## PBI Unit:

INFECTIOUS DISEASES

Ms. Tiedeman, Mr. Espino-Guerrero, and Mr. Rodriguez

**Introduction**

Viruses are the cause of many illnesses across the world ranging from the common cold to ebola. Students need to be aware of how these illnesses spread and how infectious they are. In order to accomplish this, students will be tasked with creating an informative website on a specific illness. These illnesses will include the common cold, influenza, warts, HIV/AIDS, smallpox, and ebola. The students will combine the subjects of Biology and Algebra 1 in order to describe how the illness spreads, model the growth of the illness, and describe preventative precautions.

"Project-based learning allows students to learn by doing and applying ideas. Students engage in real-world activities that are similar to the activities that adult professionals engage in. Project-based instruction is a form of situated learning and it is based on the constructivist finding that students gain a deeper understanding of material when they actively construct their understanding by working with and using ideas" (Krajcik & Blumenfeld 2006).

**Five Essential Elements of PBI:**

Is this unit relevant?

Recently ebola has made an impact on our society. Not too long before that, swine flu was the main concern. Illnesses are ever changing and make an impact on our daily lives. It is important to understand what causes these illnesses and what precautions need to be taken.

Are the students engaging in Inquiry?

The students will participate in four main investigations throughout the unit. In these investigations the students will discover exponential functions, difference between prokaryotic and eukaryotic cells, the structure of virus cells, and the relation between exponential and logarithmic functions. For further see Investigations page.

Is there collaboration?

The students will be working in groups in order to come up with reasonable models for virus growth and reasonable precautions for the virus.

Are the students making use out of technology?

The students will have access to graphing calculators and will be using Microsoft Excel in order to explore exponential and logarithmic functions. They will also be using microscopes to explore different cell types.

What will the students be creating?

The artifact for this unit will be the websites created by the students. The websites will allow the students to share what they learned about cell types and how viruses grow. They will apply this knowledge in order to inform their community about infectious diseases and what precautions need to be taken if a person were to be infected.

**TEKS and Objectives**

**Math (Algebra 1)**

**TEKS:**

1. Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

a) apply mathematics to problems arising in everyday life, society, and the workplace;

b) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;

e) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

9. Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to:

a) determine the domain and range of exponential functions of the form f(x) = ab^x and represent the domain and range using inequalities;

b) interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab^x in real-world problems;

c) write exponential functions in the form f(x) = ab^x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

d) graph exponential functions that model growth and decay and identify key features, including y-intercept

e) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.

**Objectives:**

Students will be able to:

- Manipulate variables in an exponential equation to change the function from a growth to a decay function
- Use exponential functions in order to explain how the amount of virus cells and people infected increase over time
- Create graphs using technology to model the growth of a virus and people infected
- Write exponential functions using the R0 value of a disease
- Create a reasonable precautionary plan using evidence from calculated data

**Science (Biology)**

**TEKS:**

4. Science concepts. The student knows that cells are the basic structures of all living things with specialized parts that perform specific functions and that viruses are different from cells. The student is expected to:

a) compare and contrast prokaryotic and eukaryotic cells;

b) investigate and explain cellular processes, including homeostasis, energy conversions, transport of molecules, and synthesis of new molecules; and

c) compare the structures of viruses to cells, describe viral reproduction, and describe the role of viruses in causing diseases such as human immunodeficiency virus (HIV) and influenza.

5. Science concepts. The student knows how an organism grows and the importance of cell differentiation. The student is expected to

a) describe the stages of the cell cycle, including deoxyribonucleic acid (DNA) replication and mitosis, and the importance of the cell cycle to the growth of organisms; Readiness Standard

c) describe the roles of DNA, ribonucleic acid (RNA), and environmental factors in cell differentiation; and Supporting Standard

d) recognize that disruptions of the cell cycle lead to diseases such as cancer.

**Objectives:**

Students will be able to:

- Describe the differences between prokaryotic, eukaryotic, and viruses
- Explain normal cellular function of different cells
- Describe the process of how viruses infect host cells
- Explain how Viral DNA goes through the lytic and the lysogenic cycle
- Recognize that disruptions of the cell cycle lead to diseases

**Common Alternative Conceptions**

Many misconceptions in algebra have to do with solving equations and solving for one variable. This can pose a problem when trying to understand exponential and logarithmic functions. Another misconception students have is about the rate of change of these functions, especially since the rate of change depends on the exponent. In biology, some students find it difficult to understand how viruses live "a borrowed life" and why they are not considered to be alive. Students may also find it difficult to understand how viroids and prions can act as infectious agents to spread disease. Bell ringers, exit slips, and formative assessments will allow the teacher to visualize student thinking in order address these misconceptions and fix them before the end of the unit.