MSP:MiddleSchoolPortal/Math Fairs and Competitions

From Middle School Portal

Motivating Middle School Math: Family Nights, Fairs, and Competitions - Intro

What motivates a middle school student to learn math? to enjoy math? According to NCTM’s Principles and Standards,
Middle-grades students are drawn toward mathematics if they find both challenge and support in the mathematics classroom. Students acquire an appreciation for, and develop an understanding of, mathematical ideas if they have frequent encounters with interesting, challenging problems. (p. 211)

As you have seen in your classroom, these students are growing in their cognitive powers, so are able to generalize, reason, communicate, and even invent strategies for solving problems. But the problems they find worth solving often lie outside the math textbook. To motivate them to investigate a math problem, we must find contexts that are interesting and important to them---and then allow them choice in deciding which they would like to explore.

The resources offered in this resource guide address not only cognitive but also social needs of the adolescent. Educator Glenda Lappan noted, “As you think of the socialization of the middle school level, there is a natural match between the mathematical need to deeply understand ideas and the social need to interact with ones peers around tasks that are of interest.” (p. 30) We think that math nights, fairs, and competitions can motivate students by answering these needs.

A family math night brings younger middle school students together with family members to play a game or explore bubbles and their dimensions or to use a balance to reason through this basic algebraic idea.

A math fair opens booths to the whole school as well as families. Students can run these, present and explain the games or the experiments. Projects have as real a place here as they do in a science fair; in fact, these can be interdisciplinary efforts. The deep-down motivation is finding the why in the experiment.

Competitions can be the drawing card for those students interested in testing their skills. The contests presented here are generally national in scale, sometimes team-oriented, often calling for a math club to be created and run by a coach.

Hopefully, these resources will motivate your students and enhance your school math events!


Math Family Nights

Getting students and their families together for math lets each help the other in working with solving problems. This can be especially good for parents who were taught in traditional settings and can’t imagine what-where-how their children are doing math today. Activities can range from making and flying paper airplanes (average distance flown), working with geoboards (finding area and perimeter), playing with a “balance” (algebra, weight), and more.

The online games and activities offered below give ideas on family-friendly games. Some require a computer but not all, and most can be adapted to paper-and-pencil handouts. If you can provide access to computers, however, that’s always a plus for parents as well as students. See what you think of these math activities.

Builder Ted In the game scenario, players help Builder Ted by placing the decimal-numbered bricks on a ladder in order. At the first level of difficulty, all numbers are positive, but the two higher include negative numbers as well. If a number is placed incorrectly, all the bricks immediately fall and the player begins again. Definitely an online game.

MathFROG MathFROG stands for Math Fun, Resources, and Online Games. These lessons combine online mathematics games with paper-and-pencil follow-up exercises. The site offers you a set of activities to choose from. Among those listed for grade 6 are Decimal Mania, Decimultiplication, Place Value! and Ordering Decimals.

Towers of Hanoi (Grades 6-8) This online version of the Towers of Hanoi puzzle, which can be duplicated offline, features three spindles and a graduated stack of two to eight discs, a number decided by the players, with the largest disc on the bottom. Players work together to move all discs from the original spindle to a new spindle in the smallest number of moves possible, while never placing a larger disc on a smaller one. As players observe the patterns, the final question is: What if you had 100 discs?

You will also find excellent ready-to-use activities in the books Family Math and Family Math: The Middle School Years, plus plans on how to carry off a math night in Bridging School and Home Through Family Nights: Ready-to-Use Plans for Grades K-8. Check your library for these titles. You can also find ordering information on

Math Fairs

How could we organize a math fair? And what kinds of projects would our students present? I’m not thinking here of projects that would be judged, as in a science fair, but rather investigations and activities that would engage middle school students and be presented for the whole school as well as for parents. One idea comes from a 7th grade teacher at Frisbie Middle School in Rialto, California.

Multicultural Math Fair Ten activities for the fair, each based on a different cultural heritage, are well described in both Spanish and English. Included here are tips on how to set up a math fair as well as student handouts and free software for specific activities, such as the Tower of Hanoi. You will also find links to resources for related activities, such as studying symmetry and patterns in Navajo rugs. A unique teacher-created site!

Another non-judging math fair is explained by the SNAP Foundation as student-centered, non-competitive, all-inclusive, and problem-based: SNAP Math Fairs focus on student solution of well selected math puzzles, and student-run presentations of puzzles to visitors. The site offers a description, sample puzzles, and even ideas on assessment.

But if you’d like a different fair, where projects are judged, you might consider this idea for grades 5-8: Math Celebration Fair. A teacher explains how her school has students create, over a two-month period, math games worth judging. Many how-to’s and three sample games are included.

Project Ideas

Many fairs can be patterned on the science fair idea of investigating a topic and presenting the results. Students work in teams to explore the math, write up the presentation, and design the analysis. The following are some project ideas that I think would make great fair presentations and involve students in learning sound math.

Pascal’s Triangle Here are three ways to explore the famous triangle: by finding patterns and relations within the triangle, solving a pizza toppings problem in Antonio’s Pizza Palace, or working with an interactive web unit. The set of three investigations could work well as one fair project.

