Lesson Title: Islands PBL
Grade level: 7th and 8 th grade

The teacher may select from any of the objectives below, depending on her or his focus for the lesson. Included are some of those found in implementation to be most relevant to the activity.

Ohio Mathematics Academic Content Standards Grade Level Indicators:

Patterns, Functions and Algebra

Grade 7:

• Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions.

Grade 8

• Relate the various representations of arelationship; i.e. relate a table to graph, description and symbolic form.
• Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems.
• Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems.
• Solve 2by 2 systems of linear equations graphically and by simple substitution.

Ohio Mathematics Academic Content Standards Process Standards:

By the end of the 5-7 program:

• Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives.
• Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations.
• Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.
• Recognize whether an estimate or an exact solution is appropriate for a given problem situation.
• Use deductive thinking to construct informal arguments to support reasoning and to justify solutions to problems.

By the end of the 8-10 program:

• Formulate a problem or mathematical model in response to a specific need or situation, determine information required to solve the problem, choose method for obtaining this information, and set limits for acceptable solution.
• Apply mathematical knowledge and skills routinely in other content areas and practical situations.
• Recognize and use connections between equivalent representations and related procedures for a mathematical concept; e.g., zero of a function and the x-intercept of the graph of the function, apply proportional thinking when measuring, describing functions, and comparing probabilities.

Ohio Science Academic Content Standards:

Grade 7: Earth and Space Sciences: Earth Systems

• Explain that Earth's capacity to absorb and recycle materials naturally (e.g., smoke, smog and sewage) can change the environmental quality depending on the length of time involved (e.g. global warming).
• Analyze data on the availability of fresh water that is essential for life and for most industrial and agricultural processes. Describe how rivers, lakes and groundwater can be depleted or polluted becoming less hospitable to life and even becoming unavailable or unsuitable for life.

Grade 7: Diversity and Interdependence of Life

• Investigate how organisms or populations may interact with one another through symbiotic relationships and how some species have become so adapted to each other that neither could survive without the other (e.g., predator-prey, parasitism, mutualism and commensalism).

Grade 8: Abilities To Do Technological Design

• Design and build a product or create a solution to a problem given more than two constraints (e.g., limits of cost and time for design and production, supply of materials and environmental effects).
• Evaluate the overall effectiveness of a product design or solution.

Grade 8: Scientific Inquiry Doing Scientific Inquiry

• Read, construct and interpret data in various forms produced by self and others in both written and oral form (e.g., tables, charts, maps, graphs, diagrams and symbols).
• Apply appropriate math skills to interpret quantitative data (e.g., mean, median and mode)

Lesson Materials :

• PBL Scenario^* (2 pages, including letter and island detail page)
• access to internet, calculators, newspaper, library or personal or classroom book
• Islands PBL Rubric
• Islands PBL presentation rubric (this second rubric is optional and depends on the teacher's desire to require and to grade a presentation)

Teacher-student interaction:

• Grouping: Students will be grouped by 4s
• This lesson is a multi day lesson with introduction and planning on day one, and with the work on the remaining days determined by access to computer labs, the amount of outside on-line work expected, and the number of class sessions that can be allotted to such a projet.

Students will do the following tasks during this unit:

1. Teacher will introduce the Islands PBL to students and respond to initial questions.
2. Students each will be given a photocopy of the initial letter from the Do The Right Thing Center of Ethical Decision-Making, a copy of the details about the islands, and a copy of the Islands PBL rubric.
3. Through short discussion facilitated by the teacher, students will learn about the possible needs for contacting Dr. Learner for more information and how to do that. They also will learn about the potential uses of the internet in the project.
4. Students will then be asked to:
• generate a list through brainstorming of all of the possible elements one might encounter in beginning to solve this problem.
• Develop a plan of action that includes:
  • tasks for each member of the group,
  • products each member is expected to bring to the group,
  • questions to ask Dr. Learner and a plan for contact,
  • directions for internet searches (including each group member's responsibility and focus in such searches (make the best use of the time),
  • and other details the group might find relevant to address.
• Prepare the first progress report for Dr. Learner (see #7 below).
5. After the initial introduction and brainstorming session, students will work independently, both through monitored lab time, small group in-class discussions, and outside of school internet access.
6. Classroom debriefing sessions will also be held. These debriefing sessions will include discussion of findings from internet searches, and developing questions or issues around mathematics, science, problem-solving, and social factors of the potential solutions to the PBL.
7. Groups will be expected to submit two electronic copy progress reports to Dr. Learner prior to the final project, to inform the center of progress to date.
   • Progress Report 1 will be due within 24 hours of the initial class introductory session.
   • Progress Report 2 will be due within 24 hours of a second in-class session, to be determined by the classroom teacher.
8. Paper copies of these progress reports will be due to the classroom teacher on the same due date as the electronic submissions to Dr. Learner.
9. Monitored computer lab sessions, small group sessions, and debriefing sessions would be times for the teacher to help students find direction and focus by suggestion of search keywords or questions to e-mail to Dr. Learner
10. The final product will include a formal report, meeting the needs of the center as outlined in the problem details distributed on day 1.

Formative (non-graded) Assessments:

Questions for the teacher to use in supporting student progress on the projects:

• Does everyone in your group have a clear understanding of concepts across the whole solution? If so, how do you know? If not, what can you do about that?
• Do all members of the group show proficiency in applying concepts and procedures? If not, what can you do about it?
• Do you have multiple solutions? How do they differ? What criteria and what perspectives can you use to decide which are better than others?
• How can you use other sources of information (books, TV, interviews, internet newspapers) to strengthen your solution?
• How can you make sure that your commitment to the social, environmental, and economic issues on which solutions depend are clear and highlighted?
• How can you make your report more clear? How do you know your explanations are clear and thorough?
• How do you feel about your own personal responsibility towards your solutions?

Summmative Evaluation:

The Islands PBL Rubric will be used to assess student products. The presentation rubric may be used for any presentation that may be required. Additionally, one may chose to design a rubric to assess group collaboration.

The mathematics and science content evaluated will be determined by the objectives selected from those listed above.

Other content area objectives, such and social studies or language arts may also be selected for inclusion in such a project. We chose not to do that at this time.

Presentation Rubric (pdf)

Report Rubric (pdf)

^* This PBL Problem was adapted from a problem in Building Houses, Navigating through Algebra in Grades 3-5, (Reston VA: NCTM) which was adapted from Linda Holden Charles, Algebraic Thinking: First Experiences – Collection (Mountain View, CA: Creative Publications, 1990).)