Triangular Bicycle Flags

Article excerpt

The goal of the "Problem Solvers" department is to foster improved communication among teachers by posing one problem each month for K-6 teachers to try with their students. Every teacher can become an author: pose the problem, reflect on your students' work, analyze the classroom dialogue, and submit the resulting insights to this department. Every teacher can help us all better understand children's capabilities and thinking about mathematics with their contributions to the journal. Remember that even student misconceptions are interesting.


Classroom Setup

Spend time discussing this problem with your students. Although some students may need help understanding the problem, avoid giving too much guidance. Encourage your students to use words to describe the differences in the triangles they create on their geoboards. Collect student work, make notes about interactions that took place, and document the variety of student approaches that you observed in your classroom. Feel free to adapt the problem to fit the level and experience of your students. For older students, you may want to sort and classify the different triangles that are created or discuss specific properties of each type of triangle.

As you reflect on your experience with this problem, keep in mind the following questions:

* What difficulties did students have in understanding the problem?

* How did students approach this task?

* What strategies did students try?

* Were any student responses or interpretations surprising to you?

* What questions or justifications arose from students' explanations of their plans?

We are interested in how your students responded to the problem (or your adaptation of the problem) and how they explained or justified their reasoning. Please send us your thoughts and reflections. Include how you posed the problem and samples of students' work. Send your results with your name, grade level, and school by July 1, 2004, to Kim Hartweg, Mathematics Department, Western Illinois University, Macomb, IL 61455. Selected submissions may be published in a subsequent issue of Teaching Children Mathematics and acknowledged by name, grade level, and school.


Courtney wants to make a plastic flag to put on her bicycle safety pole. She wants to make it in the shape of a triangle. Help Courtney by creating as many different types of triangle flags as possible using your geoboard and/or geoboard dot paper, as shown below.

A virtual geoboard for use in the computer lab or a one-computer classroom is available online at Dot paper can be found at

RELATED ARTICLE: Where's the Math?

The Triangle Bicycle Flags problem is an example of an informal geometry exploration. This problem will allow students to explore, visualize, create, take apart, and make observations about triangles. By constructing different types of triangles, students will compare and begin to classify triangles by appearance and properties. …