Pattern walk at the Field Museum

posted by Lindsay Maldonado

Today I visited the Field Museum of Natural History. Another one of my favorite Chicago museums. The Field Museum houses thousands of artifacts from dinosaur bones to pottery and clothing from ancient civilizations. Again you may be thinking, math? Isn’t this a natural history museum? With thousands of artifacts on display, math is easy to find. Just a quick walk through the halls brings you upon any number of dioramas with countless animals of all shapes and sizes.

It’s easy to count animals (Big Idea: Counting) or classify animals (Big Idea: Sets) by their varying attributes like size or color – but when you start to delve deeper into the exhibit halls you’ll come across other kinds of artifacts. There are cases upon cases of decorative clothing and art from cultures near and far. In my recent visit I happened upon the Hall of Native North Americans exhibit.

Native North American exhibit

At first you’ll be enamored by the craftsmanship. You’ll wonder how long it must have taken to create something so beautiful and intricate. You’ll wonder why Native North Americans wore such adornments but then you’ll notice something else; you’ll notice the shapes and patterns woven together or threaded with beads that make up each artifact. There are circles, squares, rectangles, diamonds, and triangles intricately designed to create simple and complex patterns. We see color patterns too.

Patterns exist in the world, as we see here, and also in mathematics. Through patterns, we find sequences bound by a rule (e.g., a chess board is made up of black and white squares, with a predictable black-white, black-white or AB, AB pattern) that brings predictability and allows us to generalize. Hence, we can predict, with a good amount of certainty, what comes next. Let’s look at a couple of these objects. What patterns can you find?


beaded ornaments

beaded bagThe beaded bag has blue and orange flowers arranged in a simple ABAB pattern. Each row alternates orange flower, blue flower, orange flower, blue flower, etc. It’s easy to predict what comes next. We see a similar ABAB pattern in the beaded ornaments (i.e., yellow blue, yellow blue). One big idea of patterns is just this; the same pattern can come in different forms.

We also see more complex patterns when you look more closely at shapes. Can you see the pattern?


decorative artPatterns are found in many places and children are particularly attuned to patterns. As we observed, patterns offer a sense of predictability, which children desire (e.g., we create routines for children to add order and predictability to their lives). When children understand the rule of a pattern they are able to extend that thinking to other situations.

Keep talking about patterns in the classroom! You can search for more activities about patterns here.

How (and Why) to Introduce Tesselations to Preschoolers

posted by Emily Grosvenor

tessalation-coverWhen I wrote my math picture book Tessalation!, I had a specific reader in mind: My son, who was 6 at the time. I was sure he was just the right age for learning to identify what a tessellation is (a tiled interlocking pattern with no spaces in between).

But something happened when we finally had the book in our hands. It was my other son, 3, who began pointing out tessellations wherever we went. He sees them everywhere — in the chain-linked fences, on the floors of restaurants, or even, once, on a stranger’s leggings. 2worldtessellationday

Really, I shouldn’t have been surprised. As early as pre-school, children can recognize patterns. Building with blocks, decorating a dollhouse, figuring out how nesting dolls fit together, doing simple puzzles — these are all ways children have their first experiences in organizing space. Building spatial relationships is part and parcel to this age group.

Preschoolers and spatial recognition 

The more children have a chance to play with space, the richer ideas they will form. And preschool is the best time to cultivate spatial reasoning in children because they naturally gravitate towards activities that build those relationships.

Spatial reasoning is a necessary component of human survival, but in a practical sense, it also primes children for success in a number of other important pursuits. Lessons learned about how to organize space can boost success in building later skills such as map reading, design, construction, or simply moving an object through the world, like a bike or a car.

What’s more, some educators posit that introducing spatial relationships to children at a young age will help predict success in science and technology later on.

How I introduce tessellations to preschoolers 

I wrote Tessalation! specifically to teach children about tessellations, a concept that has held my imagination since I was a child.

p141The book tells the story of a little girl, Tessa, who hides in the patterns of nature, and consists of 16 pages, 8 of them story pages and 8 full-color tessellation pages.

In the months since its publication I’ve talked to math teachers who have used it in the classroom, parents who read it to their children, and have tested out some ways of talking to preschoolers specifically about tessellations.

Here’s how I do it: 

1. Read Tessalation! When I read the book at events and to children’s groups, I am struck by how mesmerized the children are by the patterns and how easily they recognize what a tessellation is. As we read, I invite them to look for Tessa hidden in the patterns.

2. Talk about what a tessellation is

After we read the book, I ask them what their favorite tessellated page was. Then we take a closer look at that page to discuss what a tessellation is. What do they notice about the pattern?

3. Make the connection to their lives

Once we’ve established what a tessellation is, I invite them to tell me about patterns they have seen in their lives. Not all of these are tessellations of course, but it’s fun to discover just how much the children are paying attention to their surroundings.

