Next Generation Science Standards

Performance Expectation

Apply concepts of statistics and probability to explain the variation and distribution of expressed traits in a population.

• Clarification Statement: Emphasis is on the use of mathematics to describe the probability of traits as it relates to genetic and environmental factors in the expression of traits.
• Assessment Boundary: Assessment does not include Hardy-Weinberg calculations.

It all started with persistent Mendel and his peas. He found that, due to a single gene, pea traits are inherited in a mathematically predictable way; not too shabby for someone who didn't even know what a gene actually was. Dominant and recessive alleles, combined during reproduction, dictate a number of human traits and students can learn to model patterns in trait expression caused by one or more genes.

This performance expectation covers basic probabilities, Mendelian genetics, and chi-square statistics, and it ties these topics together with population genetics. As far those Hardy and Weinberg dudes, they'll have to wait because they're not covered here.

It's going to take a solid understanding of basic genetics in order for students to perform mathematical calculations that solve genetics problems. To tackle this performance expectation, you can start with basic probability exercises, work through some Mendelian-type examples, incorporate some harder statistics for individual inheritance patterns, and build up to attack population-level trait distribution problems.

Here are some handy-dandy activity ideas and resources to guide your teaching from the basics to the harder stuff:

• When it comes to genetics and probabilities, it doesn't get more on-the-nose than Punnett squares. Have students examine their own family trees for Mendelian traits they can study, then have them reverse-engineer the probabilities for particular combinations of alleles for various members of their family.
• The coin-toss: a perfect analogy for the chances of getting different allele combinations during sexual reproduction. You can have students follow a trait (like an allele for indestructible nose hair) through the generations by flipping a coin, then comparing its prevalence in their results to other students'.
• Sickle cell anemia is a serious human disease caused by a single gene. The Howard Hughes Medical Institute has created resources on a bunch of genetics topics, including pedigrees and chi-square statistics. It introduces the effects of the environment—malaria—on positive selection for the sickle cell trait.

Disciplinary Core Ideas

LS3.B – Variation of Traits: Environmental factors also affect expression of traits, and hence affect the probability of occurrences of traits in a population. Thus the variation and distribution of traits observed depends on both genetic and environmental factors.

The main focus of this performance expectation is to apply stats and probability to variation in traits, but students should know that DNA isn't the end-all-be-all when it comes to the expression of traits. Sure, genes are a big part of it, but the environment plays a big part in it, too. Beyond driving natural selection, the environment can cause some traits to be expressed and others to be repressed.

A simple example would be exposure to light causing pigmentation. Bask in the sun (with sunscreen, of course), and fairer-skinned folk can get a rockin' tan. No exposure to light and they're left with pasty skin. Yum. Same deal with fur color in some animals and quite few other examples.

The moral of the story is that while things like Punnett squares are great for predicting the expression of traits, it's certainly not perfect, because the environment likes to throw curveballs.

Science and Engineering Practices

Analyzing and Interpreting Data: Apply concepts of statistics and probability (including determining function fits to data, slope, intercept, and correlation coefficient for linear fits) to scientific and engineering questions and problems, using digital tools when feasible.

Here comes the math. This performance expectation really taps into the opportunities for your students to gather empirical data and use algebra to understand trait patterns in populations. At the most basic level, they can figure out probabilities of dominant and recessive traits being expressed using Punnett Squares.

The most awesome thing you can teach your students—something that will serve them well in any area of science—is the chi-square distribution. Relatively simple statistical tests using this distribution are unbelievably powerful, because they can show students how well their data fits a distribution, whether there are differences between experimental groups, and the likelihood that their observed effect is really real.

Also, although Hardy-Weinberg on the face of it would fit well with the goals of this performance expectation, students won't need to know how to do the actual calculations on formal assessments. So how can we fit more math practices into this performance expectation?

This Excel spreadsheet calculator tying together the chi-square test and the Hardy-Weinberg theorem spares students the fuss of doing calculations by hand and instead allows them to focus more on patterns and the bigger picture.

Crosscutting Concepts

Scale, Proportion, and Quantity: Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth).

At their core, the subjects of single- (Mendelian) and poly-gene inheritance, heritability, and response to selection are mathematical descriptions of how traits are passed along and distributed in a population. As we get deeper into the distribution of traits, it stands to reason that the math can get a bit more complex than simple ratios or percentages.

Just remember, this performance expectation doesn't include Hardy-Weinberg calculations, so no need to punish your students.

Science is a Human Endeavor: Technological advances have influenced the progress of science and science has influenced advances in technology.

Students should know that scientific discoveries are made by people who develop and use technologies (instrumentation, protocols, and tools). These scientists inform the direction speed at which science advances. 20th and 21st century techniques like the polymerase chain reaction (PCR) and high-throughput genome sequencing have greatly accelerated the progress of genetics as a field. This progress, in turn, informs the questions scientists ask and the types of technologies that need to be developed in order to address those questions.

Science is a Human Endeavor: Science and engineering are influenced by society and society is influenced by science and engineering.

Ah, to be a student again and not have to worry about student loans, continuing education, staff meetings, and parent-teacher confrontations…. Feel free to burst that bubble with a dose of real life.

Students should know that available funding, politics, public opinion, and information coming from the media and the internet all influence how and what type of science is done, who gets to do the research, where research can be performed, and who benefits from scientific discoveries. The progress of gene therapy, for example, has been affected by to politics, public opinion, and the types and amount of information available for people to educate themselves about its risks and benefits. Because funding and public support have increased in recent years, some of the basic research has translated into clinical trials, benefiting the population's health.

The interplay between science and society is complex, especially with a topic like genetics where we are fiddling around with life. It is important to carefully monitor the ethical implications of this type of work; do you really want to see mutant clones walking around?