I. Fermi Off-the-Wall Goals and Objectives: Fall 2016
Updated 9/20/16; based on a model from theMath Forum, Drexel University
● Fermi problems are designed to foster growth in the areas of problem solving, analytical thinking, and creative thought and technology skills.
●Fermi problems offer students an opportunity to develop skills in the standards outlined by the National Council of Teachers of Mathematics (NCTM) including numbers and operations, mathematical reasoning, data analysis, problem solving, measurement skills, geometry, communications, and representation (modeling).
●Students use high-interest, non-routine problems to encourage creative mathematical thought.
●Students have an opportunity to practice constructed responses (writing about math) similar to ones they may encounter on standardized math tests.
●Students develop the use of the internet as a standard reference tool, developing the ability to discern information and its helpfulness.
●Students discover the joy of exploring challenging math problems with someone outside their math class, enhancing communication skills as they discuss and develop their problem-solving techniques.
●Students enhance the four areas of creative thought: fluency, flexibility, originality and elaboration. See end of this page.
II. Grade Level
Student problems are designed for grades 1-2, 3-4, 5-6 and 7-9. Problems for the 1-2 division will be patterned after problems for the older students, but will incorporate a Family Math flavor. The emphasis for grades 1-2 will be PROCESS and PRODUCT. Parents are important partners at this level. They do most of the solution writing and leading. Please teach calculator use, but don't make the solving process too hard!
Students must send their weekly entries via google docs. These pages are done independently, and are hosted through the student's home ISP. All four portions of the weekly entry must be included in the answer, but the presentation is a google doc or slide presentationformat. The weekly problem is sent in a doc to the appropriate Fermi dropbox for your grade level.
III. Problem Solvers
●Solutions will be accepted from individuals, pairs, and groups of 3 or 4. Group teaming can be arranged. Contact Karen.
●Problem solvers must be registered to be entered in the competition.
● All teams will be identified by team name/alias.... this is a matter of security. No "real" names are to appear in the models. Let's be safe.
●Teams will receive group credit and no individuals will be recognized. Each member receives a certificate, ribbon and/or medal.
●Awards (medals, certificates and ribbons) will be made at the end of each session. All top team members will receive medals.
IV. Submitting a Solution
Teams submit a solution to the Fermi Problem of the Week by placing their solution in the appropriate google folder that contains the text of the answer that contains the weekly answer. These parts are: the solution, the list of questions (brainstorming) and the story of the solution (metacognition/structured response) and a model that includes a "sample size". This sample size indicates ONE of the unit being described in the problem- e.g. one square inch of bird seed = 100 seeds, one Olympic Torch = 80 cm., one baseball = 52 double stitches, etc.
Entries must be submitted as Google Slide presentations. One of the slides should be able to stand alone as a model- with team name/school included. Don’t forget the sample size in the model.
Here's a sample of an entry
Subject Line sample: Wk 2 PhermiPhreeks
The google slide presentation will include each week:
· Team name/ school /grade level
· \
· The answer to the problem, given in rounded form with a label (inches, feet, square yards, cubic spitballs, etc.) Round off right away. We love zeros.
· The supporting questions asked that led to the answer - 10 is highly recommended. These questions are worth 1 point a piece- up to the maximum of 10.
· A detailed description of the steps you used to solve the problem including your assumptions. This description is called the metacognition (thinking about your thinking) or the constructed response and should include what you learned that was new or different. This may not be a bulleted list. It is like a solution essay.
A model of the solution is included as a google slide in the presentation. It is important to label your Team name and the sample size that describes your basis for calculations. Don’t forget to include the sample size on your model. One entry is allowed per week per team.
A scanned drawing or photo is satisfactory in a google model. Archived models from prior competitions are available on our Fermi website. The submission process is part of the learning experience. We do not expect perfect spelling and grammar from all students at all times. Google slide entries are limited to 10 slides. Be sure to indicate which slide is the model. Entries may be dropped in folder in powerpoint format, but the owners must have a google account in which to read responses.
Students in the Grades 1-2 division will need adult help. Taking dictation is a very helpful thing; parents may need to help younger students learn "about" multiplication and division in general terms- and how to use a calculator. PLEASE do not make the problems too difficult for these children. We want the problems to be thought-provoking, but not developmentally inappropriate. If your youngster finds the problems too easy, consider moving up to the next division or trying another problem for that week.
We prefer that Grade 5-6 parents do as little editing as possible, and provide their coaching help "on the side." Parents should not be doing the research or math FOR their students, but work WITH youngsters move toward more sophistication. Locating materials and resources for creating the models are great helps to kids. Please help the children learn to use technology- especially applications like Photoshop, Paint and Powerpoint- and try not to do too much for them.
Providing a too-abstract lesson in discrete mathematics is not a help. Please contact Karen if you have questions. Your gifted/talented teacher, math teacher or media/technology teacher may help you access the technology you need if you don't have access to it at home. These people can be your mentors.
V. A WORD TO THE WISE re: Wikipedia use: Wikipedia is a great place to start investigations and inquiries. It is very dangerous to use Wikipedia as your only source of information. Anyone can add information at this site, and it contains many errors, especially measurements. Always double check and confirm your research at several corroborative places. Karen uses the Airline Pilots' Creed: In God we trust; everything else we check.
VI. Timeline and Deadlines
The problems will be posted on Tuesdays. See our main page.
Younger students may choose to do the 3-4 or 5-6 problem, but not vice versa. You may only make one submission per week. Choose wisely.
Submissions will be accepted through the Tuesday following the week of the problem, i.e. answers for the October 11 problem will be accepted through October 18 at 4:00 p.min your time zone. Late submissions will be accepted with good reason. An email to Karen will provide an opportunity to discuss the reason for lateness. She is patient. We work through holidays and vacations. Plan ahead! Teams who have submitted solutions to the problem will appear on our google site. Be sure to use only alias names on models. We will not put up models with children's real names attached. Ever.
VII. Scoring
Students will receive up to 40 points per week for each of the four weeks. Please review the Scoring Rubrics for ideas to evaluate your own entry before it is submitted. The scoring is subjective, and the rubric might help you think about your thinking in a new way. Kid-friendly checklists are included.It needs to be a great job to earn a 10 in any category.
Weekly points will be awarded for:
10 points / a reasonable answer using appropriate units of measure and lots of zeroes (estimation IS the key to success)10 points / quality of supporting questions used to solve the problem (recommend: 10 questions) This is a fluency exercise that builds the ability to create many possible assumptions and ideas. Don't minimize the importance of this exercise.
10 points / creativity/resourcefulness of solution process and completeness of metacognition or the constructed response.See the rubrics for detailed scoring criteria.
10 points / graphic display /model used in solving the problem. It should include the "sample size"- ONE of what is being measured or compared. We urge the children to use lots of technology in their models. ONE .jpg attachment is allowed.
VII. Contact
Karen Newell
Intermediate District 287 Academic Services
Gifted Outreach
Fluency is the ability to think on many different responses or examples of a question. Fermi brainstorming is a fluency exercise.
Flexibility is the ability to think of multiple applications for an idea or concept. What are 15 other things you can do with a knitting needle besides knit? This exercise uses flexibility to modify thinking. Flexible Fermites often show their models in unique and off-the-wall ways.
Originality is seeing the unique application for the usual…bright mathematicians often find original ways of problem solving. Originality is often tied to flexibility.
Elaboration is the ability to embellish or add decoration to an idea. Words and graphics can be elaborate. Please cite all graphics' copyrighted source.