Place Value from the Ground Up

This textbook attempts to immerse students in a microworld of blocks, groups of blocks, counting, and regrouping. There is very little direct instruction on place value. Instead, students learn by exploring, navigating, and solving problems within the microworld itself. They start by counting by ones and rapidly build their understanding until they are using paper-and-pencil algorithms for multi-digit arithmetic. This approach is similar to how a student might learn how to play a video game by trial-and-error or learn a second language by living abroad for a semester.