Deep Math Projects

Deep Math Projects are open-ended projects that you can extend by continuing to ask new questions. The problems often have multiple solutions and/or solution paths. The activities are self-differentiating. Students may enter and exit them at points that suit their level of understanding. The grade levels are approximate suggestions, because students can think of the problems and questions on many levels.

Tips for using the projects

  • Be patient. This is a new way of thinking about math for most children and adults. It takes time to get used to it!
  • Join in the spirit of adventure with your student or child! Be prepared for the unexpected. Enjoy getting lost and finding your way back.
  • Make your own fun! Create stories, characters, and/or pictures to go with the math problems. If you share them with me, I may be able to publish some of them on this page.
  • Break it up. You don't have to do the activity all at once. If you get bogged down after a few days (or weeks!), come back to it again later in the school year.
  • Don't worry about finishing. These projects are challenging!  It's better to spend time digging deeply into one or two questions than rushing to complete everything. This is one of those "it's more about the journey than the destination" situations.

Each activity is a free download. Just click on the title of the project!

Magic Numbers (grades 2 - 4)

Students solve problems and explore patterns involving properties of addition and subtraction. The patterns can lead to new calculation strategies and even discoveries about even and odd numbers, fractions, negative numbers, etc.

Multiplication Table Patterns (grades 3 - 4)

The multiplication table is a treasure trove of patterns just waiting to be discovered. Students develop number sense, algebra, reasoning, and communication skills as they make and test predictions about these patterns.

Hopping Home (grades 3 - 4)

Students explore number properties and connections between multiplication and division as they "hop" from one number to another using only two operations.



Building Fractions (grades 2 - 4)

Students draw pictures that show multiple creative ways to represent simple fractions. As they search for many ways to make one whole, they may even begin to discover strategies for adding and subtracting fractions—with and without the same denominators.

Area Challenge (grades 3 - 4)

Students create and compare a variety of polygons that have an area of 4. They explore connections between area perimeter.

Step Up! (grades 3 - 5)

Students use visualizations to discover shortcuts for adding long strings of numbers that follow patterns.

Sharing Marbles (grades 4 - 5)

Students explore properties and patterns in divisibility and remainders as they imagine different ways to share marbles between groups of people.