Teachers play a critical role in determining not only the mathematical content in their lessons but also the ways their students think about that content. Although many mathematics teachers want their students to develop the ability to problem solve and think critically about mathematics, the tasks they select and use for their lessons lack the cognitive demandthe kind and level of thinking needed by students to attain a solutionappropriate for developing these skills. In this qualitative case study, I investigated the practices of three high school mathematics teachers with respect to the tasks they selected and used in instruction. I paid particular attention to the relationship between cognitive demand and the use of instructional technology in these tasks. I observed one class period a day of each participant over a 2-week period. Each participant also participated in two in-depth interviews, one preceding and one following the observation period. Each participant had his or her own reasons for selecting the tasks used in class, and the cognitive demand of these tasks varied across participants. The strategies used by participants to maintain the cognitive demand of the tasks they used also varied. Two aspects of students technology use affected cognitive demand: (a) examining the mathematical features of the task to determine the appropriateness of technology use and (b) connecting the mathematical context of the task to a technological representation of it. From these findings, I suggest a technology-oriented addendum to Stein, Smith, Henningsen, and Silvers (2000) framework for analyzing the cognitive demand of mathematical tasks.