The Noon Day Project: Measuring the Circumference of the Earth In the course of this online project, students learn about Eratosthenes and his experiment, do a similar experiment by collaborating with other schools, and analyze and reflect on the collected data to determine the accuracy of their measurements and what they learned. The project provides detailed instructions, activities, reference materials, online help, and a teacher area.

The Global Sun Temperature Project This website allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Educators can find project information, lesson plans, and implementation assistance. Participants can submit their project data, pictures, and final reports.

The Data Library contains an extensive list of ongoing data-sharing projects that would work well as fair projects. It also offers a great set of links to data on population, baseball stats, minimum wage, etc., excellent for students working on any statistics project.

Polyhedra in the Classroom A set of activities developed for middle school students on aspects of polyhedra. The teacher-creator, Suzanne Alejandre, includes not only instructions for each activity but also assessment suggestions and her mathematical objectives for the unit.

Down the Drain An Internet-based collaborative project that allows students to share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students determine the average amount of water used by one person in a day. They then compare this to the average amount of water used per person per day in other parts of the world. Students publish reports, photos, or other work for the fair presentation.

The International Boiling Point Project People from all over the world boil water at different elevations and post data to discover which factor in the experiment (room temperature, elevation, volume of water, or heating device) has the greatest influence on boiling point. Anyone can boil water, record information, and send it in for inclusion in the database of results. Students analyze the data to answer the question: What causes a pot of water to boil?

Designs with Circles A small project, but the artwork could make it a good math project entry for a fair, a classroom display or a math night.

Magic Squares always a good topic for a display. A wealth of material here!

Math Projects for Science Fairs A collection of ideas from the Canadian Mathematical Society. Listed by math topic, these are ideas that you or your students would have to expand and investigate. Most consist of intriguing questions, such as, “Consider tiling the plane using shapes of the same size. What's possible and what isn't? In particular it can be shown that any 4-sided shape can tile the plane. What about 5 sides?” For most ideas, references to books on the subject are given.

Sources of Statistics for Use in Student Investigations

Sourcebook of Criminal Justice Statistics brings together data from more than 100 sources about many aspects of criminal justice in the United States. Supported by the U.S. Department of Justice and the Bureau of Justice Statistics , this rich site is updated regularly as new statistics become available. Among the sections in the Sourcebook are: public opinion on criminal justice, crimes and victims, arrests and seizures.

The Data and Story Library An online library of datafiles and stories that illustrate the use of basic statistics methods. Each story applies a particular statistical method to a set of data. Each datafile has one or more associated stories.

Math Competitions: Go, Team!

If you want to encourage your middle school students to "be the best they can be," here are three competitions for you to consider. All are national and aimed at promoting high achievement through regular math meetings. At least one person on staff will have to head the program, teach the high standard mathematics required on the tests, hold practice contests, and generally push, encourage, and applaud. Good luck to your team!!!

MATHCOUNTS is a national competition developed for U.S. middle school students. Its program promotes mathematics achievement through grassroots involvement in every U.S. state and territory. You will find here all the information on how to register and how to prepare your students for the yearly competitions held throughout the country.

Math Olympiads for Elementary and Middle School Created for grades 4-6 and 6-8, this program aims to enhance students’ problem-solving skills. I especially like the two grade ranges. Math clubs meet weekly for an hour, when students explore a topic or strategy in depth, or practice for the contests. All information on how to structure the clubs and prepare students is included here.

Calculation Nation from NCTM Students can challenge opponents from anywhere in the world to play games organized around content from the upper elementary and middle grades math curriculum. These are online strategy games that allow them to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area. The element of competition adds an extra layer of excitement.

Finally, here is a fourth contest, not strictly mathematical, but you and a science teacher might find it challenging for your students who like to work “hands-on.” The West Point Bridge Design Contest is a challenge for U.S. students age 13 through grade 12. The purpose of the contest is to provide middle school and high school students with a realistic, engaging introduction to engineering. They can learn about how engineers use the computer as a problem-solving tool, about truss bridges and how they work, about engineering through a realistic, hands-on problem-solving experience, and about the engineering design process. Students design a truss bridge using the award-winning West Point Bridge Designer software (absolutely free!). At the site, you can register for this year’s competition and also learn how to set up a local bridge design contest.

SMARTR: Virtual Learning Experiences for Students

Visit our student site SMARTR to find related math-focused virtual learning experiences for your students! The SMARTR learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities.


The FunWorks Visit the FunWorks STEM career website to learn more about a variety of math-related careers (click on the Math link at the bottom of the home page).


Lappan, Glenda. (2000). Mathematics in the Middle: Building a Firm Foundation of Understanding for the Future. In Mathematics Education in the Middle Grades, pp. 23-31. Washington, DC: National Academy Press.

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.

Author and Copyright

Terese Herrera taught math several years at middle and high school levels, then earned a Ph.D. in mathematics education. She is a resource specialist for the Middle School Portal 2: Math & Science Pathways project.

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Copyright January 2010 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0840824. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.