I’ve done math-based themes before (like one on shapes), but for this one I wanted the exploration to be loose, broad, and focused on how much fun you can have with mathematical concepts. So here you’ll find puzzles, food, games, paint, and a few tricks that feel like magic. (There are some practical bits and pieces, too, of course.)
What Kids Will Do
In these explorations, kids might…
- Built a human-sized kaleidoscope
- Act out the Monty Hall problem
- Play with mirror symmetry
- Make patterns with Easter eggs
- Make tetraflexagons and hexaflexagons
- Play number hopscotch
- Make tortilla fractions
- Play the solution to the Tower of Hanoi on a xylophone
- Make paint fractals
- Arrange tessellating cats
- Eat Fibonacci sequence snacks
- and more
Designed for preschool and lower elementary students, but many parts will be enjoyable for older children and adults, too.
- Amazing Visual Math, DK [Amazon | Bookshop] — This beautiful, incredibly engaging book is nothing but flaps and pull tabs, covering some basic addition (making ten), 2- and 3-D shapes, multiplication and division, and fractions. It’s only 17 pages, so it’s not a full course, but it’s a wonderful way to engage with math: by pulling a tab to explore multiplication, folding loads of nets to make 3-D solids, and spinning a wheel to work with fractions. Plus, there’s a flap-based quiz at the end and the whole book is printed in eye-poppingly bright colors. A truly impressive piece of paper engineering and a fun look at math, too.
- What’s the Point of Math?, DK [Amazon | Bookshop] — This brilliantly fun math book is structured as a series of “how to” questions: how to track time, how to measure the Earth, how to keep secrets, how to catch a cheat, how to win a game show, how to escape prison. All of the answers, of course, use math. And it’s packed with history, too, about ancient civilizations, famous mathematicians, and major breakthroughs. I found it compelling enough that I read it cover-to-cover — though I stopped plenty of times to do more research on the bits and pieces I learned in the book. Although much of the book is too complicated for early elementary readers (in fact, some of it is better suited to much older kids and grown-ups), there is still plenty to enjoy here even for them.
- Getting Started with Math, Katie Daynes and Stefano Tognetti [Amazon | Usborne] — This terrific, readable introduction to math is perfect for preschool through mid-elementary. It features chapters on adding and subtracting, fractions, measuring, telling time, money, shapes, patterns, data, and more, all clearly written, cleanly presented, and beautifully organized. Cute insects comment on the text, too, so it feels fun and approachable. If you want an overview for young children, this is a fantastic one.
- Eat Your Math Homework: Recipes for Hungry Minds, Ann McCallum and Leeza Hernandez [Amazon | Bookshop] — This ingenious cookbook offers brief, clear lessons on mathematical topics, followed by clever recipes inspired by them. The recipes themselves are simple (fraction tortilla chips and Fibonacci snack skewers, for instance), but the book encourages kids to play with their food, too — to solve math puzzles about trail mix, to combine different fractions to make a whole. The food is uncomplicated and the activities are fun. Really enjoyable and so well done.
- This Book Thinks You’re a Math Genius, Georgia Amson-Bradshaw and Harriet Russell [Amazon | Bookshop] — This series of activity books is one of my favorites: it always gives clear, concise explanations and the activities and experiments are top-notch, the kinds of things you’d actually want to do. Some of the math here is appropriate for early elementary students, but some is a bit more advanced. So there’s a range, covering shapes, measurement, mazes and networks, patterns, codes and ciphers, logic, and a section appealingly titled “math carnival.” The “Math Lab” section at the back takes up nearly half the book and is full of things to cut out (and, thankfully, each project is on its own sheet, so you don’t have to destroy one project to do another). I love this series — really fun.
- More, Fewer, Less, Tana Hoban [Amazon | Bookshop] — Tana Hoban’s books of photography are some of my favorites for kids. They’re wonderfully free of directions and full of detail, so there’s always something new to notice and talk about. This one features big color photographs of scenes that invite kids to count and compare: a market display of scissors, bowls of fruit, a truck overflowing with pumpkins, a colorful stack of shopping baskets. Her books belong in every home library.
- How Many?, Christopher Danielson [Amazon | Bookshop] — If you love Tana Hoban’s books, here’s a more modern take on a similar concept: a collection of photos, (mostly) free of directions, that invites kids to think creatively, count, and compare. What will you count in each picture? The eggs? Or the cups in the egg carton? Or the holes in the carton? Or the cartons themselves? In Danielson’s book, it gradually becomes clear that the photos are thematically linked (someone is making a meal) — there’s a delightful cleverness to the design. And at the very end, he asks a few questions about the preceding pages, questions intriguing enough to make you go back and examine it all over again. This is math for kids as it should be done.
