Other subject areas to be included, if any: environmental science

Key Knowledge and Understanding

(CCSS or other standards)

8.F.1 – Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.2 – Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

8.F.3 – Interpret the equations y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
8.F.4 – Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situations it models, and in terms of its graph or a table of values.
All 8 mathematical practices

Success Skills

(to be taught and assessed)

Critical Thinking/Problem Solving - students will use various types of reasoning (induction, deduction, etc) to make predictions about linear functions in context to this particular problem as well as other examples. They must also analyze how parts of a whole interact with each other to produce common outcomes in complex systems using conventional and innovative strategies.

Self-Management – Throughout this unit, students will develop self-confidence, self-reliance, responsibility, and independence. They will exhibit persistence and effort, goal setting, time management and organization, and study skills in order to be successful with the content and learning.

Collaboration - – students must demonstrate the ability to work meaningfully, respectfully, and effectively with other students in various grouping situations. They must also exercise flexibility and willingness to make compromises to accomplish a common goal.

Other: Global awareness / environmental literacy – students will work collaboratively with diverse cultures, religions, and lifestyles in a spirit of mutual respect in order to come to common conclusions and understandings about the state of our environment and the circumstances and conditions affecting it. Information, Media, and Technology Skills – Access and evaluate information, use information accurately and creatively for the issue or problem at hand, use technology as a tool to research, organize, evaluate, and communicate information.

Project Summary

(include student role, issue, problem or challenge, action taken, and purpose/beneficiary)

Topic: Deepwater Horizon Oil Spill

Information Source: http://www.cnn.com/2015/04/14/us/gulf-oil-spill-unknowns/index.html

Introductory Paragraph

Scenario: In April of 2010, high-pressure methane gas from the Deepwater Horizon well expanded in the drilling riser and rose into the drilling rig where it ignited and exploded, engulfing the platform. 94 crew members were rescued and 11 were never found. Following the explosion and sinking of the Deepwater Horizon oil rig, the oil gusher continued to flow for 87 days until it was capped. Due to the months-long spill, extensive damage to marine and wildlife habitats were reported.

Paragraph 1

On April 20^{th}, 2010 in the gulf of Mexico, a final cement seal of the oil rig Deepwater Horizon failed to stop a leak that caused the worst environmental disaster in U.S. history taking the lives of 11 rig workers. For 87 days straight, oil and methane gas continued to poor out for the uncapped well that was located well over a mile below the surface of the ocean. The federal government has estimated that 4.2 million barrels of oil spilled in the Gulf of Mexico, but BP was found to only be responsible for 3.1 million barrels by a ruling judge in the case.

Paragraph 2

Environmentalists knew that they must prepare for an environmental collapse on a massive scale. Scientists still continue to study the environmental effects 6 years later. The long-term negative effects remain unclear and are, in many cases, highly disputed. The spill area hosts 8,332 species of fish, birds, mollusks, crustaceans, sea turtles, and marine mammals. There were many immediately negative impacts to the environment right after the spill to the wildlife and the people around the spill.

Statement

The implications of a large scale oil spill such as the Deepwater Horizon incident are highly dangerous. If operators had taken more care in reporting errant test reading and developing a better response system, they may have been able to prevent this catastrophic event.

BP ended up settling out of court for the amount of oil that they were responsible for leaking. How would the court have benefited from a mathematician going on the stand against BP? What kind of numbers or information might they have been able to give so that BP could be held responsible? What different options did the operators have at their disposal and which one would have been the best choice mathematically?

Task:

Make a real problem for students. Give them a role. Provide a goal and expectation. This task includes:

Role: You are a leading mathematician and consultant for environmental linear models that is advising on potential oil spills around the world. British Petroleum is expecting to begin pumping oil from a newly discovered prospect and would like to use your expertise to build a model for the rate of flow of the oil. A group of environmentalists has also requested your expertise in predicting what kind of damages can occur in the radius of the town for evacuation purposes should the people in the town need to be warned.

Goal: Create a model of the oil flow so that operators will know in case of emergency when they need to shut particular valves off and what measures need to be taken in order to respond to the situation.

Driving Question

What kind of tools or models could the court have benefited from in order to hold BP fully responsible for their actions? What are your predictions about the difference in money that a model could have determined they would have to pay and what they actually paid? Why would it be important to know how much oil leaked into the ocean? How can we calculate that amount given the information that we already have about the leak? What system of checking would you suggest in order for the employees to have gotten more accurate information? What do think is the environmental effect of the oil leaking into the ocean, the beaches, and surrounding areas? How long will it take for things to go back to normal for these elements? How much methane had leaked out by the time the explosion took place?
Essential Question: How can linear models help us to make accurate predictions?

