**It has been over** thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but do you know why there is still an officially designated exclusion zone? The Chernobyl Disaster Task (see Figure 1) combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.

Mathematical modeling is “a process that uses mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena” (Garfunkel and Montgomery, 2019, p. 8). Mathematical modeling tasks provide multiple points of entry for students, many solution pathways, and the opportunity for students to express various ways of thinking as they use mathematical reasoning to justify their models. Integrated mathematics and science modeling tasks, like the Chernobyl Disaster Task, offer a way to make difficult-to-study, real-world phenomena accessible for a rich and authentic learning experience (Hjalmarson et al., 2020). Following a description of the task’s implementation with high school students, we will offer insights to support you in using this task with your students.

## CHERNOBYL DISASTER TASK

To begin, the teacher facilitates a class discussion to formatively assess students’ prior background knowledge of the event. Students then view a video and images of the aftermath (see video from Radio Free Europe/Radio Liberty [2016], Slideshow 1 [link online]), providing additional background information. Students wonder about the effects of the radioactive substances based on these discussions. Students are provided with the task (Figure 1) and a spreadsheet with radioactive substances data (Figure 2). A class discussion follows about when a radioactive substance is considered safe (when the amount falls below the exposure limit).

*Sample of Radioactive Substances From the Spreadsheet Given to Students*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Sample of Radioactive Substances From the Spreadsheet Given to Students*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Sample of Radioactive Substances From the Spreadsheet Given to Students*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

Students work in teams to address the task. Students are provided further information, including data on river and tree contamination, health effects, and reducing efforts. Students make assumptions (e.g., whether most impactful refers to health effects or the environment) and use a variety of tools (e.g., spreadsheets, Desmos) to create and justify their solution. This task concludes with student presentations.

### The Science and Mathematics of Chernobyl

The Chernobyl Disaster Task provides a real-world context for mathematics learning connected to both mathematics and science practice and content standards (Figure 3). Engaging in this modeling task provides opportunity for students to engage in many of the practice standards of both mathematics and science as they use models to understand the impacts of the Chernobyl disaster.

*The Standards Addressed by the Chernobyl Disaster Task*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Note.*Sources: National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010; NGSS Lead States, 2013.

*The Standards Addressed by the Chernobyl Disaster Task*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Note.*Sources: National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010; NGSS Lead States, 2013.

*The Standards Addressed by the Chernobyl Disaster Task*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Note.*Sources: National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010; NGSS Lead States, 2013.

This task affords exploration of the chemistry of radioactive decay and half-life (i.e., the time it takes for half a radioactive substance to decay) (Britannica, 2022; NGSS Lead States, 2013; HS-PS1-8), and the life science of matter and energy flowing through an ecosystem (HS-LS2-4). This task also addresses the impact of humans on the natural world, providing opportunities for students to design creative solutions to reduce and mitigate human impact (HS-LS2-7).

As the students explore the science of the Chernobyl disaster, they create conjectures about the impact of each substance and explore the mathematics of exponential functions (NGSS Lead States, 2013; HSF.LE.B5) through the context of half-life. In Algebra 1, students have the prior knowledge to evaluate exponential expressions to determine the amount present today and to solve a system of equations graphically (HSA.REI.C6) to determine when there would be an amount left that is below the exposure limit. In Algebra 2, students can engage in a similar approach, with the addition of also applying their knowledge of logarithms to solve exponential equations algebraically. By engaging with real-world values of the parameters of equations, students can explore the impact of the parameters on the formulas. For example, students are provided with half-life values in hours, days, or years and need to convert data values to a single time unit to be able to compare the effects of the half-life formula between substances.

## IMPLEMENTATION OF THE TASK IN THE CLASSROOM

This task has been successfully implemented in both Algebra 1 and Algebra 2 classrooms. Student approaches to this task have varied: some students chose three substances at random, used the half-life formula to calculate how much is present today, created graphs to determine when a safe exposure limit occurs (Figure 4), and then evaluated the validity of their choices. Others started by investigating effects of individual substances to determine their choices and then engaged in mathematics to justify their selection. In Algebra 1, students are afforded the opportunity to wonder about how to solve for an exponent in exponential equations, which provides a motivation for learning about logarithms in Algebra 2. We have seen that Algebra 1 students can graphically determine when a radioactive substance is safe by using a system of equations (Figure 5), and Algebra 2 students can solve algebraically using logarithms (Figure 6).

*Examples of Students Determining the Amount Present Today Using Half-life Formula*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Examples of Students Determining the Amount Present Today Using Half-life Formula*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Examples of Students Determining the Amount Present Today Using Half-life Formula*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Examples of Students Using Desmos to Determine the Exposure Limit Graphically*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Examples of Students Using Desmos to Determine the Exposure Limit Graphically*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Examples of Students Using Desmos to Determine the Exposure Limit Graphically*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Example of Algebra 2 Student Determining Exposure Limit Algebraically Using Logarithms*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Example of Algebra 2 Student Determining Exposure Limit Algebraically Using Logarithms*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Example of Algebra 2 Student Determining Exposure Limit Algebraically Using Logarithms*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

In addition to the mathematics, students also have the opportunity to learn about different radioactive substances and their impact. Because the term *impact* is open to interpretation, students must define their version of the term. Students’ definitions of *impact* may refer to the measurable effect on people, animals, the environment, the community, the future, or a combination of these. Students can use their science knowledge to aid in researching and defining the various factors that may be impacted. The task’s open-ended nature results in multiple solutions from students. For example, some teams selected Caesium-137 as the most impactful substance because of its environmental impact and impact on people, while other teams argued Plutonium-242 to be the most impactful (Figure 7). Once students present and defend their solutions, it can be shared that the International Atomic Energy Agency (2016) considers iodine, strontium, and caesium to be the most dangerous because of their health impacts and long-lasting effects.