- A Triangle for Adaora: An African Book of Shapes, Ifeoma Onyefulu [Amazon] — In this incredibly charming picture book, our young narrator takes his little sister, Adaora, go on a triangle hunt in their village. Although it’s much easier to find other shapes, his sister is adamant: find me a triangle! Much like in Tana Hoban’s books, this book shows kids how they can look for shapes in their surroundings. But here there’s a plot, too, and Adaora and her brother are a very cute and funny pair — the insistent sister and her loving but exasperated brother.
- Max’s Math, Kate Banks and Boris Kulikov [Amazon] — Max and his brothers pile into a homemade car and go looking for problems (“Because it’s fun”) in a surreal, dreamlike world of math. As they explore Shapesville and Count Town, they count, solve equations, sort items, and manipulate shapes — and they even get pulled into space on a kite and ride a constellation back down. It’s an offbeat, rather compelling read, and it pairs wonderfully well with tangram activities.
- Which One Doesn’t Belong, Christopher Danielson [Amazon | Bookshop] — This incredibly clever math book invites children to compare groupings of four items and decide which one doesn’t belong. There are no wrong answers, the book says, but you must be able to explain the answer you give. It’s a great concept, brilliantly done, and it gets everyone thinking, from preschoolers to adults. Sometimes it’s easy to come up with a few answers, and sometimes it’s much trickier. Tricky enough, in fact, that kids could come back to this one again and again.
- The Animals Would Not Sleep!, Sara Levine and Marta Álvarez Miguéns [Amazon | Bookshop] — From the excellent Storytelling Math series, an engaging book about sorting and problem-solving. Before bed, Marco wants to sort his stuffed animals, but every time he sorts them into categories — by color and by size, for example — an animal has a complaint. Can he sort his animals and satisfy their demands before bedtime? As with all Storytelling Math books, this one has a list of suggested activities at the end, but you can also make a list of what every animal asks for and evaluate whether Marco makes everyone happy with his final solution. The illustrations here are adorable, too — a great read with loads of things to notice and talk about.
- This Equals That, Jason Fulford and Tamara Shopsin [Amazon | Bookshop] — In this delightful circular book (which is actually a square), readers are asked to consider a pair of photographs. The second photograph is then juxtaposed with another on the next page, and so on, as the pages proceed like “visual dominoes.” As in Christopher Danielson’s books, there are no right answers and the photographs encourage you to be creative and thoughtful — and, of course, to think mathematically. Looking at this is fun even for adults (and it would be brilliant to take a series of “visual domino” photos yourself, too).
- Rooster’s Off to See the World, Eric Carle [Amazon | Bookshop] — A classic book that uses a plus-one growing pattern.
- The Napping House, Audrey Wood and Don Wood [Amazon | Bookshop] — Another good plus-one growing pattern book.
- The Little Old Lady Who Was Not Afraid of Anything, Linda Williams and Megan Lloyd [Amazon | Bookshop] — A great plus-one growing pattern book, this time with physical actions kids can do along with it (clapping, stomping, wiggling).
- Bracelets for Bina’s Brothers, Rajani LaRocca and Chaya Prabhat [Amazon | Bookshop] — A lovely and fun math book about patterns. Bina is making bracelets for her three brothers for Raksha Bandhan. She carefully plans her bracelets and then strings colored beads onto each one in a pattern, making sure that she avoids colors that each brother doesn’t like. This would pair so well with making bracelets, of course!
- One Grain of Rice: A Mathematical Folktale, Demi [Amazon | Bookshop]— A gorgeously illustrated folktale featuring a doubling pattern and exponential growth. As a reward for returning some lost rice to the raja, Rani asks for what seems to be a simple, small reward: one grain of rice on the first day and then double each previous day’s amount for thirty days. It seems a small thing to ask, doesn’t it? As the days’ rewards grow bigger, the book employs fold-out pages to show just how quickly Rani’s rewards have grown. It’s a terrific read and a wonderful demonstration of doubling.
- Look, Grandma! Ni, Elisi!, Art Coulson and Madelyn Goodnight [Amazon | Bookshop] — Another superb book from Storytelling Math, this time written by an indigenous author and illustrator team about Cherokee marbles and the mathematical concepts of area, capacity, and volume. Bo needs to find a vessel to hold his hand-painted marbles so that he can sell them at the festival, but the vessel has to be both big enough for all the marbles and compact enough to fit in the available space in his grandmother’s stall. And of course he has to do quite a bit of problem-solving to find the right one. The back of the book has a glossary of Cherokee words, instructions for how to play marbles, and a few great math activity suggestions, too.