4. Invite them to play I absolutely adore the Tiling Turtles created by math educator Christopher Danielson, so I always bring them when I speak with young people. These laser-cut wood turtles feel good in the hand and are immediately recognizable to children, but they are also challenging enough to use that children won’t get bored with them quickly. With this age group, I generally speak about what the child is doing as he or she discovers how the pieces fit together. I’ve seen children as young as 2 have a great time with the turtles.


5. Spot the tessellation

Once children know what a tessellation is, they will find them everywhere. Teachers can send home the request with their pupils to keep their eyes open for tessellations in the wild. In this way, it becomes a lesson to support, with fun, in the family home. With older children, we can get into making our own, but identifying and playing are the first steps to introducing the concept.

I hope you find this information useful as you look for ways to incorporate spatial learning in your classrooms!

Emily Grosvenor is the author of Tessalation!, a children’s math picture book about pattern, nature and wonder, which was successfully Kickstarted by a group of creative math educators in March, 2016. A magazine writer by profession, she lives with her family in Oregon. Follow her on Twitter @emilygrosvenor.

Large Colored Beads

Large colorful lacing beads are a wonderful tool to work on sequencing and patterns.  Many children will approach this manipulative with a certain amount of trepidation as “lacing” is hard and requires fairly developed fine motor skills and strong hand-eye coordination.  Many children work for a long time simply trying to get one bead on the string.


Take your lacing string and tie the end to a chair or tape it on the table.  One of the frustrating elements of lacing beads is once the child gets the bead on the string, it may simply slip off the other end.  Make sure this doesn’t happen before you start.

How do you support children as they use explore the beads?

Personal Care Routines and Infant Understandings of Mathematical Concepts

As the days unfold during the first year of life, infants repeatedly experience personal care routines that will set the foundation for the development of their first mathematical understandings.  Personal care routines refer to the everyday caretaking of the infant, such as feeding, diapering, and sleeping sequences.

Each personal care routine has its own rhythm depending on who is performing it.  At our house, bedtime rituals were very different if I was the one putting Noah to sleep or if Larry was.  Since I was nursing him, I sat in the rocking chair and fed him while listening to music.  Once he was drifting off, I placed him in his crib and snuck out of the room. If Larry was putting him to sleep, I would nurse him and then hand him off to Larry.  He read a book and then sang a song and then rocked him until he drifted off.  Once Noah fell asleep, he tucked him in and snuck out of the room.  Regardless of who was participating in the routine, Noah learned that the events of bedtime happened in a sequence, and that sequence was predictable.  He anticipated the rocking chair, the snuggling, the books, and the songs and came to expect them in that order.

These daily routines create patterns that infants recognize and anticipate.  The consistency of the patterns is important, as new parents learn once their infants show displeasure when their expectations are not met.  However, even the youngest children can be quite flexible and can adjust their expectations depending on who is providing for their personal care routines. (“My teacher is different than my mommy and she changes my diaper differently, but they each do it in a certain and predictable way.”)

It is important that we see the acquisition of early math skills as brain-based and innate for typically developing children.  The mathematical concepts of patterns and sequences described above are not taught outright; they occur naturally in the life of an infant and are internalized by the infant.  Consistency is the key and should be encouraged in all areas of personal care.

Numeracy – What is it?

Numeracy means different things to different people.  For some, numeracy is the foundation of mathematics; the basic skills required to do more advanced mathematics.  For others, numeracy is a term used to describe the mathematical skills required to complete job requirements or to be a mathematically “literate” person.  In the field of early childhood education, numeracy is most often seen as children’s understandings of basic number concepts and skills.

Numeracy begins long before toddlers know the word names of numbers (one, two, three, etc.).  It begins when the youngest infants begin noticing differences in quantity and develop the understanding of “more and less”.  For older toddlers and preschoolers, learning the word names of numbers and saying those words in order is another really important numeracy skill.  Counting small groups of items is often the next step. Preschoolers can practice counting groups of objects as long as they are in small sets (1-5) and distinguishing between sets of quantities when those sets are very different (3 vs. 25).

Numeracy skills, like literacy skills, should be promoted as much as possible in child care. When opportunities arise during play-based everyday occurrences, every effort should be made to enhance and highlight concepts around quantity, space, and patterns.

Next week, I am going to write more about early Numeracy and ways in which teachers can promote it.

Reading the Patterns

Do you ever ask your kids to “read” their patterns?  It is pretty simply and using a few simple techniques, you can support the children as they organize and synthesize information by using several different learning modalities.

egg 5

Take a look at the pattern above.  Clearly the child who created this understands patterns.  Next, ask him to read his pattern.  Listen as he reads, “Green, blue, yellow, green, blue, yellow.”  Encourage him to point to each block as he reads.  This reinforces the use of his tactile senses to reinforce the pattern concept.  Now ask him, “What comes next?”  If he isn’t sure, have him read the pattern again.  This action allows him to hear the words as he points.  Now he is using sight, sound and touch.

Keep increasing the difficulty of the pattern experiences by providing more and more items that can be formed into patterns.  Provide items that have attributes that can be categorized, sorted, and patterned.  Encourage the children to try new and more complicated patterns.

