Math Fair Information Pack

Purpose: The purpose of this project is for students to solve a mathematical problem using Polya’s Problem Solving Process. Then, students will use math vocabulary to write about the problem by explaining the thought processes and strategies used while solving the problem. This pack provides a step-by-step guide to completing a math fair project.

***Sample Math Fair Project. Please be creative in your board displays. Use the theme (“catchy title”) of your problem as your guide for creativity.

Polya’s First Principle: Understand the problem

This seems so obvious that it is often not even mentioned, yet students are often unsuccessful in their efforts to solve problems simply because they don’t understand it fully, or even in part. Polya taught teachers to ask students questions such as:

• Do you understand all the words used in stating the problem?

• What are you asked to find or show?

• Can you restate the problem in your own words using an answer statement?

• Can you think of a picture or diagram that might help you understand the problem?

• Is there enough information to enable you to find a solution?

• List ALL of the important information about the problem.

What do all of the numbers represent? What are you looking for?

Polya’s Second Principle: Devise a plan

Polya mentions that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:

• Guess and check • Make an orderly list

• Eliminate possibilities • Use symmetry

• Consider special cases • Use direct reasoning

• Solve an equation • Look for a pattern

• Draw a picture • Solve a simpler problem

• Use a model • Work backwards

• Use a formula • Act it out

Polya’s Third Principle: Carry out the plan

This step is usually easier than devising the plan. In general, all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don’t be misled; this is how mathematics is done, even by professionals.

Polya’s Fourth Principle: Look back

Polya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked, and what didn’t. Doing this will enable you to predict what strategy to use to solve future problems.

Problem Write-Up This is the most important part of the math project because this is where the student’s use math vocabulary, as much as possible, to explain their thought processes and strategies used to obtain their solutions. It is their opportunity to write about the mathematics. This part of the project also gives students the opportunity to use skills learned in Language Arts such as, explaining their process and strategies in sequential order and making inferences (finding solutions) based on evidence and reasoning about mathematics.

***Please use the rest of this pack and the attached rubric as a guide to completing your project. Write all of your important information in this pack before transferring it onto your board. Please remember to be as creative as possible when transferring this information to your board to display your results.

Title: ________________________________________________ Re-state The Problem: (Center of Board)

Understand The Problem: (Side of the board) List all of the important information: What does each number represent?

What question is the problem asking you to solve? What are you looking for?

Devise A Plan: (Side of the board) What strategies did you use? Did they work? Did you have to revise your plan? Record all of your trial and errors here to help you keep track of your process. When you display this part on your board, remember to include pictures, charts, graphs, tables, etc…

Carry Out The Plan: (Side of the board) When displaying this section of your board, show ALL of your work. What mathematical operations did you use (addition, subtraction, multiplication, division)? Use the space below to record your work. Work Space:

Look Back: (Side of the board) When looking back, ask yourself “Did I answer the question?” “Were all of the conditions met?”, “Is my solution reasonable?” After asking these questions, display the results.

What’s the solution: __________________________________________________________

***Display the solution on your board under the look back section. You may also want to include a model (picture) of your solution. Use the space below to draw your model before you display it on your board. Model your solution:

Problem Write-Up: (Center of Board) Use this section to write about your processes and strategies. Please use as much math vocabulary as possible; for example, instead of saying, “I added the numbers up to get …”, you could use math vocabulary to say that you found the sum of the numbers.