- Inch by Inch, Leo Lionni [Amazon | Bookshop] — A classic about an inchworm who measures, with a clever twist at the end.
- Lia and Luís: Who Has More?, Ana Crespo and Giovana Medeiros [Amazon | Bookshop] — From Storytelling Math, a tale about comparison. Siblings Lia and Luís choose their favorite Brazilian treats, but whereas Luís has one bag with many tiny treats, Lia has two individual, larger treats. So who has more? The children look at the problem from several angles before deciding on a solution.
- Prehistoric Actual Size, Steve Jenkins [Amazon | Bookshop] — I love Steve Jenkins’s non-fiction. Like his excellent Bones, this book has beautiful pictures and just the right amount of text for reading aloud. Here, whole bodies or parts of bodies of prehistoric creatures are shown actual size, from the smallest dinosaurs, to a predator’s giant teeth, to the head of a 6-foot-long millipede. It’s terrifically fun to look at, and if you’re working on lengths and measurement, this is a handy and exciting book to practice with.
- Molly and the Mathematical Mysteries: Ten Interactive Adventures in Mathematical Wonderland, Eugenia Cheng and Aleksandra Artymowska [Amazon | Bookshop] — Some books are so impressive that it’s hard to know where to start. So: first, this is a work of art, with exquisite illustrations and puzzles kids can solve by manipulating elements of the book. But more importantly, it’s a book that can make both kids and adults excited about math. Molly receives a mysterious invitation to go on a mathematical adventure, and in every new, gorgeous room she finds herself in, there’s yet another letter, with hints about how to solve the puzzle there and move on to the next one. Each spread of pages focuses on a different concept: infinity, self-similarity, tessellation, impossible objects, symmetry, fractals, and more. (The back of the book has more detail on these concepts and others, too.) Reading this is a marvelous way to expose kids to the idea that math is more than just equations — that it can be fun, mind-bending, creative, and beautiful.
- Numberphile’s YouTube channel — An absolutely superb collection of math videos. They aren’t aimed specifically at kids, but kids might enjoy many of them nevertheless.
- Talking Math With Your Kids blog (Christopher Danielson) — A thoughtful, helpful, and extremely interesting blog about doing math with kids. Danielson’s books are also excellent.
- Erikson Institute Early Math Collaborative’s book list — If you’re looking for a picture book on a specific topic, this list is very useful. The Early Math Collaborative also has fantastic lesson ideas for many of the books and videos that model how to teach math to young children.
- Math Book Magic — An excellent resource for finding great books about math.
- Mathical Award Winning Books — Yet another good place to find math books.
Read: “What Is Math?,” Getting Started with Math, Katie Daynes and Stefano Tognetti [Amazon | Usborne] 4-7
Read: “Numbers,” Getting Started with Math 8-13
Read: More, Fewer, Less, Tana Hoban [Amazon | Bookshop]
Read: “How to Track Time,” Tally Marks, What’s the Point of Math? 10-13
Look: The Ishango Bone (be aware, though, that whether these marks are tally marks is debated)
The Lebombo Bone
Activity: Tally Walk
During a walk, count something with tally marks (your choice of tallying system). Depending on the season, you could count holiday inflatables, pumpkins, door wreaths, or dogs and cats.
Read: How Many?, Christopher Danielson [Amazon | Bookshop]
Activity: Number stepping stones
Using chalk, create a number path. Depending on their abilities, kids can step along it while counting by 1s, 2s, 3s, 5s, or 10s. Full instructions (and more great ideas) here. You can also do a similar activity indoors with pillows or painter’s tape.
Read: The Animals Would Not Sleep!, Sara Levine and Marta Álvarez Miguéns [Amazon | Bookshop]
Activity: Sorting guessing game
With a collection of random objects (like toys), have a player sort the objects into two groups (by color, texture, size, function). The other players will guess the sorting criteria. Find full instructions, as well as other activity ideas for The Animals Would Not Sleep!, here.
Read: “Shapes,” Getting Started with Math 66-69
“Shaping Up,” Amazing Visual Math 4-5
A Triangle for Adaora: An African Book of Shapes, Ifeoma Onyefulu [Amazon] and/or a Tana Hoban book like Shapes, Shapes, Shapes [Amazon]
Watch: Changing Shape, Sesame Street
Read: Max’s Math, Kate Banks and Boris Kulikov [Amazon]
Read: “3-D Pops,” Amazing Visual Math 6-7
Activity: Feel for shapes
If you have tangrams, put them in a cloth (or other opaque) bag and have children reach in and describe the shape they’re touching (without looking at it). Full instructions here. If you have 3D solids, you can do the same activity with those, too.
