Punnett Square for Sickle Cell disease and theoretical and experimental probability

In the United States about 100,000 people have the Sickle Cell disease and 2.5 million have sickle cell traits.
Source Center for Disease Control

Introduction

This page has information and activities to introduce the Punnett Square and the genetics of the Sickle Cell Disease (SCD) and explore theoretical and experimental probabilities of parents with different alleles, related to the disease, will have offspring with or with out SCD traits. Instructional suggestions, activities, worksheets, data sheets, and lab sheets are included.

Pedagogy suggestions

Focus questions

What is Sickle Cell Disease?
What has been the understanding and treatment of Sickle Cell Disease (SCD)?
What is theoretical and experimental probability?
What is a Punnett Square?
How can I use it to determine the probability of parents passing their traits or Sickle Cell Disease?
If there is a treatment, why does the disease persist?

Activity sequence

Ask. What is Sickle Cell Disease?
Share the introduction.
Ask. What has been the understanding and treatment of Sickle Cell Disease (SCD)?
Share the history.
Have the vocabulary or word bank available to introduce as questions arise as to the meanings of words in the introduction, history, or activities.
Ask. What is theoretical and experimental probability?
Punnett square activity. Share the Activity lab sheets
Ask what are all possible ways parents ight combine to have offspring?
Review the theoretical probability lab sheet to find all possible outcomes of parents offspring.
Assign each of six possible parent pairs for learners to use Punnett Squares to find the possible traits of their offspring.
Use the lab sheets with Punnett Squares to calculate the possible traits for the offspring of different pairs of parents.
1. Sample Answer Key: As x As
2. Sample Answer Key: AA x As
Share the results of the Punnett Squares for the six pairs of parents and the genetic outcomes for the offspring.

Six unique parent pairs with genetic outcomes

When you actually solve the Punnett squares for all 9 combinations, they consolidate into 6 uniquely distinct genetic outcomes. Here is the master breakdown for possible pairs of parents and the exact proportions for the offspring of any couple:

Parent Pair Group: What the Punnett Square Proves (Offspring Proportions)

1. AA x AA: 100% AA
(0% chance of passing on an s allele)

2. AA x ss
(or ss x AA): 100% As
(100% of children are carriers; 0% have the disease)

3. ss x ss: 100% ss
(100% of children will have sickle cell disease)

4. AA x As
(or As x AA): 50% AA : 50% As
(An equal split of normal and carrier outcomes)

5. As x ss
(or ss x As): 50% As : 50% ss
(An equal split of carrier and disease outcomes)

6. As x As
(Both Parents Carriers): 25% AA : 50% As : 25% ss
(The classic 1:2:1 genetic ratio)

Complete the experimental outcomes simulation lab.
1. Sample Experimental probability (Simulation)
Complete lab discussion and lab sheets.
Check your understanding of probability with this probability rubric
Considerations for grading
Distinctions of genetic and mathematical probability

Introduction

Sickle cell disease (SCD) is traced to one gene. The gene that makes hemoglobin, the protein in red blood cells that carries oxygen throughout the body. In the case of sickle cell the genetic mutation makes sickle-shaped red blood cells instead of normal round cells. These mishaped cells, clog small blood vessels, reduce oxygen tranported to organs, tissues, and cells. This blockage causes extreme pain and organ damage as they move through the body.

One severe example is Acute chest syndrome (ACS), which can be severe when sickle cells wedge into and damage the lung tissue as they move through them. With less oxygen flow, cells, tissues, and organs can fail and medical pathologies can arise. Ranging from anemia, jaundice, acute vascular necrosis to blindness, debilitating strokes, cognitive impairment, end-stage organ damage, and premature death. SCD is more common in certain ethnic groups, including people of African descent. Life expectancy varies considerably between 5 to 50 years, completely depending on the availability of advanced medical care. While historical treatment were mostly limited to palliative care (relieving symptoms without curing the condition) and blood transfusions, recent medical treatments related to genetic deletion and replacement of sickle cell genes can with healthy genes will hopefully offer better treatment options.

Sickle and normal red blood cells

History

1874, First clinical description of SCD as a blood disease. The physician Dr. James Africanus Beale Horton describes the first clinical descriptions of patients as having recurrent seasonal fevers, local pain crisis during rainy seasons and abnormal blood characteristics. Characteristics of SCD.
1949, First description of SCD as a molecular disease. Dr. Linus Pauling and his colleagues first show SCD as a blood disorder caused at the molecular level, by an abnormal β-globin protein chain in the oxygen-carrying molecule hemoglobin.
1956, First description of SCD as a genetic code mutation disease. Scientist Vernon Ingram shows the exact point of the genetic mutation that changes a negatively charged amino acid (glutamic acid) with an uncharged one (valine). Which causes hemoglobin chains to stiffen and collapse into the sickle cells shape.
Modern era, Molecular biologists discover that before humans are born, they have a gene that makes a healthy gene called fetal hemoglobin. Shortly after birth, a biological molecular switch is clicks off the fetal version and switches on the adult β-globin gene, activating the sickle cariant i homozygous individuals.

A therapy

2023, First curative treatment. The U.S. Food and Drug Administration (FDA) approved Casgevy and Lyfgenia, developed and manufactured by Vertex Pharmaceuticals and CRISPR Therapeutics. Casgevy, uses CRISPR-Cas9 gene editing act like a pair of molecular scissors. Instead of replacing the faulty gene, it snips the and deactivates the genetic pepressor switch. By breaking the switch, the patient's bone marrow restarts the production of healthy fetal heoglobin, bypassing the sickle mutatio entirely.

