Principal for a Month!!

1. Principal for a Month!! Presented by Scott Jeffrey6th Grade Teacher Crowders Creek Middle School Clover School District #2Problem-Based Gifted Curriculum Unit

2. Problem-Based Learning • Problem-based learning is a pedagogical strategy for posing significant, contextualized, real world situations, and providing resources, guidance, and instruction to learners as they develop content knowledge and problem-solving skills (Mayo, Donnelly, Nash, & Schwartz, 1993). In problem based learning, students collaborate to study the issues of a problem as they strive to create viable solutions.

3. Why PBL? • Real-life problems seldom parallel well-structured problems; hence, the ability to solve traditional school-based problems does little to increase relevant, critical thinking skills students need to interact with life beyond classroom walls. • Well-structured problems with their sterile environments in which there is only one right answer simply teach students about problem solving, not how to problem solve. • Real-life problems present an ever-changing variety of goals, contexts, contents, obstacles, and unknowns which influence how each problem should be approached. • To be successful in their chosen career, students need practice solving ill-structured problems that reflect life beyond the classroom. This skill is the goal of problem based learning.

4. Cognitive Effects of Problem-Based Learning • The acquisition and structuring of knowledge in PBL is thought to work through the following cognitive effects (Schmidt, 1993): • initial analysis of the problem and activation of prior knowledge through small-group discussion • elaboration on prior knowledge and active processing of new information • restructuring of knowledge, construction of a semantic network • social knowledge construction • learning in context • stimulation of curiosity related to presentation of a relevant problem • Some theories suggest that learning occurs as students collaboratively engage with concepts in meaningful problem solving. • Problem-based learning is often referred to as a form of Inquiry-based learning (IBL), which describes an environment in which learning is driven by a process of inquiry owned by the student.

5. Principal for the Month • IntroductionThis unit is designed for fourth or fifth grade gifted students and focuses on a variety of standards based math concepts embedded in various real world problem-solving situations. The unit is also designed to provide students with an authentic problem solving environment while providing complex curriculum appropriate for their age, ability and grade.

6. Introduction to the Problem • November 14, 2007 • Dear Students in Mr. Jeffrey’s Class, • Thank you for giving me the opportunity to speak to you on such short notice. Your teacher informs me that you have been working on problem solving in math for a good part of the year. As you probably know, the job of principal is full of problem solving opportunities. Each day while you’re in class learning, I am solving problems related to every aspect of the operation of this school. • In fact, just yesterday Mr. Boulware came to me with a dilemma about ordering toilet paper. He wanted to know if we should order the soft tissue with fewer sheets of paper or the rougher tissue with more paper on each roll. They were identical in cost. We worked together to solve that problem and make a decision in the best interest of the students, teachers and the school.

7. That is just one simple example of the opportunities I have to use my problem-solving skills. As we discussed this morning, I will need your help with some of the day-to-day problems that surface. I need problem-solvers who can work together to make careful decisions. I need students who can think “outside the box” and justify their answers with written or oral responses, and students who can access multiple strategies and skills to reach a solution to the toughest problems. Problems occur suddenly and you need to be prepared to take on any problem that is assigned. Your teacher will receive the problems from Miss Glenn and he will present them to the class to be solved. • I am counting on you to shine in this special time. I await your response to my request by the end of the day today. If you have any questions about your duties, please write them in your problem log and share with your teacher. • Sincerely, • Mr. Paul Pratt Principal Griggs Road Elementary School

8. Lesson #2 Playground Committee Request • Objectives: • Students will measure the length of the walkway and experiment with various patterns using various geometric shaped pavers. • Students will estimate the cost of supplies for the playground materials. • Introduction of Lesson State lesson purpose and objectives • Recall prior knowledge of various skills possibly needed. • Explain the scoring rubric used to assess this project • Assessment: • Students will present their letter to principal. • Letters will be graded for content and form using the scoring rubric provided with this lesson. • Informal teacher assessments will be made by reading problem log and observing learning behaviors in the class.