Entry Event

I will start with a demonstration of filling a cup with water at a constant rate and ask students to make predictions about when it will overflow and at what rate the water is going into the cup. They will then be able to time me and ask me how much water, etc. in order to calculate the rate. I will then segue way into the problem scenario.
A video introduction will be shown about the 2010 BP oil spill. The video gives details regarding the numbers associated with the BP oil spill and a short reflection of the environmental impacts that occurred as a result. https://www.youtube.com/watch?v=gvuzuyEKLd8

Also, a CNN news source on the story: https://www.youtube.com/watch?v=zcZ9MLDuIl0

Products

Individual: Students will write a letter to deliver to the CEO of an environmental agency outlining the given problem, their research, and popular solution (model).

(During the Project) BP and other businesses, companies who work with oil

(End of Project) CEO of an environmental agency

Resources Needed

On-site people, facilities: none

Equipment: Access to a computer lab for research and building of linear models online, analyzing data

Materials: video to be shown on smartboard, Carnegie Learning Materials, Example models, Graphing calculators and applications, data on effects and rates surrounding the given scenario

(how individual, team, and/or whole class will reflect during/at end of project)

Journal/Learning Log - students will be required to keep an interactive notebook for the duration of the class. The notebook will be used for reflections via journaling thoughts daily about progress made and questions that they still have.

X

Focus Group

Whole-Class Discussion - many times there will be learning opportunities that can be taken advantage of in the classroom via whole-class discussion. If all groups are having a similar issue with the project, then it will be necessary to clarify in this type of format.

X

Fishbowl Discussion

Survey

Other: student created rubric for collaboration - all students will be required to create a rubric that each member of their group will be rated on for part of their group project grade. It is important for students to know what their classmates’ expectations of them are in the group work process and not just what the teacher’s expectations are.

X

Notes:

Project Design: student Learning Guide

Project: Deepwater Horizon Oil Disaster

Driving Question: How can linear models help us to make accurate predictions?

provided by teacher, other staff, experts; includes

scaffolds, materials, lessons aligned to learning outcomes and formative assessments

(individual and team):
Students will have a chance to view the BP oil spill videos again. They will then have the opportunity to create a linear model with a group in order to solve the given problem and answer all rubric questions.

8.F.1 – understanding functions – To determine whether a relationship is a function, students should be expected to reason from a context, a graph, or a table, after first being clear which quantity is considered the input and which is the output. When a relationship is not a function, students should produce a counterexample: an “input value” with at least two “output values”. If the relationship is a function, the students should explain how they verified that for each input there was exactly one output.

Quiz over terms and ideas
Sorting activity where students cut out a series of graphs and sort them into categories of functions vs. non-functions
Analysis of graphs, tables, and mapping diagrams

Chapter 3 in student textbook with worked examples
Several illustrations of functions and non-functions
Vocab picture drawing diagram for understanding (can provide copy if needed)
Peer editing

8.F.2 – comparing two functions – students should be able to examine the graphs of linear functions analyze or compare at least two functions at the same time. They will compare two different situations and identify which is increasing/decreasing as a faster rate.

Illustrate with a slope triangle, 3 different rates of change in interactive notebook
Explain in your own words what rate of change is (not using the formula)

Use of graphing calculators and/or computer software to analyze and compare two or more linear functions
Activity analyzing two different pizza companies and what they charge for pizza toppings. Which one is considered a “greater rate of change”?

8.F.3 – linear as slope intercept form y = mx +b. – Students recognize that points on a straight line will have the same rate of change between any two of the points.

Use plickers to get a quick assessment of students understanding of y-intercept and rate of change as found in an equation, graph, table, and verbal scenario throughout the lesson and at the end of the lesson.
Teacher created quiz if time allows

Matching activity to connect and compare multiple representations of the same function; slope is defined and the slope-intercept from of a linear equation is also introduced.
Slope intercept foldable in interactive notebook

8.F.4 – modeling linear relationships – students use slope and intercepts to write linear functions in the form y = mx + b. Situations may be given as verbal description, two ordered pairs, table, graph, or rate of change and another point on the line. Students interpret context of the situation.

Have students create their own written scenario to include a y-intercept and rate of change that can be represented by a graph, table, and equation.

Gallery walk for students to go around at look at each other’s examples of real world scenarios. They will be provided with stickers to use on other student’s scenarios that they feel are correct in all aspects (graph, table, and equation).

Students will have a chance to view the BP oil spill videos again. They will then have the opportunity to create a linear model with a group in order to solve the given problem and answer all rubric questions.