The challenge

While a scientific miracle, accessing these cures presents an economic and logistical problem. The base list price for the gene theraphy alone is $2.2 million (Casgevy) and $3.1 million (Lyfgenia) per patient. When you include the entire treatment, of weeks of hospitalization to harvest stem cells, intensive chemotherapy to clear out the bone marrow, and months of post-treatment recovery, then the total medical cost typically reaches $3 million to $4 million per patient, putting it far out of reach for the majority of global patients.

Source

Science. The History and Future of Sickle Cell Disease. by Adrian Woolfson. August 22, 2026. Includes a review of, Curved Air: A Biography of Sickle Cell Anemia and the Quest to Cure the First Molecular Disease.

Vocabulary - word band

Allele is an alternative sequence variation of a specific gene. Variations arise from mutations and dictate individual traits. At least one allele from each parent (sometimes more). Making at least two alleles for every gene.

Chromatin is the uncoiled, relaxed structural material composed of DNA, RNA, and associated scaffolding proteins that forms chromosomes during nuclear division cycles.

Chromosome is a highly structured, condensed molecule of DNA (deoxyribonucleic acid ) wrapped around structural proteins. Humans typically possess 46 chromosomes organized into 23 homologous pairs (one from each parent), making the full genome.

Gene is the locus of specific nucleotide sequences along a DNA strand that holds biochemical functional blueprints instructing cells on how to manufacture individual target proteins (e.g., adult β-globin).

Genome is the complete set of genes (consisting of chromosomes made of DNA) in the cell.

Genotype is the specific allelic pairing inherited at a particular locus (e.g., AA, As, ss) defining genetic architecture that determine a trait.

Phenotype is the outward, clinically observable physical features, physiological functions, or structural traits expressed by an organism resulting from its unique genotype and environmental interactions. Like: eye color, height, hair color, or anything, even different proteins.

Probability vocab

Probability is how likely it is that a specific event will happen. In math, we find this by writing a ratio (a fraction between 0 and 1).

Before an event (Theoretical): We compare the number of outcomes we are looking for to the total number of all possible outcomes.
Theoretical probability is the mathematical prediction of what should happen in a perfect scenario over infinite trials.

After an experiment (Experimental): We compare the number of times the outcome we are looking for actually happened to the total number of times we tried.
Experimental probability is what actually happens in a real-world test. They differ because real life is governed by random chance, and small sample sizes (like 20 flips) rarely match perfect mathematical averages

Determining probability

Probability is determined in one of two ways: theoretical and experimental. Either way: the probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event. Probability data sheet or data center.

This is for informational purposes only. For medical advice or diagnosis, consult a professional.

Explore the genetic nature with the following activities.

Activities

Lab Goal: to use Punnett Squares to systematically calculate and compare the theoretical probability of inheriting sickle cell traits against an active, and simulated experimental probability using coin flips.
Enjoy!

Theoretical probability lab sheet

Mendelian inharitance background information: Children always inherit one allele from each biological parent. And the matching pair dictates the child's absolute internal genotype and outward physical phenotype.

The two alleles that determine the genotype can be represented as A (normal) and s (sickle). The table below describes them and the different combinations possible.

Genetic key:

Allele / Genotype symbol	Bilogical expression & phenotype outcome
A	Dominate allele for normal, round hemoglobin production.
s	Recessive allele for sickle shaped hemoglobin production.
Possible pairings
AA (homozyygous dominate)	Normal red blood cells. Individual does not carry or pass on the sickle mutation. Normal
As or sA (heterozyygous / carrier)	Clinically healthy; has the sickle cell trait and can pass the s allele to offspring. Carrier / Trait
ss (homozyygous recessive)	Has sickel cell disease (SCD) all red blood cells are vulnerable to sickel cell disease. Sickle Cell Disease

To explore possible combinations and check to see if we have found all parent combinations, we can use a matrix (grid) where every possible father genotype(top row) is matched against every possible mother genotype (first colmn). This matching mathematically guarantees you map all 9 possible parent pairs:

All possible outcomes

	AA	As	ss
AA	Pair 1: AA x AA	Pair 2: AA x As	Pair 3: AA x ss
As	Pair 4: As x AA	Pair 5: As x As	Pair 6: As x ss
ss	Pair 7: ss x AA	Pair 8: ss x As	Pair 9: ss x ss

Note: Biologically, AA x As and As x AA yield the exact same offspring ratios, but tracking them as separate pairs ensures your population math remains proportionaly accurate.

Summary

By using the 3x3 Parent Grid to identify the cross, and then applying one of the 6 master outcomes, you will never miss a combination and you will know the exact baseline probability for the specific outcomes you are looking for.

To find out the allell pairs of two parents offspring for these six possible combinations we can use a Punnett Square to determine them.

Punnett Square - Scenario one

Suppose two people who are both carriers for the sickle cell trait decide to have children. Both the mother and father have the heterozygous genotype: As.

Use what you have learned and the rule of dominance below to comlete the standard Punnett Square for this parental pairs As x As:

The Rule of Dominance

The Capital Letter Goes First: We always write the dominant allele (capital letter) before the recessive allele (lowercase letter).
No Order of Inheritance: The final genotype is written to show what alleles are present, not the order in which they were handed down. Because of this, any "unset sA " combination is automatically flipped to unset As as a standard spelling rule in biology.

Punnett Square blank

Based on your Punnett Square matrix, write the exact theoretical mathematical probabilities as a fraction and percentage:

1. What is the probability of these parents having an offspring born with Sickle Cell Disease (ss)?