PBL – Frydryk

Title:  Cats Don’t Like Swimming… Unless it’s a Wildcat!

Description:  There’s no public pool in Harrison – until now!  With your group, you will explore all of the details of planning for, building, and managing a public pool for Harrison.  There are quite a few things to consider:  location, builders, the pool itself, employees, etc.  Create a presentation that includes all pertinent details that City Council would need in order to decide whether to move forward with opening a public pool in Harrison.

Standards:
Suggested/encouraged content:
Optimization to figure out price to charge/ideal number of customers/size of area where pool will be
Integrals to calculate volume of pool (once size is determined)
Related rates – filling the pool

Prior Knowledge Needed/When to Teach:
Calculus.  Students should be familiar with optimizing functions, solving related rates equations, and using integrals to calculate integrals.

Timing: 4 weeks total, but project may span many months as more content is learned

Materials/Resources:
Computers
Pool builders
City council/zoning/building policies

Outline:
3-4 days (blocks) at a time will be provided for this project.  As more content is learned (and students see the room for application), another Block will be provided.  With each of these Blocks, the content that is suggested to be used has not been taught yet, but is next is succession.  This is done in an effort for students to use their direct prior knowledge to recognize the need for the next topic in their project.  Suggested Blocks are given below.
Block 1: (3 days)
Groups are decided.  It is recommended that multiple group activities are done before this in order to assist the teacher in grouping students in a mutually beneficial way.
Problem is introduced.  Use a Think, Puzzle, Explore with students to individually, then in groups, then as a class discuss the problem.
Share the Final Project Rubric with the students and discuss.
Begin preliminary planning.
Reflection (see prompts below).
Block 2: (after derivatives are taught. Suggested content:  optimization. 4 days.)
Students are prompted to consider the location and physical size of the pool (maximize area, minimize resources).
Reflection.
Block 3: (after derivatives are taught. Suggested content:  related rates. 4 days.)
Students are prompted to consider filling the pool with water, max capacity (persons) of the pool, max capacity of the pool area, etc.
Possible resource:  http://mrmeyer.com/threeacts/watertank/
SHARE.  Spend 1 days sharing what students have accomplished thus far.  Each student will provide each group with one thing they like about each project and one suggestion of how to improve/move forward.
Reflection.
Block 4: (after integrals are taught.  Suggested content:  calculating volume. 4 days.)
Students are prompted to consider the shape and volume of the pool.
Reflection.
Block 5:  (whenever – 5 days)
Students are prompted to consider hiring, opening procedures, other aspects.
Final touches on the project!  Be sure all components are addressed in your presentation.
Presentations!  A city council person and/or pool manager and/or engineer can be brought in to provide feedback on ideas.
One final option, if possible, is to present ideas to city council.

Assessment:
Reflection journal entries will be done at the end of each Block (excluding the last one) as a homework assignment.  Students will address the following prompts:

1. In what ways did your small group support you in your learning in this Block?
2. What roles did you serve in your small group in this Block?
3. How did you use Calculus in this Block?
4. What math concepts do you wish you had more information on in this Block?

Final Project Rubric – Standards (provide to students at the beginning of the project)

1. Connection to Calculus
2. Consideration of Variables
3. Group Participation Ranking (students rank each other on their participation)
4. Presentation
5. Final Reflection

Final Reflection (done individually after the Presentations are done)
Same questions from reflection journal entries.

5. What is one thing you would have done differently with your project?
6. What strengths did you bring to your group?
7. Summarize how Calculus was used in your project.