The MathScape: Seeing and Thinking Mathematically curriculum is divided into 21 units - 7 at each grade level. Each unit is a coherent set of 12 lessons focusing on one or more of the four mathematical strands; these 12 lessons are divided into three or four "phases," each of which focuses on a particular sub-theme of the unit. The main component of each lesson is a hands-on investigation in which students explore mathematical concepts; the students then consolidate their understanding by posing new problems, making connections, and practicing skills in classroom discussions and homework.

Each unit begins with a pre-assessment activity that allows teachers to check for important prerequisites and find out what students already know. The lessons within each unit then build upon one another. The last lesson in each phase and the last lesson in each unit serve as embedded assessment activities for the phase or unit. In these activities, students are given the opportunity to practice mathematics skills, processes, and concepts they have learned in previous lessons.

Many of the units are set in a context that makes the mathematics being learned become more meaningful and fun for students. For example, in the sixth grade unit, Gulliver's Worlds, students explore measurement, scaling, area, volume, and dimensionality as they visit the lands of giants and tiny people. The seventh grade unit, From the Ground Up, has students learn about scaling, measurement, and area by building a model house. In the eighth grade unit, What Comes Next?, students learn about linear and exponential growth and mathematical models while examining trends in world population.