9. interoffice memo • Date: 4/23/2007 • To: G/T Students in Mr. Jeffrey's Math Class • Cc: Superintendent Jenkins, PTO President Robin Shillinglaw • From: Mr. Pratt RE: Playground Committee Request • Priority: [Urgent] • Playground Committee Request • Dear G/T Students, • Your first assignment as temporary principals is to handle the recent request by the members of the playground committee. The playground committee is considering creating a walkway in back of the school between the playground and the third and fourth grade entrance. This would enable students to go from the playground to the back doors with out tracking mud and grass into the building. The walkway will also enhance the appearance of the area behind the building. The committee is, however, concerned about the cost. Their budget is $500 and this project must be completed for $500 or less. • An anonymous parent has agreed to cover the cost of labor and other needed materials (including sand to level out the bricks/pavers). Included with this memo are possible materials that the committee would need to buy to complete the walkway, along with sizes and prices. • Help the committee by designing an attractive walkway and dete11i1ining whether it can be done with in their budget. Respond to me in letter-form describing your design, the cost of the design, the materials needed, and why your plan is worthy of their consideration. Good luck with this project and be sure to ask your teacher for guidance through out this important assignment. • Sincerely, • Mr. Pratt

10. Playground Walkway Materials

11. What Do We Need to Know?

12. Humor? • Dear Mom, • $chool i$ really great. I am making lot$ of friend$ and $tudying very hard. With all my $tuff, I $imply can`t  think of anything I need, $o if you would like, you can ju$t $end me a card, a$ I would love to hear from you. • Love,Your $on • The Reply: • Dear Son, • I kNOw that astroNOmy, ecoNOmics, and oceaNOgraphy  are eNOugh to keep even an hoNOr student busy. Do NOt forget that the pursuit of kNOwledge is a NOble task, and you can never study eNOugh. • Love,Mom A child comes home from his first day at school. His Mother asks, "Well, what did you learn today?"    The kid replies, "Not enough. They want me to come back tomorrow."

13. Lesson #3 Locker Combination Predicament • Objectives: • Students will apply square numbers and square roots to a problem-solving situation. • Students will utilize various problem-solving strategies to determine to combination for the lock. • Introduction of Lesson · State lesson purpose and objectives · Recall prior knowledge of various skills possibly needed. Explain the Scoring rubric used to assess this project • Assessment: • Students will be assessed using a rubric. Informal teacher assessments will be made by reading problem log and observing learning behaviors in the class.

14. Interoffice MeMO • Date: 4/23/2007 • To: G/T Students in Mr. Jeffrey's Math Class • Cc: Superintendent Jenkins, Coach Richie From: Mr. Pratt • RE: Locker Combination Predicament • Priority: [Urgent] • Locker Combination Predicament • Dear G/T Students, • Congratulations on a successful completion to the Playground Committee Request. The committee was extremely impressed with the quality of your work and the variety of designs your teams chose to recommend to our committee. • Coach Richie has asked for my help in solving a predicament he is facing with children forgetting their locker combinations. As you can probably imagine, a forgotten locker combination means lost time for all of the students in gym class. I told him you could help him solve this predicament by coming up with a method or formula for solving the forgotten combinations. • Here are the clues you need to know to solve this problem. • The 3 numbers in the combination are between the numbers 15 and 30. • The sum of the numbers is 70. • When you square each number in her locker combination the digits 1-9 will appear only once in the digits, of the 3 square numbers. • What is the combination of this child's locker? Show all of your work and tell how you achieved a solution by labeling all that you do. • Good Luck! • Sincerely, • Mr. Pratt

15. Assessment Rubric Locker Combination Predicament • Novice -1 The novice will not know how to get started on the task, or will only be able to focus on finding 3 numbers whose sum is 70 without regard for other parameters in the task. Little or no math language or representations will be used to communicate. • Apprentice - 2 The apprentice will attempt to solve the task, but may arrive at an incorrect solution for one of several reasons. The apprentice may not check to make sure that when the digits of the combination are squared that the digits 1-9 are represented, or may use the combinations that repeat digits. Some of math language will be used to communicate, and some math representations may be used to organize work. • Practitioner - 3 The practitioner will find the correct solution that addresses all parameters of the task. The practitioner will use accurate and appropriate math language, and will have complete and labeled mathematical representations. • Expert - 4 The expert will find a correct solution that addresses all parameters of the task. The expert will clearly explain her/his approach and reasoning. The expert will make mathematically relevant observations about the solution, such as commenting on the characteristics of the numbers in the combination, or by verifying the solution. • Student Name__________________________ • Student Score__________________ • Comments:

