Part One of each book outlines the mathematical underpinnings on which the ideas and activities are based. Part Two provides a brief instruction on the new content or approaches found in that strand. Parts Three and Four provide two authentic learning tasks, each consisting of a set of four activities with reproducible work sheets. Finally, each learning task includes further teacher background and detailed classroom instructions along with an answer key, scoring guide, and samples of student work. In the first unit of this book, students are introduced to the idea that mathematics is the accumulation of intellectual contributions from many societies and cultures.
Students explore the sequence of triangular numbers, first with manipulatives and then using tables.
In later unit activities, students work with Pascal's triangle and learn about its relationship to Chinese culture of the 14th century. In other historic connections, students learn of Arab and Hindu contributions to mathematical development and learn of Gauss's method to find an expression for the sum of the numbers from one to n. This brings them to an alternative way to derive an algebraic formula for the nth triangular number. In the second unit in this book, students use linear functions to find the most economical of three potential locations for a fund raising party. Authentic learning activities in patterns, functions, and algebra.