*Two Teams’ Justifications of Why Plutonium is Most Impactful*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Two Teams’ Justifications of Why Plutonium is Most Impactful*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

*Two Teams’ Justifications of Why Plutonium is Most Impactful*

Citation: Mathematics Teacher: Learning and Teaching PK-12 117, 5; 10.5951/MTLT.2023.0271

### Supporting Implementation

In this task, students may face challenges working with exponential functions and radioactive decay. Students struggle when there are fractions in the exponent, such as the half-life formula. This formula is complex, and students may need to be guided in using it effectively, graphically and algebraically. Students may struggle with determining when each substance will reach the exposure limit. Teachers should support students by offering tools like Desmos to solve graphically. Many students struggle with interpreting decimal notation and, as a result, misinterpret scientific notation. To assist with this, we recommend that students have a lesson before this task on scientific notation.

Students may struggle with the science component of this task if they do not have an adequate understanding of radiation and radioactivity. One way is for the teacher to co-plan and enact this task with a science teacher, who could provide a lesson about radiation and radioactivity and be there to support students as they engage in the task. Alternatively, the teacher could provide extra information and resources (in addition to the ones provided in the task) to the students. Even with a limited background knowledge of science, students will still be able to successfully engage in this task.

## CONCLUSION

The Chernobyl disaster is a real-world, high-cognitive demand mathematical modeling task, which integrates mathematics and science content for Algebra 1 and Algebra 2 students. Radioactive decay is one of the many scientific applications of exponential functions (e.g., viral spread and population growth). As Magaletto (2021) showed with the viral marketing activity, real-world exponential modeling activities can promote critical thinking and problem-solving skills. When students navigate the real world through mathematical and scientific lenses, their learning builds meaningful connections between the two disciplines. Through this task, students can learn to make assumptions, collaborate with others, and justify their mathematical thinking. While student experiences may be enhanced if students have background knowledge about radioactive substances, it is not a requirement to engage in the mathematics of the task because mathematical modeling is not only a vehicle for applying prior knowledge, but also one for learning about new content. _

## REFERENCES

Britannica. (n.d.). Half-life. In

*Encyclopedia Britannica*. Retrieved December 30, 2022 from https://www.britannica.com/science/half-life-radioactivityGarfunkel, S., & Montgomery, M. (Eds.). (2019).

*GAIMME: Guidelines for assessment and instruction in mathematical modeling education*(2nd ed.). Consortium for Mathematics and Its Applications & Society for Industrial and Applied Mathematics.Hjalmarson, M. A., Holincheck, N., Baker C. K., & Galanti, T. M. (2020). Learning models and modeling across the STEM disciplines. In C. C. Johnson, M. J. Mohr-Schroeder, T. J. Moore, & L. D. English (Eds.),

*Handbook of research on STEM education*(pp. 223–233). Taylor & Francis.International Atomic Energy Agency. (2016).

*Frequently asked Chernobyl questions*. https://www.iaea.org/newscenter/focus/chernobyl/faqsMagaletto, R. (2021). Engaging students through modeling.

*Mathematics Teacher: Learning and Teaching PK–12*, 114(2), 125–131. https://doi.org/10.5951/MTLT.2020.0025National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010).

*Common core state standards for mathematics*. https://www.thecorestandards.org/MathNGSS Lead States. (2013).

*Next generation science standards: For states, by states.*The National Academies Press. https://doi.org/10.17226/18290Radio Free Europe/Radio Liberty. (2016).

*The Chernobyl disaster: How it happened*[Video]. https://www.youtube.com/watch?v=f5ptI6Pi3GA

**Geena Taite**, she/her, taiteg1@montclair.edu, is a PhD candidate in mathematics education at Montclair State University in Montclair, NJ, and teaches high school mathematics at the Diana C. Lobosco STEM Academy in Wayne, NJ. She is interested in mathematical modeling and teacher professional development.

**Helene Leonard**, leonardh2@montclair.edu, is an adjunct professor, research assistant, and PhD candidate in mathematics education at Montclair State University. Her research interests include professional development, mathematics infusion, and equity in mathematics education.

**Amanda Provost**, she/they, provosta1@montclair.edu, is a PhD candidate in mathematics education at Montclair State University. She is interested in studying mathematical modeling, STEM education, and teacher professional development.

**Nicole Panorkou**, panorkoun@montclair.edu, is an associate professor in the department of mathematics at Montclair State University. She is interested in the ways that technology, modeling, and STEM integration can foster the utility of mathematical concepts and teaches graduate classes on the teaching and learning of math modeling in K-12 education.