Explore Early Math: Sets

The explorations below are for parents of child ages 2-6 (although teachers may find them useful and may adapt them for their purposes as well). These explorations are organized according to a list of big Ideas from The Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know (referred to as Big Ideas below) by Erikson Institute’s Early Math Collaborative. You can find out more about this book here on my blog www.mathbookmagic.com. In this book, 26 big ideas are organized under 9 topics. This post is about the first topic, Sets, and its three related big ideas.


SETS: Using Attributes To Sort Collections

Sets are fundamental mathematical objects. For example, they are basic to our number system and counting. For example, before you can count something, you have to decide what to count and that involves identifying sets. Take a look at the image below and answer the question: How many?

If you answered, 20, you probably counted all the beads. There are 20 beads. How else could you answer the question, How many? Here are a few possible answers: There are 10 animal beads. There are 5 red beads. There are 2 red animal beads. All of these counts involve forming sets before counting: a set of animal beads, a set of red beads, and the subset of red animal beads. Note: Making sets may involve physically separating out the sets or mentally identifying sets.

Here are three big ideas Erikson Institute’s Early Math Collaborative identifies for Topic 1: Sets:

Big Idea 1a: Attributes can be used to sort collections into sets. [Examples of attributes: Color, size, shape, fill patterns]

Big Idea 1b: The same collection can be sorted in different ways.

Big Idea 1c: Sets can be compared and ordered.

*The Erikson book does not include these letter labels (a, b, c). I do this for clarity. They are not meant to denote any sort of learning progression.

These three big ideas provide helpful anchors for exploring sets. The games, questions, books, resources, and activities are possible ways to engage with big ideas 1a, 1b, 1c. Be sure to listen closely for the magical ideas of your brilliant children.


SOCK SORT

On laundry day (which is basically everyday at my house). Have your child help sort socks. Discussion of the different attributes: colors, patterns, sizes, owners will naturally arise. Finding exact matches (either using socks or with memory type matching games) is a great way to start talking about sorting. You might ask: Where is the match? How are these the same? How are these different?

BUTTON SORT

We read the classic story The Lost Button (from the Frog and Toad series) by author Arnold Lobel and sorted some old buttons. Here is Landon’s selection for which buttons matched the one that Toad lost from the book. From the story, Toad lost a white (these buttons look grey, but they are indeed white), four holed, big, thick, round button. Taking each attribute individually, I asked Landon to sort the buttons until he found Toads button. For example, I asked: where are all the white buttons? [He separated the buttons into two piles, white and nonwhite].

TOY SORT

My son’s toys are in bins. In the past, I’ve written different labels on the bins. There was a bin for cars and tracks, two bins for costumes, two bins for play food and dishes, one bin for instruments, one bin for puppets. Nothing ever actually stayed THAT sorted of course. But recently I asked Landon to figure out a sort he preferred. We dumped the toys in a pile, I asked him to decide how to sort his toys. He came up with one bin for costumes, one kitchen bin, one bin for cars/planes/helicopter, one bin for tools, one Landon’s special toy bin (I suggested the name after I noticed him placing select favorite toys in a pile), Oddballs (his sister suggested this label at the end, and he liked it). Toy sorts offer opportunities to see that the same collection of toys can be sorted in multiple ways.

MATH AND CRAFTS

We used pipe cleaners/ chenille stems and made bead bracelets and heart shapes (since it was around Valentine’s Day). Stringing beads on yarn or pipe cleaners offers lost of opportunities to discuss attributes as you share how you made your design. If you used a pattern, describe it. If you used only particular beads, share this with your child. Ask your child about their design. The beads we used can be found here.

GAMES

SET is a favorite game in our house. If you’ve never played it does take a bit to get clear of how it is played, but it is so worth it! We use these directions to adapt the game for Landon (Not there is a junior version of SET for those interested, we do not have this). These directions come from math educator Kent Haines’s website Games for Young Minds which has a great selection of games in addition to SET to check out. The Erikson Website has more suggestions of games centered on sets as well.

READ

Here are some books that explore sets and attributes. Click each link for more information: Animals Would Not Sleep! by Sara Levine and Marta Álvarez Miguéns. Arnold Lobel’s Frog and Toad are Friends: A Lost Button (see Button Sort above), Tana Hoban’s books are great for noticing and wondering about attributes (here a few geometry books, but check out the book section of the post for a list of her over 100 books). A Mousy Mess by Laura Discoll and Deborah Melmon. This Equals That by Jason Fulford and Tamara Shopsin. Same, but Different by Susan Looney. Also, Erikson Website for more books centered on sets.

