Integrated Lessons Strand Overview

This strand integrates technology with mathematical problem solving and written communication. We provide examples of indepth problem solving in mathematics. In the near future, we will include lessons that link mathematics to other subjects such as science. The kinds of problems that we describe in this strand may take two to three periods or as much as a week to complete. It is our view that authentic problems are initially ambiguous, and they require careful analysis and "double checking" before results are reported. Furthermore, an important part of the process is clear communication at the end, whether this is done orally or in writing.

Unquestionably, the Microsoft Office™ programs offer considerable value to the student in terms of their common features and ease of use. They enable the student to represent information visually, numerically, and textually. In this sense, these tools provide the foundation for the problem solving exercises described in this strand.

What this strand provides are explicit suggestions for moving students through the problem solving process toward high quality products. We have found that teachers are often in a quandary when it comes to "getting started" or how to help students make the results of their work interesting or professional in appearance. This strand helps teachers in three critical stages of the problem solving process:

This strand contains descriptions of instructional strategies for these three stages and three detailed examples of how the strategies are used to solve problems. We should add that these examples can be used "as is" or modified as instructional activities if you want a model for the problem solving process.

This second version of the Integrated Lessons Strand contains three detailed example lessons. Through each lesson, students use the three key steps above in solving a business-like problem. One of the main purposes of these lessons is to show students how everyday activities that occur in schools have a substantial mathematical component to them. Moreover, the problems require careful analysis and in the case of the second problem, students need to ask a variety of "what if" questions to achieve a successful solution. The spreadsheet is a perfect tool for asking these "what if" questions.

These lessons provide models that you can use as the basis for many other kind of problem solving activities. The clear advantage of school-based problems is that students often have a ready understanding of the problem and its context. Most of them have purchased something from a school store or gone to a dance. There are any number of everyday events in a school or students' lives that can serve as a basis for the first type of problems. We have used this format to examine how best to stock a vending machine, what to sell in a student store, how to run a small business, or make decisions about extra curricular activities after school.