Overview and Background: Unit: License Plate Project, aka PL8s4U

No Performance Task

Jim Gillett : Cheney USD 268

Mathematics. : Probability : Probability

Cheney : Grades 8 - 8 : Aug. - Jun.

Title:	License Plate Project, aka PL8s4U
Topics:	Fundamental Counting Principle
Time Frame:	Two weeks
Start Date:	-

Other Designers:

Summary:
Students will learn to apply the fundamental counting principle. The students will research the number of license plates each state can create for each state and then create a non-numeric, non-alphabetic system for a mythical state's population.

Print Materials Needed:
Project intro page

License plate assignment sheet

Overhead of the Kansas example license plate picture page and the Kansas plate description page next to it from the License Plate Book listed in the resource section below.

File folder for each state with the state information from the License Plate Book.

License plate project supplements for the following mythical states; Columbus, Moo Mesa, Binford, Cowabunga, Babar, Fletch, Circle, and West Kansas.

Overhead of top 10 personalized license plates from 1995.

ZIP+4 State Directory of states from phonebook. This should show the postal service's abbreviation for each state.

Assessment Rubric

Probability information including a description and examples of the fundamental counting principal (commonly found in 7th and 8th grade math textbooks).

Resources:
Phone book showing zip+4 state codes.

License Plate Book by Thomson C. Murray, edited by Michael C. Wiener, published by Interstate Directory Publishing Company, Inc., 420 Jericho Turnpike, Jericho, New York 11753, 516-822-5966, fax 5962. (I believe a new edition just came out - I was using a 1992 edition).

Almanac or other materials showing the populations of the 50 states and D.C.

Resource Attachments:	http://www.cheney268.com/MSMath/Gillett/LicensePlateProject/LicensePlateProject.htm
Internet Resource Links:

Notes:

I am an avid collector of new license plates from all states and many of my current and former students have contributed plates so that now license plates from at least 40 states decorate the walls of my classroom. But the project came first when I was trying to connect some probability concepts with an authentic learning task for my students to "get out of our book" and do. My students that have done this project will never look at license plates the same way again!

Stage 1: Identify Desired Results

State:	KS       Standard 4, Benchmark 1, 8th grade, Knowledge Base indicator 3 extended to 10th grade knowledge base indicator 5based on
Title:	Kansas Curricular Standards for Mathematics (March 1999)
Standard(s):	8th 3. Calculates the odds of a desired outcome in a simple experiment. 10th 5. Uses permutations and combinations to determine the number of possible outcomes of an event.

Understandings:
user	Mathematics is a vehicle which allows us to solve problems of an applied nature in many fields of work. Knowledge of the total number of outcomes is important in designing a solution to a problem.

Essential Questions:
User	How can the fundamental counting principal help to more efficiently determine the total number of outcomes? How do people make decisions? Can recognition of a pattern in data help us to solve problems.

Knowledge and Skills:

K

Reading and understanding a description of a state's license plate system from a book.

S

Apply the fundamental counting principal.

Describing a pattern in numerical terms.

Stage 2: Determine Acceptable Evidence

Assessment Summary:
In teams of four, the students will research and design a non-traditional license plate system for a mythical state that will provide more than enough plate combinations for the state. This system should include the elements listed in the "Other Evidence to be Collected" section.

Other assessment evidence to be collected:
Process check
	1. Completion of fundamental counting principal initial learning activity (worksheet). 2. Written work detailing the teams passenger plate total combinations answer for their first researched state (to be critiqued by teacher and handed back to team). 3. Written work showing the answer for each team's primary states and their check states that the team is responsible for. 4. Research findings (after teams share answers) published in nice format (Word, Excel, etc.) along with populations of states. 5. Description of possible mathematical pattern(s) observed between state combos and state populations. 6. Detailed written description of new, non-traditional plate system for mythical state, including combos and population. 7. Example poster board license plate for mythical state. 8. Presentation of new mythical state's plate proposal. 9. Journal entries with reflections throughout the project.

Stage 3: Plan Learning Experiences and Instruction

Learning Activities:

W

Introduce the unit using essential questions. Post the essential questions. Have students round table in their teams how mathematics will play a part in designing a license plate system for a state. Hand them a copy of the project description sheet and rubric.

H

Project the overhead of the top 10 personalized license plates from 1995, and give each team a limited amount of time to determine what the plate means. Show a Kansas license plate and pose the following question for teams to discuss, "How many passenger plates could the state of Kansas create?". Students should then write a quick reflection in their journal about their thoughts so far.

E

Teacher leads mini-lesson in the following:

-Applying the fundamental counting principal to determine the total number of outcomes of simple events as routinely shown in normal 7th and 8th grade math textbooks.

-Using an overhead of the Kansas pages in the License Plate Book, teach students how to understand the different sections and information to look out for.

-Applying the fundamental counting principal to the passenger plate example on the Kansas pages. Show students how to take good notes explaining how the system works (the alpha and numeric codes of the license plate).

-Explain that there will be some "weird" things that some states do in their systems and that they should do their best to catch those and interpret them as far as how that affects the total number of outcomes.

-Acquaint students with the location of the state folders containing hardcopies of the states information from the License Plate Book and the procedures for using them (ie. only one state per group out at any one time, replace in alphabetical order, pay attention to the plate(s) that I have circled as that state's passenger plate).

Team activities:

- Each team uses their "License Plate Assignment Sheet" to i. research all 20 or 21 of their states and all members are required to keep copies of their written work; ii. compare their data with the other group that is designated as their check group. If differences exist, work out differences and agree on the number to share with the rest of the teams; iii. share their primary states information with all other teams in a quickly written summary (be brief).

-Create Word or Excel document showing states in alphabetical order with their total passenger plate combinations, and populations.

-Draw for a mythical state

-Create a detailed, written description of a plate system that will produce more than enough plates for the state. One wrinkle though, your team can't use alphabetic characters or numerical characters. Creativeness is a premium in applying the fundamental counting principal with different types of characters.

-Create an example poster board license plate for the team's state.

-Set up, practice, and deliver your proposal.

R

Students write a journal entry on what was learned, based upon their experiences with the project. During the period of the project where the teams are sharing their answers for their check states with the another team, students are also obtaining feedback in terms of the soundness of their results. This occurs prior to each team sharing their final state results with the class and then drawing their mythical state to begin creation of their new plate system.

E

Teams present their finished proposals, including the Word/Excel document containing their answers for all 50 states + D.C., their written pattern(s) they observed between the plate combinations and populations, the detailed write-up of how their mythical plate system works, and their example license plate.