A semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. This activity fit well into Standards-based classrooms as well as within the constraints of the college semester.

Students explore the Pythagorean theorem and an extension using jelly beans to measure areas. Deductive thinking and algebraic notation help establish connections as students can work in groups at stations. These activities using jelly beans are beneficial and enjoyable for students, prospective, and in-service teachers. Extension activities are included.

Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. The teachers created, interpreted, and discussed the various representations to develop and enhance their understanding of fraction division.

To guide problem-solving activities in the classroom, this article presents a strategy similar to the reading model found in literature circles. The goal of mathematics circles is to provide guidance and structure to problem-solving activities so that students can internalize the strategies needed for them to develop into mathematicians. Examples of student work are included. Activity sheets included.

Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in algebra textbooks. Students are active participants in their learning through use of their kinesthetic, spatial, and mathematical intelligences.

Several activities that are based on the ancient method of false position, also called false assumption, are presented in this article as a way to motivate students to find the solution of literal equations in beginning algebra. With a historical connection, the activities described engage students in solving linear equations in a novel way. Extension exercise included.