Support vector classifiers are one of the most popular linear classification techniques for binary classification. Different from some commonly seen model fitting criteria in statistics, such as the ordinary least squares criterion and the maximum likelihood method, its algorithm depends on an optimization problem under constraints, which is unconventional to many students in a second or third course in statistics or data science. As a result, this topic is often not as intuitive to students as some of the more traditional statistical modeling tools. In order to facilitate students' mastery of the topic and promote active learning, we developed some in-class activities and their accompanying Shiny applications for teaching support vector classifiers. The designed course materials aim at engaging students through group work and solidifying students' understanding of the algorithm via hands-on explorations. The Shiny applications offer interactive demonstration of the changes of the components of a support vector classifier when altering its determining parameters. With the goal of benefiting the broader statistics and data science education community, we have made the developed Shiny applications publicly available. In addition, a detailed in-class activity worksheet and a real data example are also provided in the online supplementary materials.