The subject of algebra has always been important in American secondary mathematics education. However, algebra at the elementary level has been garnering increasing attention and importance over the past 15 years. There is consequently a dire need for ideas, suggestions and models for how best to achieve pre-algebraic instruction in the elementary grades. Planting the Seeds of Algebra will empower teachers with theoretical and practical knowledge about both the content and pedagogy of such instruction, and show them the different faces of algebra as it appears in the early grades. The book will walk teachers of young children through many examples of K-6 math lessons and unpack, step by step, the hidden connections to higher algebra. After reading this book, teachers will be better equipped to reflect on their teaching, renew their thinking, and change parts of their practice in order to transform their classroom culture into one where both students and teachers are attuned to algebraic thinking, reasoning, talking, writing, and doing.

Beyond Making 7—More Problems to Explore

Beyond making 7—more problems to explore

Detailed answers to the nontrivial questions under the section below titled “For Your Own Learning” can be found in the companion website for this book at–12.

For your Own Learning

1. Connecting to “Opposite Change”

You may be familiar with a first-grade, child-friendly addition algorithm sometimes called the “opposite-change” method (e.g., this phrase is used in early editions of the Everyday Mathematics curriculum). For example, you can solve the addition problem

by making a simple change in the first addend (add 1), and making the opposite change in the second addend (subtract 1). You could also add 2 to 18 and subtract 2 from 29. In either case, you obtain a zero in the ones ...

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