# 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.

**GRADE 3**

Magic Numbers

Magic Numbers activity

Magic Numbers guide

Magic Numbers solutions

Building Fractions

Building Fractions activity

Building Fractions notes

Building Fractions solutions

Building Fractions assessments

**GRADE 4**

Multiplication Table Patterns

Multiplication Table Patterns activity

Multiplication Table Patterns solutions

Sharing Marbles

Sharing Marbles activity

Sharing Marbles solutions

**GRADE 5**

Magic Squares

**GRADE 6**

Sports Formulas

Sports Formulas activity and solutions

Patterns in Polyhedrons

Patterns in Polyhedrons activity and solutions

**GRADE 7 (Pre-algebra)**

Integer Interpreter

Integer Interpreter activity and solutions

Best Location for a Machine

Best Location for a Machine activity

Best Location for a Machine solutions

Stories That Formulas Tell

Stories That Formulas Tell activity and solutions

**GRADE 8 (Algebra 1)**

Step by Step

Step by Step activity and solutions

Aquarium Equations

More or Less the Same