Grades 6-8
32 activities—204 pages

A visual understanding of multiplication builds a firm foundation for performing operations of algebraic multiplication algorithms.

Multiplication the Algebra Way takes students from their familiar environment of arithmetic and brings them into an understanding of algebra. The explorations in this book will have students learning why they are doing something, and seeing it visually all the way through. This important process allows students to smoothly transition from the concrete to the abstract.

The distributive property plays a central role in arithmetic, algebra, and beyond. A deep understanding of the distributive property requires students to have a thorough understanding of important number base concepts. It may come as new insight that the “unknown x” in algebra imbeds these number base concepts.
Initial activities require students to constantly attend to the “ten-ness” of our numeration system. This is followed by learning to think in terms of “three-ness,” “four-ness,” and “five-ness.” Finally, all of these understandings are incorporated into thinking in terms of “x-ness.” This sequence helps students to build a firm understanding of multiplication that will serve them well in their study of algebra.

Throughout this book, students use three forms for representing expressions and equations: physical models constructed with base ten materials and algebra tiles, pictorial sketches, and abstract statements. There is a constant interplay among the three forms to help enrich understanding.

Activities include the multiplication of integers, decimal fractions, mixed fractions, and expressions with variables. Using algebra tiles, students model and find the product of algebraic expressions such as (x+2)(x+3) and factor expressions such as x2 + 4x +3.