Step by Step
A Deep Algebra Project
The Step by Step project is about exploring step graphs. Students begin by figuring out how the greatest integer function works. They continue by drawing graphs and discovering some of the ways in which changing a formula affects its graph. In the process, they analyze the definition of a linear function and its rate of change, explore connections between different representations of functions (especially formulas, tables, and graphs), and learn how to stretch and compress graphs vertically and horizontally. In the final stage, they apply what they have discovered to model a real-world situation about a parking ramp.
About Deep Algebra Projects
The Deep Algebra Projects are rich, complex mathematical and real-world investigations designed specifically to stretch advanced learners beyond their comfort zones and to enhance their ability to think independently, flexibly, and with deep understanding. The projects are ideal for use in self-contained pre-algebra and algebra courses for highly capable or motivated students and in pullout or push-in environments for these students. The projects may also be offered as options in mixed-ability settings if students are given extended time, appropriate expectations, and sufficient support.
Each project contains a set of approximately five to twelve problems organized into three stages that dig progressively deeper into a targeted set of algebra concepts. The projects (the third stages especially) have very high ceilings in order to stretch the thinking of even the most advanced learners. Consequently, most students will not attempt every problem but will progress as far as they are able. Projects may often take weeks rather than hours or days to complete.
Each project includes:
The Deep Algebra Projects are not generally meant as handouts to fill time for students who finish other work, because conversation is a very important part of every project. Students will need to talk with each other and with you in order to experience the full depth and richness of the mathematical ideas. Collaboration is strongly encouraged! It energizes the problem-solving process, exposes students to more ideas, and increases opportunities for success.
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|Grade levels||7th Grade, 8th Grade, 9th Grade|
|Resource types||Critical Thinking, Inquiry|
|Is editable content included?||No|
|Supported file formats|