Read: Which One Doesn’t Belong, Christopher Danielson [Amazon | Bookshop]
Activity: Make tetraflexagons and hexaflexagons
For a video guide to making tetraflexagons (and fractal tetraflexagons from the cut-out centers), see this video. For hexaflexagons, see this video and these templates. If you’re working with younger children, tetraflexagons are quite a bit easier to make and flip, but both of these projects are terrifically exciting.
Activity: Make a Möbius strip
For instructions on how to make one and also more amazing Möbius strip demonstrations (like how to make an interesting Möbius strip sculpture), watch this video.
Read: This Equals That, Jason Fulford and Tamara Shopsin [Amazon | Bookshop]
Activity: Visual dominoes
From Fulford and Shopsin’s book, a downloadable set of visual dominoes to play with. Download them here.
Watch: Symmetry (from Numberock)
Optional Watch: Symmetry
Activity: Create symmetrical paper objects
In this valuable classic lesson, use folded paper and scissors to create a variety of symmetrical objects
Activity: Explore symmetry with mirrors
Print out large letters and shapes and find which ones are symmetrical — is there a way to place the mirror that finds a line of symmetry? Find instructions here. I typed out the letters myself, but I used this image of polygons. And I’ve used these flexible, shatterproof mirrors in loads of projects.
Activity: Magnatile symmetry
If you have Magnatiles (or tangrams), set them up by a mirror and create symmetrical designs. I used these flexible, shatterproof mirrors and stood them up using binder clips.
Activity: Mirror movements
Have children face each other (or face you) and mirror your movements, using your hands or your whole body.
I also highly recommend these wonderful tessellating turtles. They’re so beautiful and there’s just the right amount of challenge to putting them together.
Read: “Fractions,” Getting Started With Math 42-45
Watch: Fractions (from Numberock)
Read: Luna’s Yum Yum Dim Sum, Natasha Yim and Violet Kim [Amazon | Bookshop]
Activity: Make fraction chips
Lightly fry and divide a series of tortillas, then mix and match the pieces to make wholes.
(From the excellent Eat Your Math Homework 14-17)
Optional activity: Fraction fill-in
For older kids, you might try this clever game.
Patterns and Sequences
Read: “Patterns and Sequences,” Getting Started with Math 72-73
Activity: Make a pattern with Easter eggs in an egg tray
From Christopher Danielson, this activity is extremely simple but so popular with kids. Full instructions here. You can also do other incredible things with Easter eggs, as below (you can find the small sport rings, useful for all sorts of activities, here).
Read and do: The Little Old Lady Who Was Not Afraid of Anything, Linda Williams and Megan Lloyd [Amazon | Bookshop]
or The Napping House, Audrey Wood and Don Wood [Amazon | Bookshop]
As with Rooster’s Off to See the World, you can map out the patterns in these books with Duplo or icons or, in the case of The Little Old Lady Who Was Not Afraid of Anything, with household objects (clothing items and a pumpkin bucket, should you have one). You might find this teaching video about The Napping House helpful.
Read: Bracelets for Bina’s Brothers, Rajani LaRocca and Chaya Prabhat [Amazon | Bookshop]
Activity: Make patterned bead bracelets, as in Bracelet’s for Bina’s Brothers
Read: “Fibonacci Snack Sticks,” Eat Your Math Homework 7-11
Activity: Make Fibonacci snack sticks
As in Eat Your Math Homework, spear small foods on bamboo skewers to mimic the Fibonacci sequence.
Read: “Fun with Fractals,” The Language of the Universe 18-19
Watch: Fun with Fractals
How Fractals Can Help You Understand the Universe
Mandelbrot Fractal Zoom
Activity: Make fractals
Using CD jewel cases and paint, you can quickly make beautiful fractals. Gloss paint will dry quickly, but I used acrylic and the fractals turned out really well, too. (Just leave them on a shelf to dry for a few days.) Full instructions here.
Optional read and watch: The Unit Is the Thing That You Count
Read: “Measuring,” Getting Started with Math 46-51
Inch by Inch, Leo Lionni [Amazon | Bookshop]
Prehistoric Actual Size, Steve Jenkins [Amazon | Bookshop]
Activity: Measuring with different units
Select toys or other objects to measure, then measure them with a ruler, paper clips, or even other toys. (To the right is a block measured with a ruler, paper clips, and toy cars.)
