Do you have collectors in your midst? Those young children who can turn a five-minute walk into a 15-minute treasure hunt? The children who fill their pockets with treasures and then load up your pockets with the overflow?  I love these kids. They can wreak havoc with our daily schedules, but they help us slow down, take a breath, smile and find beauty in unexpected places. They also make me smile when I remind myself that these impromptu, child-led collecting and sorting expeditions are worth their weight in gold as we work with young children to build a strong foundation for later math learning.

We collect lots of natural loose parts like acorns and buckeyes, feathers and rocks. But we also collect colored gems, bottle caps, keys and other odd items. This, my friends, is the rock-solid, hands-on play that lays the foundation for number sense.

At all ages, children classify intuitively to make sense of a world that seems largely out of their control. By the time infants are two weeks old, they can distinguish between objects that they suck on and those they do not. By the age of two, toddlers form sets of similar objects. In preschool, children begin to sort objects into categories according to a given attribute.

If it attracts their attention and they touch it, that’s the moment the child-led learning begins! So grab a bag, a basket or a bucket, take a walk and see what sparks the imagination of the children in your life. A good pocket comes in handy on these expeditions!

Along the way, observe the collecting habits of your budding mathematicians. What captures their attention? What treasures do they deem worthy of pocketing? Does one of the younger treasure hunters in your group need guidance or mentoring?

During your expeditions—and other daily outings—keep your eyes out for heart rocks. It’s a great opportunity to build some early math skills, whether you’re waiting for a table to open up at a restaurant or killing time before an appointment. Hidden in those landscape rocks, there is sure to be a heart rock!

Children will naturally begin to sort their collected treasures into piles or “sets.” Separating will come very naturally as children sort acorns into one pile and bottle caps into another. They may group by colors, shape, texture or weight. They may also organize their objects in a line by size or other attributes.

As they sort the objects that they collect, children are building their analytical thinking skills, which are the lifeblood of mathematics. This is a great opportunity to introduce vocabulary words such as more and less.  Young children have an inborn sense of more and less. They always know if someone has more than they do!  Children can learn number sense simply by playing with their collections!

If the grouping of sets leads to counting, this is another great opportunity for young children to build foundational math skills. Regardless of how high a preschooler can rote count, a child’s sense of what those numbers actually mean develops gradually. We call this “understanding number sense,” and it requires relating numbers to actual quantities.

There are three core counting principles:

Counting Sequence 
There is an ordered sequence of number names. Counting involves using the same sequence each time, starting with one. By using counting songs and moving each object as you give it a “name,” you can help children learn the counting sequence.

One-to-One Correspondence
One number from the counting sequence is assigned to each object in a collection. Instruct the children to put each object into a container or slide it across the table as it is counted.

Cardinality
The last number assigned to an object when counting a collection indicates the total quantity of objects in the collection. Ask: “How many?” If the children don’t know the answer to this question, count the objects together and note the last number that you counted as you push the objects all together into a group.

By turning counting into an enjoyable, hands-on activity, you are also introducing the children to mathematical concepts such as place value and addition.

Remember to take it slow and make it fun. Children develop at different rates and have different learning styles. They will master early math concepts in their own time and in their own way.

So let the children set the pace. Enjoy the cooler fall temperatures as you embark on your collecting expeditions—and see what collections land in your pockets!

Looking for some great activities to introduce sorting and counting to your early learners? Look no further than the Early Math Counts lessons page.

Here are a few of my favorites to help you get started:

• Cereal Sorting
• Laundry Sorting
• One Fish, Red Fish

Over here at the Ginkgo Tree House, we are quite intentional about setting up math environments that don’t scream MATH CENTER. We try to have authentic materials that are fun to touch and play with and then we sneak in materials that will create deep math investigations all on their own. Children learn math at their own pace by using many different skill sets that don’t always come in a specific order. So we give them lots of options to let the learning come in their own unique style. By keeping it playful and hands-on, we set them up for math success.

The new math that is being taught in schools is actually quite wonderful. I’ve watched my own grandchildren gobbling it up because it makes so much sense and there are so many ways to reach the correct answer. They use ten frames a lot! So what is a ten frame?

