This book provides background and an overview of the content in the Guzinta Math: Ratio Names math lesson app available at https://guzintamath.com. In this book, we discuss additive and multiplicative reasoning--their similarities, but more importantly, their differences. We also discuss the very nature of ratios and how students can make sense of them from the beginning. Various perspectives are presented which are used to think about ratios: from a simple number-to-number transcription, to the "multiplicative move" of assigning a quantity to the value "1 unit" in order to compare the other quantity in relation to it. We also discuss visual ratios and the "for every" phrasing used when talking about ratios. Finally, some common mistakes and misconceptions regarding ratios are raised.
Ratio Names