and their possible use in agriculture (e.g., biotechnology, bio-chemical, mechanical, etc.) (T4.9-12.e)

Education Content Standards


Biotechnology Systems Career Pathway

  • BS.03.04
    Apply biotechnology principles, techniques and processes to enhance plant and animal care and production (e.g., selective breeding, pharmaceuticals, biodiversity, etc.).


HS-LS3 Heredity: Inheritance and Variation of Traits

  • HS-LS3-3
    Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.

Common Core Connections

Reading: Anchor Standards

    Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.
    Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.

Speaking and Listening: Anchor Standards

    Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.
    Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.

Mathematics: Practice Standards

    Reason abstractly and quantitatively. Students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
    Construct viable arguments and critique the reasoning of others. Students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.


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