Educators recognize that group work and physical involvement with learning materials can greatly enhance the understanding and retention of difficult concepts. As a result, math manipulatives--such as pattern blocks and number lines--have increasingly been making their way into classrooms and children's museums. Yet without the constant guidance of a teacher, students can easily become distracted, confused, or frustrated. Math games with tangible user interfaces can address the needs of the modern learning environment by providing the guidance that a teacher would while allowing students to work together in a physical environment. This paper describes how math games with tangible user interfaces can be rapidly developed using a library of functions that were designed specifically for tracking visual tags in math games. The paper also discusses pedagogical principles and an approach to designing and developing games that utilize tangible technologies. Examples of math games that have been prototyped this way are presented. The paper concludes with a study that suggests that this approach helps children to stay focused, think about math problems in new ways, and complete the problem at hand. It also suggests that tangible math games may help children to develop problem-solving skills that transfer to similar problems.