Ten frames are equal-sized rectangular boxes in a row where each box is large enough to hold a counter.

The five frame is arranged in a 1-by-5 design.                                                     

Five and ten frames allow students to physically place items, each within a single box, to create a visual representation for numbers from 0-10 to help students visualize given numbers in a set. This creates a strong foundation for math computation in the years to come. There are endless ways to create a ten frame, from egg cartons, cups and tape to chalk on the sidewalk—to name a few. 

I love wooden ten frames, but they are ridiculously expensive. I have blogged before about my love for mancala boards. I have been finding mancala boards at thrift shops and yard sales for years.  We have a collection that we use for playful math. This year, I had the grand idea of taping the ends of our mancala boards to create ten frames! Tada!

Yes, yes, I was feeling quite giddy. But I just couldn’t leave well enough alone.  

So I cut them down. Yikes! What? I know, I know, but it’s that good, strong foundation we talked about in the last blog. So,I did it. I cut the mancala board into a ten frame!

  Then I realized with my group, five frames would be even better because we currently have a boatload of two-year-olds in our program. With a five frame, students are using smaller set sizes that are within their developmental counting range. Five frames expose our early learners to a tool that they will recognize in the academic world. Incorporating a five frame into their collection play sets them up for future math wizardry.  By now, I was a bit saw happy, so I created a three frame to use with subitizing and a two frame and a one frame for one-to-one correlation. Remember, we are young and we are keeping this developmentally appropriate for the youngest in our program.  

And, finally, we brought in our collections from last week! Voila! Math play.

While your children are playing with their collections and frames, you can mentor the counting by putting a counter in each square of the frame and saying, “One, Two, Three, Four, Five—you have five buttons.” When a child counts, “1,2,3,4,5 buttons,” knowing that the last number represents the number of buttons in the collection, that is known as cardinality. It’s a school standard for kindergarten. Your child just thinks it is fun. 

Just a reminder,  we are keeping it fun. Playful math. Developmentally appropriate. It might look like this:

It’s a great foundation for future academic success! Let the fun begin!

Here are our book recommendations for this week!

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Do your children play with ten frames?  Share your ideas with all of us! I know that many of us have a love/hate relationship with math. But, trust me, this new math is going to change all that for our children. It’s good! Really, really good!

Diann Gano is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means to earn fees by linking to Amazon.com and affiliated sites.

I am so honored and excited to be the Math at Home blogger for the next year! I love math, and I love watching math happen with children every day. My goal for the next year is to avoid how high and fast our children can rote count. I want to build the deepest, strongest foundation for learning and let the children build their own house of math on that foundation. I hope to give you a collection of pictures from my own program, quick-reading ideas, some great books to find at the library to build on the literacy skills and math understanding and a question to get some dialogue going about math and kids and life. We want to immerse them in math environments without worksheets or set times for math. It will come naturally, through play. I promise to keep it fun and easy.

Let’s start with a quick look at the brain. We know that the right brain develops first. It is really busy building our children’s imagination, creativity and intuition for the first three to four years of life. The left brain starts to kick in developmentally at about the age of seven. It gives us logic, language, literacy, numeracy. The right brain is full of sensory, play, relaxing. I like to think of it as RIGHT BRAIN=RECESS. That left brain over there…whoa, that looks like school/office to me. My own students are in the right-brain zone, age-wise. They are playing with rocks and friends, being creative and using their imaginations while learning how the world works. I really like recess, just like I did when I was five. So let’s stay out here in recess land for as long as we can! It will build the foundation for that school/office side of learning. I promise that play really will get us ready for the left-brain part of life. So, let’s get started!

Collections

Do you have a collector in your midst? That small child who can turn a five-minute walk into a 15-minute treasure-discovering adventure? You know, that child who slows us all down to look at the world below our feet or above our heads?  I love these kids. They make me crazy, wrack my nerves and raise my blood pressure, but they also make me slow down, take a breath, smile and find beauty in the oddest of places. And they make me smile really, really big, when I remind myself that this is the gold treasure chest of math’s foundation.

