Challenging with 'Rich' Problems

What makes a problem "rich?" In my opinion, rich problems have multiple entry points, force students to think outside the box, may have more than one solution, and open the way to new territory for further exploration. The problems in these resources can challenge your students and enliven their study of mathematics.

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Problems with a Point http://mathforum.org/library/view/19803.html

A collection of problems designed to help students in grades 6-12 learn new mathematical ideas by building on old ones, this resource is exceptional in the quality of the problems. Varying in difficulty and approaches, the problems can be searched not only by topic but also by problem-solving strategy, class time, technology needed, and students’ mathematical background. Each problem offers ideas for exploration, classroom discussion, and extensions. MSP full record

Ohio Resource Center for Mathematics, Science, and Reading http://ohiorc.org

Among this site’s resources is a collection of rich math problems intended generally for the high school level, but the following three could appropriately challenge middle school students. MSP full record

What Is the Average Birth Month? http://www.ohiorc.org/pm/math/richProblemMath.aspx?pmrid=37

What is the average month for births? The class may start out with assigning a number to each month — January = 1, February = 2, and so forth — and then find "the average". Examining just what "average" means in this case leads to selecting and graphing the best way to find an "average" with categorical data. Next, students examine class data and are asked if this information is representative of the entire population. In this way, students explore a question that engages them even as it leads to deeper understanding of basic statistical concepts. Questions for class discussion and teaching tips are included. (From Ohio Resource Center for Mathematics, Science, and Reading - MSP full record)

The Mouse http://www.ohiorc.org/pm/math/richProblemMath.aspx?pmrid=56

City Hall has a rectangular lobby with a floor of black and white tiles. The tiles are square, in a checkerboard pattern, lined up with the walls: 93 tiles in one direction and 231 in the other. There are two mouse holes, at diagonally opposite corners of the floor. One night a mouse comes out of one mouse hole and runs straight across the floor, and into the other mouse hole. How many tiles does the mouse run across? A complete solution and handouts are provided. (From Ohio Resource Center for Mathematics, Science, and Reading - MSP full record)

Let’s Go on a Penny Walk http://www.ohiorc.org/pm/math/richProblemMath.aspx?pmrid=27

Start at 0 on the number line. Flip a penny. If it is heads, move to the right a distance of 1 unit. If it is tails, move to the left a distance of 1 unit. Keep this up. From this simple beginning, the teacher can pose such questions as: What is the probability that you are at a certain position after a certain number of flips? What is the probability that you will ever return to your starting point at 0? Students will be able to see how far they can get using elementary counting methods. Several other questions lead to interesting solutions. (From Ohio Resource Center for Mathematics, Science, and Reading - MSP full record)

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Copyright December 2007 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. 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.

This work is licensed under a Creative Commons License.