#EarlyMath: A Math Story Stuffed with Magic

With a 4 year old preschooler at home, I’ve been particularly interested in magical resources that illuminate the mathematical horizon of early math. As I mentioned in my last post, Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know by Erikson Institute’s Early Math Collaborative provides a helpful anchor into the big ideas of early math. The first big idea they outline is SETS: Using Attributes to Make Collections. This post is about a magical picture book that explores sets.

The Book

The Animals Would Not Sleep! is one of seven books (!) published in 2020 as part of the Storytelling Math series from Charlesbridge. Two books from the series, The Animals Would Not Sleep! and Lia & Luís: Who Has More? (by Ana Crespo
and Giovana Medeiros), recently won Mathical book awards.

Storytelling Math books “offer a wide range of math topics, feature main characters of color, appeal to a broad audience, and are written by a diverse array of authors.” [From Storytelling Math website] I can’t wait to share more magic from this amazing series. But first, here’s more about this wonderful book.

Written by Sara Levine and illustrated by Marta Álvarez Miguéns, The Animals Would Not Sleep! tells the story of Marco’s bedtime woes. Marco must pick up his stuffed animals before bed. However, the stuffed animals are not happy with how Marco has sorted them into their baskets. Marco explores different sorts in the hopes everyone can peacefully go to bed.

From The Animals Would Not Sleep! by Levine and Álvarez Miguéns

In addition to her work as an educator and author, Sara Levine is a veterinarian. Her love of animals shines through her story which pairs perfectly with Álvarez Miguéns’ vibrant, delightful illustrations. For more about the author and her books go here. For more about the illustrator and her art go here.

The sweet spot for this book is ages 3 to 6.  

The Math

The math in this book is sets and sorting. Here are the big ideas involving sets identified by The Big Ideas of Early Mathematics.

SETS

Big Idea 1a*: Attributes can be used to sort collections into sets. [Examples of attributes: Color, size, shape, fill patterns]

Big Idea 1b: The same collection can be sorted in different ways.

Big Idea 1c: Sets can be compared and ordered.

*The Erikson book does not include these letter labels (a, b, c). I do this for clarity. They are not meant to denote any sort of learning progression.

In Animals Would Not Sleep!, Marco uses different attributes to sort his stuffed animals (Big Idea 1a). He begins sorting by mode of travel (e.g., flying animals, swimming animals, animals that move on land) , then size (see image above), then color before finally settling on a solution. In this way, readers observe Marco sort the same collection in different ways (Big Idea 1b). While not explicit to this book, a discussion of comparing sets (Big Idea 1c) came up when Landon wondered which bin had more (images below from the book).

From The Animals Would Not Sleep! by Levine and Álvarez Miguéns

For more information on the math of sets and some ideas on how to play around with sets at home: check out my new post at www.fairymathmother.com. Additionally, the Charlesbridge website offers Animals Would Not Sleep! activities here (be sure to select the “Downloadables” tab).

The Magic

The magic of this book lies in pairing a mathematical content with something many children adore. Carrie Finison did it with doughnuts here. And Sara Levine does it with stuffed animals. As a kid, I carefully arranged my stuffed animal at the head of my bed and my children do the same now. Here is a photo of Landon’s bed and my daughter Siena’s bed.

My favorite thing to do with Landon is reading picture books. We call it “Story Snuggle Time” and it is right before lunch. As we cuddled under the covers with The Animals Would Not Sleep!, Landon was captivated from the first page. The illustrations offer a lot of variety. Landon was pointing and noticing the different animals (their colors, the animal species). “Look there’s one like giraffy” Landon said pointing to one like his own stuffed giraffe.

Landon made an empathetic “aw” when crying bear was unhappy and a relieved “awww” when Marco found a sweet resolution on the final spread. On this last spread (which I won’t share as it gives away the ending), Landon snuggled in close to get good look and asked me to read it again. As I turned back to the front cover, he left the room. Minutes later, he came back with an armful of stuffed animals, climbed up, carefully arranged them on the bed and told me “OK, go!” And we did. I knew at that moment, this book belonged to our magical set of math picture books!

You can purchase The Animals Would Not Sleep! from Charlesbridge, Bookshop, Indie bound, Barnes and Noble or Amazon.

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