See how Maricela encourages the children in her care to work on patterns.

Another Cool Sorting Tool

I spent a lot of time this summer organizing (or trying to anyway) different areas of my house in an attempt to clean and minimize the accumulations that have built up over the past 20 years.  In some ways, I was successful.  I finally got rid of clothes from the 80’s (even if they do come back in style, I am not wearing them again) and rearranged our poorly designed kitchen.  I spent a lot of time at the container store, staring at organizing systems trying to imagine how they might work in our teeny tiny house.  I never ended up purchasing any of them mainly because I thought buying more unnecessary plastic objects to organize the piles of unnecessary plastic objects that were already in the house, didn’t really make sense.

pill boxes

One day, while still looking for organizing tools, I was browsing in our local Walgreens, I came upon these large pill organizers.  They make them really big now, so that they can be easily opened, labeled, and filled with many pills.  I got to thinking about how these would be interesting as a sorting tool for children.

1.  They are labeled with the days of the week and when put side by side, they create a pattern.

2.  They are large enough that items can be put inside and then closed up. (Beware of small items that may be a choking hazard.)

3.  There are buttons on the side that lock to close, and then release them to open.

What do you think?  Could these pill boxes be used in your classrooms?  How?

One Tool – Many Uses

Last week, I wrote about egg cartons as a tool that is easy-to-find, free, and versatile.  You can’t imagine my excitement when I find these eggs at our local Costco.

eggs 2 dozen

I immediately started imagining all of the ways I would use this empty carton in my classroom, if I still had one. As a sorting tool, the lid is perfect.  It has 3 sections and manipulatives can be presented either already sorted, or mixed-up, and in need of sorting. Look at the 2 examples below.

egg 9

egg 1


Which way would you present the materials?  Do you think there is value in both ways?  You might consider presenting the colored blocks one way, and then the next day, present them in another.  Watch and see how this changes the way the children approach the materials.

You might also present the beginning of a pattern…

egg 5and then ask the children to match the pattern.

egg 6


Children might create their own patterns…

egg 7and you can finish theirs or talk with them about their intentions.

“This first row looks like the pattern is green, blue, green.  Should I put blue next or another color?”

“Your next pattern has 2 yellow and then a green.  What should I put next to complete the

Later, you might present another tool, like a pair of tongs so the children can use them to put items into the carton.

egg 3

Depending on the materials you put out, the tongs might be very tricky to use.  Softer materials like these pom-pons are much easier to pick up with tongs.

Ask the children to create a pattern with the pom-pons.  Remember to only ask for children to think about one attribute of the materials at time so they can focus on that aspect.  Here I asked for pattern of large, small, large, small.


I think it might be worth the $40 dollar annual membership fee at Costco just to be able to buy eggs in these cartons.  They are so great.

Can you think of other interesting ways to use this versatile tool?




Stickers – A Wonderful Tool

As I sit here and write this, I can only hope that when you saw the title of this post you did NOT think about stickers as rewards.  I can’t stand when children are rewarded with stickers or other small items for doing what they are supposed to in school.  Remember, we don’t praise expected behavior, we EXPECT expected behavior.  If children learn early that there is an external reward system, some may only perform if they are rewarded. Internal satisfaction is what we strive to for as children develop autonomy.

So, why write about stickers?  Stickers are a wonderful and inexpensive way for children to participate in activities, as a viable option to drawing or writing.

If you were at the dollar store and came across a rack of stickers, I would buy them up, especially if they were thematically organized.  Imagine having a wonderful set of insect stickers such as these.

Bug stickers photosYour children can graph their favorites, play a matching game, (create this game using 3 X 5 notecards and 2 sets of the stickers), describe their attributes, identify their parts, look for patterns, etc.  The list goes on and on and can be replicated with any good set of stickers.

Using stickers to enhance your study of Bugs is a cheap and cheerful child favorite.


Big Beads for Little Hands

The other day I observed a room of younger toddlers, none of whom was older than 20 months.  One child spent his whole morning playing with this large set of beads.big beads 2They come with a long string that is easily pushed through the large holes.  The string has a helpful plastic cylinder on the end that fits into the holes and stays put.  big beads 1

The child spent the morning stringing the beads and then dragging the whole thing around like a puppy dog. big beads 4He had the best time.

Sometimes when working with infants and toddlers rather than thinking about “beading as a means of creating patterns,” it is enough that they experience beading as an engaging activity.  I watched this child attend to his task for far longer than anyone thinks an 18 month should be able to.  He negotiated with his classmates when one of them tried to take his beads away – he wasn’t having any of that!  He manipulated the beads, one after another onto that string, and then pulled and pulled and pulled so he could get one more bead on.  He found an adult when he wanted help getting them off and was perfectly happy to start all over again.  He showed the tenacity and the perseverance of a much older child and although he got frustrated for s quick second, he was completely immersed and engaged in his play for the better part of an hour.

Yes, recognizing and creating patterns is important. But the other day, so was all of the rest of this stuff.