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Planting the Seeds of Algebra, 3-5

Planting the Seeds of Algebra, 3-5
Explorations for the Upper Elementary Grades

Forewords by Francis (Skip) Fennell and Keith Devlin

December 2014 | 248 pages | Corwin

Give your students a foundation of algebra for math success – now and in the future!


Algebra is not something to be feared, but something to be embraced with a sense of wonder. Planting the Seeds of Algebra, 3-5, introduces algebra as an accessible way of seeing the world that is necessary to our students’ futures.


Students and teachers must become friendly with algebraic foundations, as they have increasingly become the gateway to careers in the STEM fields. Monica Neagoy empowers teachers with theoretical and practical ways to introduce Algebra to 3-5 grade students, making vital connections to concepts they will encounter in middle school and beyond. You’ll discover

  • Four explorations to help you weave key algebraic ideas into everyday mathematics
  • Step-by-step lessons from real classrooms that will guide you in teaching concepts and in establishing their relevance and applicability
  • New teaching methods that break down difficult algebraic concepts and build a critical foundation for higher math

Awaken new awareness and change attitudes by sowing the seeds for a vibrant, useful, and rich experience with mathematics.

"While reading this book I experienced the sense of wonder and aha moments alongside the students themselves. This book will move your faculty to new depths of understanding about mathematics and will instill the passion to explore a myriad of algebraic concepts.”

— Bob Weiman, Director

St. Stephen’s & St. Agnes School


“She’s done it again! Monica Neagoy has authored another book that deftly presents important foundations of algebra while celebrating mathematics through carefully crafted explorations, all of which include student and teacher vignettes and comments about the mathematics they have learned and are teaching. Wow. When I read this book I felt like I was in a classroom!” 

Francis (Skip) Fennell, McDaniel College
Past President of the National Council of Teachers of Mathematics

Foreword by a Mathematics Educator by Dr. Francis (Skip) Fennell
Foreword by a Mathematician by Dr. Keith Devlin
About the Author
Exploration I. Geometry, Measurement, and Data: An Algebraic Perspective
Chapter 1. Circling Circles: The Lesson (Grade 3)
Chapter 2. Behind Circling Circles: Algebra Connections
Chapter 3. Beyond Circling Circles: More Problems to Explore
Exploration II. Patterns and Functions: What’s Their Connection to Algebra?
Chapter 4. Fancy Fences: The Lesson (Grades 4–5)
Chapter 5. Behind Fancy Fences: Algebra Connections
Chapter 6. Beyond Fancy Fences: More Problems to Explore
Exploration III. Making Sense of Multiplication: The Importance of the Distributive Property
Chapter 7. Multiplication Musings: The Lesson (Grades 3–4)
Chapter 8. Behind Multiplication Musings: Algebra Connections
Chapter 9. Beyond Multiplication Musings: More Problems to Explore
Exploration IV. Fundamentals of Rational Numbers: Beyond Part–Whole Relationships
Chapter 10. Fractions in Action: From Work With Teachers, Students, and Parents (Grades 3–5)
Chapter 11. Final Thoughts

Free resources

"The classroom demonstration lessons are so detailed that after perusing the lesson, creating a few charts, and gathering materials teachers will be able to implement the lesson immediately."

Stacey Bennett Ferguson, 4th grade teacher
North Bay Elementary School, Bay Saint Louis, MS

“This book will make classroom instruction more effective while transitioning to Common Core State Standards requirements.  Elementary students will benefit greatly after making meaningful connections to foundational algebraic concepts in later grades.”

Nancy J. Larsen, 6th grade teacher
Coeur d’Alene, ID

"This book is terrific! Well-written and FULL of information.  The writer is SO knowledgeable and presents the information SO well.  Background information and sample lessons are provided that will make the teacher the expert and the students active learners who carry a positive attitude and better understanding of math with them to middle and high school."

Joyce Sager, Inclusion Math Teacher
Gadsden City High School, Gadsden, AL

"Discover how math is about more than just learning the algorithm to get the right answer. If given stimulating problems to explore, children can discover how to solve problems using algebraic thinking! Teachers who engage in the strategies presented in this book will be able to support students as they learn.  Whether you love math or find it intimidating, this book will lead you to enjoy thinking mathematically."

