# Outbreak: Analyzing An Epidemic Using Quadratic Functions

 Author: Caitlin Halkiu Unit Title: Outbreak: Analyzing An Epidemic Using Quadratic Functions Grade: 8 Subject: Algebra 1 Estimated Duration: 7 days Unit Activities: Activity 1: Epidemic Activity 2: Epidemic Simulation Activity 3: Investigating Regression Curves for a Cure Activity 4: Presenting a Cure Date: June 28, 2017
###### The Big Idea (including global relevance)

Investigating treatment of epidemics and their impact on society.

When everything goes as predicted in life, all is well.  But when there is a disruption, the potential for chaos increases.  In the United States in the 19th century, there was a tuberculosis (TB) epidemic.  TB is a contagious disease and preventing its spread became the motivation foe the first large scale public health campaign.  In the 1940s, antibiotics were developed and they provided a more efficient method to diagnosis TB.  Today many diseases which were previously epidemics are prevented through vacinnations.  Other epidemics include yellow fever, cholera, small pox and cholera.

Mt Pleasant, Ohio was founded in 1817 was renamed Mt. Healthy following a cholera epidemic in which many of its citizens survived while those in the surrounding area (Cincinnati) did not.  Cholera is spread by drinking water or eating food contaminated with human feces.  Since Mt Healthy has a higher elevation than other parts of the city, the people there did not come in contact with the same drinking water.

###### The Essential Questions:

What is an epidemic

What are some solutions?

What are potential side effects of solutions?

How do doctors, researchers, etc. determine the best solution to an epidemic?

Justification for Selection of Content:

✓ Students previously scored poorly on standardized tests, end-of term test or any other test given in the school or district on this content.

✓ Misconceptions regarding this content are prevalent.

✓ Content is suited well for teaching via CBL and EDP pedagogies.

###### Misconceptions:
• Analyzing graphs that do not have the same intervals, but assuming they do.
• Determining that the quicker something reaches zero on a quadratic the better it is without think of the context of what zero means.

###### The Challenge and Constraints:

 Description of Challenge (Either Product or Process is clearly explained below): List the Constraints Applied Students must analyze given data on three different treatment approaches.  They may use their own bias in deciding what approach is best and support their decision with mathematical evidence and reasoning.  They will revise their treatment plan based on a “role card” they will be provided.  They will re-analyze the data and alter their treatment plan for that individual on their role card. time plan must align with role card must choose between 3 treatment types
###### Anticipated Guiding Questions (that apply to the Challenge and may change with student input.):
• What is an epidemic?
• What are the treatments?
• How quickly do the treatments work?
• Do the treatments work forever?
• Is there a possibility of a future outbreak?
• How can we treat the most people quickly and potentially inexpensively?
• How does someone decide what the best treatment is?
• Is the best treatment the same for everyone or does it change?
• Does it need to be treated to go away or can it go away over time?
###### Engineering Design Process (EDP):

How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.

Students will share their plan through a class discussion.  They will offer feedback on the feasibility of their treatment plan and the “public” opinion of their treatment plan.  Students will revise their treatment plan based on feedback from other students and input from a role playing card that better represents an overall public opinion on treatment options and the epidemic.

How will students present or defend the solution?  Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.

Student will present their treatment plans to their class in a formal presentation.  Students will attempt to convince their classmates that their treatment plan is the most effective using mathematical evidence and reasoning.  Students must use visuals to support their plan.

What academic content is being taught through this Challenge?

###### ACS (Real world applications; career connections; societal impact):

Real world applications:

This strongly applies to the real world because there are constantly diseases in the world that need to be analyzed and treatment arranged.  There are many types of treatments that have benefits and consequences.

What activities in this Unit apply to real world context?

Activity 2 and 3

Societal Impact:

­­­­­­­­­­­­­­I think this is strongly showing societal impact because there are always new epidemics and old epidemics that return.  Each time the public looks to teams of doctors and researchers to determine the best solution to this epidemic.

What activities in this Unit apply to societal impact?

Activity 3

Careers:  What careers will you introduce (and how) to the students that are related to the Challenge? (Examples: career research assignment, guest speakers, fieldtrips, Skype with a professional, etc.)

• Biomedical engineering

###### Next Generation Science Standards (NGSS):

Science and Engineering Practices:

Crosscutting Concepts:

###### Ohio’s Learning Standards for  Math (OLS) or Common Core State Standards -- Mathematics (CCSS)

☒ Make sense of problems and persevere in solving them

☒ Reason abstractly and quantitatively

☒ Construct viable arguments and critique the reasoning of others

☒ Model with mathematics

☒ Look for and make use of structure

###### Post Implementation- Reflection on the Unit:

1)Why did you select this content for the Unit?

I selected this content for this unit because quadratic regression is not supported well in our curriculum and students frequently struggle with it.

2) Was the purpose for selecting the Unit met? If yes, provide student learning related

evidence. If not, provide possible reasons.

The purpose of the unit was met.  Student post test scores averaged 90% following implementation of the unit.  Students showed a significantly greater understanding of quadratic regression and analyzing data from regression plots.  Students were able to give thorough presentations of their data that supported their conclusion.

3) Did the students find a solution or solutions that resulted in concrete meaningful action for the

Unit’s Challenge? Hyperlink examples of student solutions as evidence.

Yes, students were able to find a solution that resulted in concrete meaningful action for the challenge.  Students were able to understand bias and how bias can be used to skew data for various audiences. Students had meaningful conversations around bias, possible solutions, and creating a final solution that would support society as a whole.

4) What does the data indicate about growth in student learning?

The pre and post assessment data supported growth in student learning.  On the pre assessment students scored an average of 40%, and an average of 90% on the post test.

5) What would you change if you re-taught this Unit?

If I retaught this lesson I would add a couple more days to the unit.  We had a really good opportunity to investigate piecewise functions, rate of change in non-linear functions, and x-intercepts.  We were able to discuss these to a point but the students did not have a deep enough understanding to create a strong argument based on any of those topics.  I think this project would be even more powerful if we were able to add a couple days to dig deeper.

6) Would you teach this Unit again? Why or why not?

I would teach this unit again.  It went over really well and the students were able to connect to it.  It was also very powerful because our 8th graders talk about the Black Plague in Social Studies class and genes and traits in Science class that allow humans to survive various things.