17. Lesson #4 Greener Grass • Objectives: • Students will multiply and divide using whole numbers and decimal numbers Students will determine the best buy for the sod for the new field • Students will access geometry~ area & perimeter, and various computation skills to solve this problem • Students will build a scale model of the field using green paper scaled down to represent the new sod • Students will use various measurements to come to a conclusion • Introduction of Lesson • State lesson purpose and objectives • Recall prior knowledge of various skills possibly needed. • Explain the scoring rubric used to assess this project • Assessment: • Students will be assessed using problem-solving rubric. • Students will be assessed on their ability to communicate ideas orally in a clear and organized way. (see evaluation form) • Informal teacher assessments will be made by reading problem log and observing learning behaviors in the class.

18. interoffice memo • Date: 4/23/2007 • To: G/T Students in Mr. Jeffrey's Math Class • Cc: Superintendent Jenkins, Coach Richie • From: Mr. Pratt RE: Greener Grass • Priority: [Urgent] Greener Grass • Dear G/T Students, • Congratulations on finding the combination for Coach Richie. I agree that you could not come up with a set formula unless you clues were given before starting. I'm sure it was fun trying and your teach told me that you worked extremely hard. Good work! • I have another problem that has surfaced just today. With the nice weather comes greener grass, flowers and leaves on the trees. Unfortunately, this winter has done a number on my personal golf course behind the school. I am considering replacing the existing grass golf course (fairway and putting green) with new sod that is softer and more plush. This new grass will be perfect for sending the ball a long way and it will provide a cushion for my aching knees. • I am looking for the best buy for the limited money available for this project. Below are price quotes from various nurseries: • 6 ft. X 2 ft roll $1.35 • 6 ft X 6 ft roll $4.00 • 8 ft X 3 ft roll $2.75 • 6 ft X 3 ft roll $2.25 • The dimensions of the golf course is 120 yards X 160 feet. • Which is the best buy? • How many rolls of sod will be needed? • What is the total cost of the sod? • I am looking forward to visiting your class and listening to your presentations. Good Luck! • Sincerely, • Mr. Pratt

19. Assessment Rubric Greener Grass • Novice -1 The novice will have no solution. The explanation will be unclear, and there will be little evidence of mathematical reasoning and/or language. The novice won't know where to begin, and will not have a strategy for even getting started toward a correct solution. • Apprentice -2 The apprentice will have some understanding of the task. The apprentice might be able to convert yards to feet while finding the area of the golf fairway. The apprentice may be able to determine the number of pieces of sod that are needed, but will have no strategy for determining the least expensive. There will be some evidence of mathematical reasoning and/or language, and perhaps an attempt at a mathematical representation. • Practitioner - 3 The practitioner will have a solid understanding of the problem. The practitioner will be able to convert yards to feet, finding the area of the golf fairway. The practitioner will be able to determine the number of pieces of sod that are needed, and will have a strategy for determining the least expensive. The practitioner will use mathematical language and representations to communicate clearly, and will use sound mathematical reasoning. • Expert - 4 The expert will have extensive understanding of the problem. The expert will have efficient strategy for finding a solution, and will compare the 4 different costs of the reader. The expert will use sophisticated mathematical language", and may make mathematically relevant comments or observations about her/his solution, such as discussing the significance in decimal amounts when determining the cost per square foot. • Student Name_______________________ • Student Score____________ • Comments:

20. Let’s Give It a Try! • Calling All Students • Mrs. Forest wanted to plan how to contact her students by phone in case the field trip they were going on the next day needed to be canceled. She decided to call one student who would then call 2 other students. Each of these students would then call 2 other students. This would continue until all students had been called. Mrs. Forest has 31 students. How many students will need to make phone calls if Mrs. Forest calls the first student? • Find a rule for determining how many phone calls will be made for any number of students.

21. Wait, there’s more!!!!! • If you would like a copy of this Problem-based learning unit, please write your name and e-mail address on the pad and I will send it to you via email. • Door Prize Time - ready

22. See if you won! • Look under your seat for the golden ticket. • Thank you all for coming and listening.