Amy Krumich, 3rd grade teacher
Middleburg, VA

"Dr. Neagoy artfully combines theory, research, and practice to transform the way elementary teachers think about and teach algebraic concepts. Teachers who read this book will enter the classroom with enhanced knowledge, confidence, passion, and a deep understanding about how teaching algebraic concepts will delight and inspire students while setting them up for future mathematical success. If you want your teachers to understand foundational algebraic principles, read detailed math explorations that they can replicate in their classrooms, learn how upper elementary mathematics leads to higher level algebraic thinking, and inspire their students to love math, then give them a copy of Planting the Seeds of Algebra 3-5."

Bob Weiman, Lower School Director/Assistant Head of School
St. Stephen's & St. Agnes School, Alexandria, VA

"This is an invaluable resource for any teacher hoping to offer their students a deeper understanding of mathematical concepts. Filled with engaging and interactive activities and lessons based on extensive research. It will help teachers learn the math in depth, allowing for greater differentiation in their teaching."

Ann Bremner, Math Resource Teacher
FCPS, Fairfax, Virginia


"Monica Neagoy's extensive knowledge of mathematics is surpassed only by her exceptional ability to impart that knowledge to others. She thrives on helping educators and their students arrive independently at solutions in order to construct their own understanding of concepts. In this text, Dr. Neagoy directly addresses the teaching of many of the most challenging topics in elementary mathematics, explaining them in clear and precise terms. This enriching text belongs on the bookshelf of every mathematics teacher."

Kerianne Gritt, 5th Grade Teacher
St. Stephen's & St. Agnes School, Alexandria, VA

"This book demonstrates Dr. Neagoy’s deep commitment to helping  our students  think critically and develop a deep understanding of mathematical concepts. Dr. Neagoy describes where we can incorporate algebra concepts into our classrooms so our students are better prepared."

Jay Tucker, 4th grade math teacher
Georgetown Day School

"Dr. Monica Neagoy´s passion for mathematics is contagious: it comes through her writings and even more when she presents her ideas in person. Working with Dr. Monica Neagoy over two years, and getting her book ideas first hand, has given me a deeper appreciation for mathematics and has made me a stronger math teacher. Her energy inspires teachers, students, and parents to want to learn more about the magic of algebra."

Jennifer Gibbs, 5th grade teacher
Benjamin Franklin International School, Barcelona, Spain

"Dr. Neagoy’s lessons and ideas dramatically changed my approach to teaching mathematics and my students' approach to thinking mathematically. Math time became about solving complex problems, debating over solutions, and articulating processes in ways that demonstrate deep understanding. My students became collaborators and co-constructors in their own learning. Through Dr. Neagoy's work, I realized that I no longer need to be the content expert and impart that content to my students through tired lessons. Rather, I am the facilitator of guided discovery and rich discussions."

Mollie Cura, International Educational Consultant
Cura Literacy Consulting, Dublin, Ireland
Key features
  • Through the examination of four explorations Planting the Seeds of Algebra provides details for how algebraic thinking can be effectively incorporated into the teaching and learning of 3-5 mathematics. Key ideas of algebra are weaved into these explorations, such as the difference and connection between variable and unknown, equality and equivalence, expressions and equations. Also, the relationship between patterns and functions, functions and algebra, and consequently patterns and algebra will be clarified.
  • Each chapter offers profound discussions on topics such as number properties, basic facts, computation, fractions, ratios and rates, patterns, geometry, measurement, probability, math games, and so on, all of which are of direct concern to elementary school teachers.
  • Each chapter contains a section that revisits the different stages of the lesson and discussion, bringing to light the connections to algebra that teachers are sometimes unaware of. The purpose of this section is therefore to guide teachers to become mindful of the rich potential of laying a solid algebra foundation through the mathematics they already teach every day.

Sample Materials & Chapters


Chapter 1

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ISBN: 9781412996617

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