This is an important question that should be discussed with curriculum planners at your school (other TTA teachers, department heads, etc.) prior to the start of the school year. There certainly are schools using TTA in creative ways to supplement their algebra courses, but we recommend carefully considering the integration of the materials. Critically helpful to this kind of planning is to have a clear understanding of the scope and sequence of TTA, which is unlike a traditional pre-algebra or algebra course. Page 14 of the Series Overview includes a mapping of typical Pre-Algebra and Algebra I topics with the units of TTA that may be useful in this process.
TTA is intended for use in an approximately 45-minute class period while students are concurrently enrolled in a traditional 45-minute Algebra 1 course. Contexts that are similar (such as a single 90-minute block), can be modified to match this intended approach as well as possible (such as by teaching TTA for 45 minutes and teaching from a traditional algebra text for the other half of the period). Contexts that are significantly different (such as one 45-minute period for both algebra 1 and TTA) will require more planning ahead of time, and decisions should be made based on the goals of the school's implementation. The authors of TTA have seen successful implementations in a variety of 'off-label' contexts including using TTA as a stand-alone pre-algebra course and using TTA alongside an integrated math 1 course. One factor that stands out as especially important to success, at least anecdotally, is high fidelity to the philosophy of the materials. Teachers can achieve this by carefully reading the provided materials including the Series Overview, the Teacher Guides, and if you have a copy, the Making Sense of Algebra teacher professional book.
TTA was written to be usable alongside any Algebra 1 course, so it is not directly aligned with any specific text. It is expected that the two courses will cover some ideas (such as graphing) at different times. This is not significantly different from students' experiences with other topics taught across multiple courses (such as learning quadratics at a different time in mathematics class than in physics or learning about some part of history at a different time in a social studies class than in English). TTA follows its own coherent trajectory that builds over the course of the year, and while it may seem appealing to reorder the units of TTA so as to align with the traditional algebra course, the TTA authors and researchers highly recommend that teachers follow TTA as written so students experience a coherent building of the conceptual ideas of algebra.