Download Full Text (8.7 MB)

Download Chapter 1: Getting Ready to Learn Mathematics (912 KB)

Download Chapter 2: Proportional Reasoning and Linear Functions (1.6 MB)

Download Chapter 3: Using Linear Functions to Solve Problems (520 KB)

Download Chapter 4: Introduction to Quadratic Functions (3.4 MB)


Beginning Algebra Made Useful addresses the needs of learners to make sense of algebra by quantifying and generalizing everyday occurrences such as commuting to work, buying gas or pizza, and determining the better deal. It requires learners to actively engage with algebraic concepts through physical and thought experiments in ways that help them connect ideas, representations, and contexts, and solve problems that arise in their daily lives. The text helps learners grow their brains and develop growth mindsets as they learn algebra conceptually. Problem sets continue the process, extending work begun in each lesson, applying new understandings to new contexts, and considering ideas that arise more fully in upcoming lessons. Longer assignments that can be used as group projects are included in the text. Group work is encouraged throughout the text; suggestions for orchestrating group work are included.

The text is open access and free for download by students and instructors in .pdf format. In the electronic format, graphics are in full color and there are live html links to resources, software, and applets.

Publication Date



Grand Valley State University Libraries


Allendale, MI

Creative Commons License

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.


Beginning Algebra, Mathematics, Conceptual Understanding, Real Life, Contextual, Experiential, Growth Mindset, Growing your Brain, Group Work, Remedial Mathematics, Middle School, High School, College University


Algebra | Mathematics


In addition to the permissions granted by the CC-BY-NC-SA license, the author grants permission for bookstores and/or print shops at K-12, colleges, and universities to reproduce and sell print copies of this book. Other commercial uses of the book are not permitted.

Beginning Algebra Made Useful

Included in

Algebra Commons