Projects That Never End
Introduction to Projects That Never End
This page contains a collection of open-ended projects that can be extended indefinitely by asking new questions. The problems often have multiple solutions and/or paths to solutions, encouraging students to use creativity and imagination as well as reasoning. The activities are self-differentiating. Most students will not find every solution or finish every problem. They may enter and exit them at points that suit their level of understanding. The key is for students to work hard on problems that are just beyond their comfort level.
The grade level categories below are suggestions. They correspond approximately with the Common Core Content Standards. However, the projects extend the standards in terms of depth and complexity—and sometimes even in terms of content. They are flexible enough to be used effectively with students of different ages. When choosing problems, you will need to take into account each student's age, experience, perseverance, and capacity, as well as the amount of time available.
New projects are added periodically. Please check back regularly to see what's new—and feel free to contact me to share your experiences and suggestions. I especially appreciate seeing samples of student work.
Notes to Students and Teachers
The activities on this page may look different than what your students are accustomed to. The notes below, which are taken from my Advanced Common Core Math Explorations series, will let you and your students know what to expect from the problems and will promote a mindset that builds confidence and success with challenging problems. I am also including a set of motivation strategies to support the development of habits and beliefs that enable students to make the most of their mathematical talent.
Multiplication Table Patterns
Patterns in Polyhedrons
GRADE 7 (Pre-algebra)
Best Location for a Machine
Stories That Formulas Tell
GRADE 8 (Algebra 1)
Step by Step
More or Less the Same