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## What is a Magical Math Book?

Formulating definitions is an important part of creating mathematics. The definition you choose has implications for how you sort examples and non-examples of a particular term.  The mathematical term trapezoid is a well-known (and often debated) example of this choice. Here are two definitions of trapezoid.

Definition 1: A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Definition 2: A trapezoid is a quadrilateral with at least one pair of parallel sides.

If you are using definition 1, a rectangle (see rectangle ABCD shown below) is not a trapezoid because it has two pairs of parallel sides ( sides AB and DC are parallel as are sides BC and AD. Sorry about the bad notation, ie., segments over AB, DC, stilling learning learn how to insert equations in wordpress.).

For many, a rectangle doesn’t fit their image of what a trapezoid should be. But if you are using definition 2, rectangle ABCD is a trapezoid.  For more about why anyone would choose definition 2 over definition 1, go here.

While there are many un-magical math books, I promise that are many magical ones to be found. Before I share examples of magical math books, I’ll describe my process for formulating a definition for a magical math book.

First, I recalled the math books I’ve read as a student, teacher, and parent. I use the term math book to refer to picture books with explicit mathematical themes, math problem-solving books, math textbooks, and any other math-focused book on the market (electronic formats included).

Using my intuitive sense of what magic is to me, I separated these books into two categories: magical and un-magical. [You may want to do this for yourself. If you do, I’d love to hear about your magical booklists and/or your thoughts about this process in the comments.]  With my magical math booklist in hand, I made a list of qualities I felt these books shared.

Next, I searched dictionary definitions of magic and used these to formulate a definition of magic that aligned best with the qualities of my magical math booklist books. Below is the definition of magic that I chose.

Magic: A quality that inspires wonder, excitement, and delight.

However, once I came up with this definition, I felt something was missing. I have read math books that are good, but on a first read through, I don’t feel much wonder, excitement, and/or delight. Then I read them to my children or my friend’s children and something magical happens.  This has been particularly true of math picture books. Thus, I have found that the search for math book magic should be a joint one. Here is the complete definition of a magical math book that I will use to sort math books for this blog.

Magical math book: A math book that inspires wonder, excitement, and/or delight for both reader and listener.

There. Done. A definition. Now we can move on to the fun stuff.

Magical moments aren’t easily explained with words.  I will try my best through the blog posts to share the magic that particular math books inspire. I realize that what is magical to one person may not be magical to another. However, my hope is that this blog will inspire others to find and share their ideas about magical math books. In the [revised] words of the magical children’s book writer and poet Jane Yolen, my hope is that blog readers  will “Touch [math book] magic…pass it on.”

Have you already read a math book that inspires wonder, excitement, and/or delight for both reader and listener?  Connect on twitter @KellyDarkeMath and use the hashtag #mathbookmagic to share and/or share through process described in the Shared Booklist .

## Math Board Book Magic ✕ 4

Mathematical thinking begins in the early years with real-world exploration and conversation. This post features a lovely set of board books for exploring and talking math with young children.

The Book(s)

The Charlesbridge Storytelling Math series brings the magic once again. This time with their four board book collection by author/illustrator Grace Lin. Grace Lin has written and/or illustrated over 25 books. From her picture book A Big Mooncake For Little Star (winner of the 2019 Caldecott) to her early reader Ling & Ting: Not Exactly the Same! (winner of the 2011 Geisel) to her middle grade novel Where the Mountain Meets the Moon (winner of the 2010 Newbery), you can’t go wrong with a Grace Lin book. Grace explains how this board book project came to be.

When my daughter was born eight years ago (before We Need Diverse Books came onto the scene) I was pretty frustrated with board books. I found very few starring babies of color, and most were part of the Global Fund for Children series. Those, however lovely, still gave the impression that non-white babies were slightly “exotic” and not commonplace in mainstream America. So, that planted a deep seed in me to create a board book that showed babies of color doing ordinary, everyday things. A few years later, during an NCTE conference, I saw the Baby Loves Science series at the Charlesbridge booth. I was extremely excited and told senior editor Alyssa Mito Pusey about how I had been wanting to make similar books. We brainstormed a couple ideas but nothing seemed right.

[Source: Horn Book interview. Grace shares a similar story in this wonderful video about the Storytelling Math]

Luckily, a year or so later, the right project did come along. Alyssa contacted Grace again and explained Charlesbridge was teaming up with TERC to create a Storytelling Math series. Grace recalls the conversation between her and Alyssa.

