# A Modeling Approach to Algebra (AMAA)

A Modeling Approach to Algebra (AMAA) provides students with opportunities to use modeling in solving problems. The investigations are motivated by practical questions from application contexts and other interesting questions based on pure mathematics. Students use aspects of modeling to interpret problem situations; understand the goals of a problem; represent, test, and revise various approaches to solving the problem; and report on results.

## Content

The content of this curriculum targets specific high school standards from the section, Traditional Pathway: High School Algebra I, in the Common Core State Standards for Mathematics while also emphasizing the eight Standards for Mathematical Practice, which are at the foundation of the mathematics standards. The materials were originally developed for Hawai‘i public schools, and this version has been adapted for availability to a wider audience.

Significantly, the Modeling Cycle from the Common Core State Standards for Mathematics can be a tool for organizing the work throughout AMAA. It provides a flow of the processes used in taking a situation from problem to report. Modeling as a mathematical practice appears throughout the high school Common Core State Standards for Mathematics. Students have opportunities to create and interpret several different types of models; they decide what data to include and define conditions for including that data; they choose methods for computing when computation is required; they represent various actions with modeling; and they assess the validity of their model and its usefulness in solving new problems.

## Pedagogy

The pedagogy is student-centered, giving students many opportunities to try new strategies and engage in behaviors outlined in the Common Core State Standards for Mathematical Practice. Students explain their thinking, question their own and others’ ideas, and analyze suggested strategies. The debriefing discussions should focus on ideas students share with the class. Students should be encouraged to offer alternate solutions and solution methods, question others’ methods and results, and reflect on their own understanding.

## Teacher Notes

The Teacher Notes support lesson planning by providing information that addresses content, pedagogy, and pedagogical content knowledge. Sections of the Teacher Notes contain a summary of the content and objectives for the investigation, highlight opportunities to model with mathematics, and anticipate student thinking and possible responses—including common misunderstandings.

## Annotated Student Pages

The Annotated Student Pages comprise the material in the student book, notes for managing the investigation, and discussion questions. The questions, highlighted by shading, do not have to be asked verbatim but indicate what mathematics topics and ideas should be considered deeply by teacher and students. As students get used to the instructional approach, they will raise these issues themselves or pose the questions spontaneously.

## Digital Version

The entire A Modeling Approach to Algebra (AMAA) curriculum is provided in a digital format using the TI-NspireTM Teacher Software PublishViewTM feature. The AMAA digital version contains all the Student Pages, Teacher Notes, and Annotated Student Pages as well as interactive TI-NspireTM documents to use with the whole class or, if available, the TI-NspireTM handhelds. The files found in the digital version of AMAA are an important component of the AMAA curriculum. The digital version contains TI-NspireTM documents and web links that are integral to developing student understanding of algebraic concepts found in a number of the AMAA lessons and projects.