# Deep Algebra Projects

Introduction

*Deep Algebra Projects* are rich, complex mathematical and real-world investigations that stretch advanced learners outside their comfort zones. The projects enhance students' abilities to think independently, flexibly, and with deep understanding. Most people initially use the projects as supplementary activities for advanced learners. As you become more familiar with them, you may eventually find that many of the projects work especially well as vehicles to *teach* concepts.

Each project contains approximately five to ten problems organized into three stages that dig progressively deeper into targeted algebra concepts. The projects have very high ceilings in order to stretch the thinking of even the most advanced learners. Most students will not attempt every problem but will progress as far as they are able. The projects may take weeks rather than hours or days to complete.

*Deep Algebra Projects* are ideal for self-contained pre-algebra and algebra courses for highly capable or motivated students and in pullout or push-in environments. In mixed-ability settings, students may need extended time, more moderate expectations, and greater support. In all settings, you can energize the problem-solving process, expose students to more ideas, and increase opportunities for success by encouraging students to collaborate.

Most projects include:

A general

*Introduction*A focused introduction for each of the three stages

Descriptions of

*What Students Should Know*and*What Students Will**Learn*in each stage*Student Handouts*(one problem per page) with plenty of room to write*Conversation Starters*for each problem to help you guide discussionDetailed

*Solutions*showing multiple strategies and ways of thinking*Diving Deeper*suggestions for extending selected problems even further