“Would you be interested in making math board books?” Alyssa asked.

“Math?” I hesitated. “Like numbers?”

“No, we want to show that math is more than numbers, that math is ordinary and just a part of our everyday lives.”

[Source: Horn Book Interview]

Grace was in! The project resulted in four math-themed board books spanning four seasons. Up To My Knees explores the measurement of sunflowers planted in spring. Circle, Sphere explores bubble shapes popping in the summer sun. What Will Fit? involves collecting and comparing fall harvest items. And The Last Marshmallow explores sharing on a cold winter day.

Lin’s vibrant images and simple text provide the perfect launch into real-world exploration and math talk as children follow the experiences of three friends: Mei (inspired by Lin’s daughter), Olivia, and Alex.

This set of board books is perfect for ages 0-2 and makes a great baby shower or first birthday gift.

The Math

These board books explore math in everyday life. In Up To My Knees, Mei uses measurement as she compares the height of a sunflower plant to different heights on her (e.g., up to her toe, her waist). In Circle, Sphere, Mei, Olivia and Alex explore shape. While experimenting with bubbles, the children observe some shapes are flat (2-dimensional triangles, circles and squares) and some shapes are round (dimensional spheres or balls) and wonder what shapes different bubble wands will make. What Will Fit? explores spatial sense and how shapes fit together in different ways. In the The Last Marshmallow, Mei and Olivia have to decide how they will share three marshmallows fairly between two.

The last page of each book gives examples of ways to explore the mathematical concepts more with children.

The Charlesbridge website does a great job offering more ways to engage with the mathematical ideas from each book. For example, if you go here and click on the “Downloadables” tab, you’ll find more explorations for the mathematical ideas in Up To My Knees.

The Magic

Math Book Magic is about sharing books that inspire wonder and joy and recently it brought me so much joy to give this set of board books to a friend to celebrate the birth of her baby. Even though my children have aged out of the board book stage, I shared all four books with my 5 year old and here is some of the magic that resulted (my 11 and 9 year old even joined in some of the fun).

The Last Marshmallow is a sweet story about sharing, which is a great context for math stories. Landon is always concerned whether all will work out fairly in the end. [Here are some other magical books featuring sharing we’ve shared here, here, here, and here.]

When we got to the page where Mei and Olivia are deciding how to share their marshmallows, I asked Landon who he thought would get the last marshmallow. He chose one of the girls and started to make a “Mmmum, mmmmum, mum, mum” cookie-monster sound. And then on the page where the sharing of the one marshmallow is solved, Landon face lit up , surprised to see it was possible to share one marshmallow! And once again, he made ‘mmmmummmm, mmmum, sound, pretending to eat his own imaginary marshmallow. Last Marshmallow had the magical ingredient of surprise and engagement.

Circle, Sphere is about blowing bubbles and when you combine bubbles and children you are bound to see something magical. This was definitely the case with this book. Check out this awesome page spread below. What shapes do you think these shapes make?

After I read the book, I ordered these wands to play with. They worked well, even though they ended up a lot bigger than expected. I’ll leave the answer to the question above for you to find out with the wands, by reading the book or better yet, both!

As with The Last Marshmallow, Circle, Sphere had the magical elements of surprise and engagement as well and I can imagine magical moments to be had with the other two books, especially coupled with some spring planting and farmer’s market shopping.

Grace Lin, TERC, and Charlesbridge make a great team and one magical set of board books!

***

If you’d like to receive these magical math book posts every month, be sure to follow this blog in the side bar of this page. Be sure to follow my other blog, www.fairymathmother.com as well as I will be combining both blogs under one site, www.fairymathmother.com , in the future. Thanks and see you soon!  Touch #mathbookmagic, pass it on.

## Explore Early Math: Number sense

The explorations below are for parents of child ages 2-6 (although teachers may find them useful and adapt them for their purposes). 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. In this book, 26 big ideas are organized under 9 topics. You can find out more about this book here on my blog www.mathbookmagic.com. We wrote about the first topic, Sets, and its three related big ideas here. This post continues with the second topic, Number sense, and its three related big ideas.