Read: (About area), Getting Started with Math 53
Activity: Cracker area calculations
Using a set number of Wheat Thins or other square crackers, make different configurations with the same area. (From Look, Grandma! Ni, Elisi!)
Read: (About volume), Getting Started with Math 57
Look, Grandma! Ni, Elisi!, Art Coulson and Madelyn Goodnight [Amazon | Bookshop]
Activity: Pouring experiment
Gather a variety of different containers: big, wide ones; tall, thin ones; shallow ones. Pour a set amount of water from one to the other, predicting how much of each vessel the liquid will fill.
Activity: Measure the volume of your foot
Place a large casserole dish onto a baking tray and fill it with water. Have kids step into the dish, then measure how much water is displaced to find the volume of their feet (or hands or other objects).
Read: Lia and Luís: Who Has More?, Ana Crespo and Giovana Medeiros [Amazon | Bookshop]
Read: “Telling the Time,” Getting Started with Math 58-61
And/or “How to Tell the Time,” What’s the Point of Math? 56-9 (on the history of time-keeping)
Activity: Hula hoop clock
Set up a hoop on a piece of paper and label it. When you call out times, kids can move stick hands to set the correct times. You could also do this outdoors and label it with sidewalk chalk. Full instructions here. For the small sport rings I used in this and other activities, you can click here.
You can also find a useful online clock tool here.
Read: “How to Win a Game Show,” What’s the Point of Math? 112-115
And/or watch: The Monty Hall Problem
Activity: Act out the Monty Hall problem
You might think this is a stretch with younger children, but I’ve found that it’s wildly popular and thrilling (particularly if you use an edible prize, like marshmallows). Label your “doors” (any boxes will do) with sticky notes and put dud prizes in all but one. (We used dinosaur skeletons and marshmallows.) Try selecting first by sticking with your original choice, then try switching your choice after the host’s reveal. Do it at least ten times each, keeping track of the results. Which strategy was more effective? Then try it with more doors (like 5) and see how the results compare.
Activity: Probability trail mix
Make trail mix with a variety of small, similarly-sized pieces (raisins, nuts, chocolate chips, candies). Put in different amounts of each, but keep track of how much is in each bag and label them. Then have kids reach in a set number of times and record what they draw out each time. How often did they pull out the most common item? The least common? (From Eat Your Math Homework.)
Optional read: “Towers of Hanoi,” This Book Thinks You’re a Math Genius 63-64 (it’s a bare-bones read, so only bother if you’ve already got the book)
Watch: Key to the Tower of Hanoi (for first few minutes — or for as long as it’s of interest)
And/or: Towers of Hanoi: A Complete Recursive Visualization
Activity: Tower of Hanoi (moving stacks)
I still had a baby’s stacking toy, but you also could do this with little boxes or cut-out circles in assorted sizes. I marked the three spots on the floor, too, to help the kids keep track of where the blocks could be moved.
Activity: Play the optimal solution to the 6-level Tower of Hanoi puzzle
The brilliant Numberphile video above uses tones to help show the solution to the puzzle. We discovered we could play the solution on a child’s small xylophone. Simply write down the moves from the video (starting here) and try playing it (1 is C, 2 is D, and so on). It’s a fun challenge and really helps in understanding how the pieces move in the puzzle.
It’s difficult to explore infinity in a hands-on way, so we made do with with the illusion of infinity, or just really big numbers. (But it’s great fun.)
Watch: Infinity Paradoxes (just the first chapter)
Activity: Look Into Infinity
This activity works well with these flexible, shatterproof mirrors. Full instructions here.
Activity: Build a human-sized kaleidoscope
Once you figure out the right pieces to order (I ordered three of these, though you can find similar pieces at many plastics stores), this super-impressive activity is incredibly simple. I just used duct tape to attach the mirrors to each other and then balanced the kaleidoscope on top of a large, sturdy, open cardboard box. This way, kids could sit in the box with their heads inside the kaleidoscope and not worry about having to hold it up (even though it isn’t glass, it’s a bit heavy for a child). Since then, we’ve left it on the floor and it’s regularly played with, often filled with toy arrangements that seem to stretch out into infinity. Full instructions here.
Read: Molly and the Mathematical Mysteries: Ten Interactive Adventures in Mathematical Wonderland, Eugenia Cheng and Aleksandra Artymowska [Amazon | Bookshop]
I love reading this book at the end, in part because it draws upon so many of the ideas covered here and in part because it’s so beautiful and impressive that it feels like a proper finale, a gift. You certainly could read bits and pieces of it as you do the activities, but since it’s a mystery, I think it’s best read it in one go.
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