Every activity at Math On-A-Stick has two design principles:

  • It should be obvious how to get started: kids should want to interact with the materials, and whatever they start doing is just right.
  • The longer you persist, the more mathematics will spontaneously emerge, as you start thinking about designs, patterns, how many, will this work, why...

Each of the activities below fits those principles. Whether you are organizing your own math event or looking for activities to play with kids at home or in your classroom, please consider this as the main rule for grownups at Math On-A-Stick: 

Let the children play!

Feel free to play alongside your kids, to be an interested observer, to pay attention to their thinking and ask them to tell you about what they're thinking. We've found that when grownups try to turn these activities into mathematical challenges and give kids tasks to complete with the materials, the kids don't keep playing after they're "done" -- but when kids are left to play and explore, they spend LOTS of time with each item and the math gets deep in a way that's meaningful to the child.

Here are some more tips for hosting your own Math On-A-Stick event.

Stepping Stones

Kids of all ages love to walk, hop, skip, leap, and of course count on the stepping stones. We overheard lots of counting (forwards and backwards) in English, Spanish, French, ASL, Arabic... Questions we heard included, "What comes next?" "What comes before 0?" "How many stepping stones are there?" "0, 3, 6, 9, ... what's next?" "How far can you leap?" "Can you step on just the prime numbers?"

Resources and materials:

Play at home: Use paper plates, sidewalk chalk, or painter's tape to mark off 24 separate "stepping stones" in the hallway, on the sidewalk, or on a patio or blacktop. Number them 0 - 23 and let the hopping, skipping, and jumping commence. Tip: a good spacing for the stepping stones is one small child step from center to center. 

Pattern Machines

Pattern Machines are fun for making patterns and designs, exploring shapes like squares and rectangles, discovering and creating symmetries, and counting. Plus they are so fun to touch, pushing the buttons up or down and racing to push them all.

Resources and materials:

Play at home, Pattern Machines: Look online, at garage sales, or ask at elementary schools for your own Self-Teaching Math Machine. Then ignore the math facts printed on them by covering them up with tape, turning them into open-ended machines for exploration. Let your child play with the Pattern Machine for as long as they want, and listen and watch them to notice when they: make patterns, such as pushing every other square; notice or create shapes like squares and rectangles; create designs that have different symmetries; count out loud or use counting to make their designs; race to push all the buttons as fast as possible. Ask questions about what they are noticing or trying and enjoy the conversations about "How did you decide?" "How many?" "How do you know?"

Eggs and Cartons

Like Pattern Machines, Eggs and Cartons are fun for making patterns and designs, exploring shapes like squares and rectangles, discovering and creating symmetries, and counting. Plus Eggs and Cartons are just the right size for little hands and come in such great colors -- it's inviting to sort, arrange, and design with them!

Resources and materials:

  • Plastic eggs in 5 or more different colors
  • Egg cartons, lids removed, ideally in different sizes (most grocery stores have cartons for 18 eggs; stores for bulk-buying might have cartons for 24 or 30 eggs). Or tape together several cartons to make new arrays to fill.
  • Volunteer handout [pdf]

Play at home, Eggs & Cartons: Save the cartons from buying eggs. Buy a larger than normal amount of eggs to get bigger cartons, or cut up and re-tape together several cartons saved over time to make a 5-by-6 or bigger egg carton to fill with eggs. Buy (or find in the basement/attic/playroom/storage) some cheap plastic Easter eggs in at least 5 different colors. Hand over the big carton and eggs and let the play begin. Watch your child and notice: do they try to fill the whole carton? Do they use colors haphazardly or with purpose? Do the designs get more purposeful over time? Do they leave some holes in the carton empty? Do they use whole eggs or half eggs? Do they count out loud or as part of their designs? As their designs become more purposeful, it's a great time to ask questions like, "How did you decide?" "How many?" "How do you know?"

Lizards and Turtles


Our Lizards and Turtles are tessellating tiles -- sort of like puzzle pieces that can be assembled in all sorts of ways (all of which are the right way!). Visitors of all ages loved exploring how the pieces fit together and designing different shapes and patterns with them. 

Resources and materials:

  • Tiling Turtles, for sale from the Talking Math With Your Kids store
  • Other tessellating toys (our lizards are not for sale, but if you can get your hands on an old Shmuzzle Puzzle, they're very similar)
  • Or have volunteers cut out other tessellating patterns from cardboard or heavy cardstock. Here are some sources for tiling patterns: 

Play at home: Consider buying some Tiling Turtles, finding a Shmuzzle Puzzle, or cutting out your own tessellating toys from a pattern you find online, for some hands-on fun for everyone. For older kids who can use the computer, there are lots of cool websites and software to play with tessellations. Start with the virtual Shmuzzles, then check out some tutorials for designing your own tessellating patterns! 

Tiles and Patterns

These tiling blocks brought out the mathematical designers in everyone who played with them -- from filling the whole table with no gaps, to making beautiful repeating designs, to making specific geometric shapes like squares, triangles, and even quilting patterns, to making 3-D towers, there are lots of ways to play with these simple blocks. The key is to make sure each block is twice as long as it is wide, to ensure plenty of ways to fit the blocks together.

Resources and materials:

Visiting Artists

Over the course of the fair, visiting artists came and brought awesome crafts, games, and activities. Here are some of the activities that were shared by each artist. These might make lovely additions to your math event or family math play, but also consider finding your own visiting math artist by consulting local college and university math departments, or local artists whose art is particularly math-y!

The Number Game

Young mathematicians count their way around the fair, looking for sets of objects they can count, from sizes 1 through 20. For example, they might count four legs on a cow, or four tires on a tractor, or four yellow squares on a particular quilt. Finding the number four written on a bumper car or someone's jersey would not count... the goal is to count objects and define sets that are just the right size.

Resources and materials: (note: shopping links are just suggestions, not endorsements or recommendations)

Play at home: Make your child a Number Game card and take it with you on your next errand or fun outing. Or just look for sets of objects around the house, or even in a single room. Eight dinner plates? One "Happy Birthday" mug? Four measuring cups?" How long until the Number Game changes the way you look at the world?