An assessment tool that uses student-written word problems to provide meaningful information regarding the depth of mathematical understanding. Students’ word problems representing 6 ÷ 1/2 were classified using the scoring categories described in the NAEP. By categorizing the problems, students' levels of understanding with regard to division by a fraction were revealed. Descriptions of the categories and sample student problems are included.

The value of problem solving in setting the stage for future math studies. Discusses three problems that can be solved verbally and algebraically.

Seven problems connecting the Pythagorean theorem with a variety of prealgebra topics to provide genuine problem-solving opportunities. Solutions and student samples are provided.

Student experiences with quilt blocks to construct understanding of perimeter, area, probability and transformations. Also provides list of ideas for further explorations, sample quilt patterns, and student samples.