At the Ginkgo Tree, we are full of collectors!  We collect lots of nature’s loose parts like acorns and buckeyes, feathers and rocks. But we also collect colored gems, bottle caps, keys and other oddities. THIS, my friends, is the rock solid, hands-on, building the foundation of great solid math brain that we look for in early childhood play.

If it attracts their attention, and they touch it, they own it. They own their learning at this moment! Grab a bag, basket or bucket and take a walk and see what speaks to your children. A good pocket is priceless. Keep your phone in your own pocket and give your child the gift of time. What treasures do they find? What captures their attention? Do you need to mentor collecting? Keep your eyes out for heart rocks. We love a good heart rock, and it’s a great pastime when waiting at restaurants or appointments. Hidden in those landscape rocks, there is sure to be a heart rock!

When you return home, dump those treasures out. Before we can begin to count our collections, we need to figure out which are acorns and which are bottle caps. This will come very naturally as a child sorts the acorns into one pile, the bottle caps into another. We can sort into groups, we can arrange by size, color, shape, texture or weight! Remember, back in kindergarten and first grade, these were referred to as sets. Before you could count sets, you needed to separate into sets. If your child hit the jackpot on a particular item, you may wish to give it a special home. Perhaps a small box, a canvas bag, a Ziploc bag or an egg carton. These treasure are chock full of math potential.

Regardless of how high a preschooler can rote count, a child’s sense of what those numbers actually mean develops gradually. We call this “understanding number sense,” and it requires relating numbers to real quantities.

Young children have an inborn sense of more and less. What is fair or equal? Who has more ice cream, acorns or toy cars? They know! Children learn math sense by working with small sets of collections. Math sense refers to relating numbers to real quantities. Slow it down and let’s work on small groups. One to three objects for the wee ones, five objects for our preschoolers. If the grouping of sets leads to counting, try moving each object and giving it a number. Number sense is the ability to understand that the quantity of the set is the last number name given in that set. By making counting hands-on fun, children are learning place value and addition. Take it slow and keep it fun. Children will be exposed to the idea that the same collection can be sorted in different ways. Sets can be flexible. (Ugh oh, I saw your math brain go to sixth-grade math, where sets started getting a bit confusing. Pop out of that left brain! Get back here in recess!) Math is being taught a whole new way. They are removing that obstacle, your left brain might not have learned this new way, so relax and just sort the rocks!  Remember, not all skills come in a certain order. They will come at different times for different children and in different learning styles. It will come. Baby steps. Strong foundation. Let’s stay out for recess and enjoy the ride.

So, that’s it. Collect some treasures and we will meet later in the month and start putting those collections into play. In the meantime, head to your local library, neighborhood bookstore or Amazon and cozy up with your child for some great books on collections!  Amazon is easy, fast and convenient, but we want to keep our book resources alive in our neighborhoods!

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Left-Brain Adult Lounge

I would be absolutely terrified if I knew how many hours my brain has tried to come to terms with my students playing with…bottle caps. Beer caps, specifically. Craft brewers are knocking out some crazy creative bottle caps! They are fabulous for sorting! I DESPISE branding and have removed most of it from our program, so am I branding alcohol preferences to my three-year-olds? Is this early math politically correct?  Am I totally overthinking this? I asked the parents of the students for guidance. They looked completely baffled and said, “I know you have thought this out, and you must have good reason for it!” If they only knew. So, I observed the kids as they separated the caps by features (dogs, colors, whatever popped out at them.) They can’t read. The letters are foreign to them because, remember, that’s left brain and their brain development isn’t there yet! I grew up next to a state park, and I collected bottle caps as a kid. They clinked like coins, they were easy to find, carry in a pocket and sort into categories.

I flip, I flop, I struggle. Somehow, bottle caps always win. And here’s why:

Numbers and Letters!

Sequencing!

I kid you not!  How funny is this?

Same but different!

HELP! What are your thoughts on this topic?  Am I overthinking all of this? Do I justify all the goodness of a bottle cap?  Apologies in advance, if this sends havoc to your brain space on the ethics of early childhood education! Have a great week!