When you think of early math, I’m sure counting comes to mind. I hate to admit it, but I am guilty of comparing my children with others when it comes to counting. Your 1 and 1/2 year old can count to 20?! Oh no, my 3 year old can barely count to 7! Ahhh!! Then thankfully I come to my senses and remember counting is not a competition! And if I make it a competition, I’ll miss the magic that comes with observing and wondering with children as they develop facility with this integral skill. Learning the counting sequence is an amazing feat. But it is not all there is. We can’t assume that the child who can correctly count to 20 or higher understands their numerical meaning. And for the child who can’t count to 20 yet, we must remember children have a wealth of informal knowledge about quantity and developing a robust number sense takes time.

Number sense is a key building block for arithmetic, which makes up the majority of a K-8 math content. Erikson Institute’s Early Math Collaborative defines number sense as” the ability to understand the quantity of a set and the name associated with that quantity.” (Big Ideas, p. 30). Here are three big ideas associated with Topic 2: Number Sense.

Number Sense: Developing a Meaningful Sense of Quantity

Big Idea 2a*. Numbers are used in many ways, some more mathematical than others. Ever stop to think about all the ways we use numbers? Some numbers are nominal or categorical (e.g., sports jersey numbers). Some are referential (e.g., time and temperature). Other numbers are ordinal (1st, 2nd, 3rd). For these numbers, order matters. Other numbers are cardinal (5 cupcakes is more than 1 cupcake) and provide answers to the question, How many? There is a huge psychological difference between ordinal and nominal numbers for young children when it comes to which is more. For example, it you are #1 (1st) in the race (ordinal), that is good. But if you only have 1 cupcake (cardinal) and your sister has 3 cupcakes, not so good. Further, ordinal and cardinal numbers are inherently mathematical. However, typically, categorical numbers don’t indicate quantity, rank or any other measurement and while we can rank and compare referential numbers, we usually don’t perform mathematical operations with them.

Big Idea 2b. Quantity is an attribute of a set of objects and we use numbers to name specific quantities. This big idea centers on developing a concept of “fiveness”. “The idea of 5 must be constructed in your head, since it is a quality that we best in in relationships between sets.” (Big Ideas, p. 33) When we count the oranges in the bowl, we say “1, 2, 3, 4, 5” and the last number we count is the answer to how many oranges in the bowl. There are 5 oranges in the bowl, even though we said all the numbers 1 through 5. It is important to remember that numbers are abstract. The abstract nature of numbers is why Erikson talks about not using “naked numbers” with young children and highlights the importance of attaching a concrete object to numbers (saying “5 oranges” versus “5”) .

Big Idea 2c. The quantity of a small collection can be intuitively perceived without counting. There are times when a child will tell you how many without counting one by one. This is called subitizing and it part of a visual number sense. Two types of subitizing are perceptual and conceptual. With perceptual subitizing, a child can instantly tell you how many are in a small set (5 of less). They sometimes can do this even before they can count up to 5. Conceptual subitizing is recognizing smaller groups within a larger set and adding those small groups together, such as two dots plus three dots equals five dots. More about subitizing here.

*The Erikson does not include these letter labels (a, b, c) in Big Ideas. I do this for clarity. They are not meant to denote any sort of learning progression. For more on learning progressions, you might find Graham Fletcher’s summaries helpful.

These three big ideas provide helpful anchors for exploring counting and number sense in early math. The games, questions, books, resources, and activities are possible ways to engage with big ideas 2a, 2b, 2c in informal ways throughout your day. Be sure to listen closely for the magical ideas of your brilliant children.

NUMBER HUNTS

Number scavenger hunts around your neighborhood or home are great way to observe the different ways numerals show up (e.g., license plates, house numbers, mailboxes) and link number names to objects (e.g., 1 fire hydrant on our block, 4 stops signs at the corner, 5 petals on a flower, 2 robins on the lawn). Here is a number game printable from Math on a Stick booth at the Minnesota State fair and here’s a lovely description of using this number game from Kent Haines’s website. This number game focuses on finding hunting for a quantity (3 of something) as opposed to the numeral 3. [Big idea 2a, 2b]

We’ve also picked a card from a standard deck or Tiny Polka Dots deck (see below) and go on a hunt for that number. Here is an image of some 3s around our house. [Big idea 2a, 2b]

TOOLS

Fingers are a convenient counting tool (image is of my oldest child, my grandmother, my mother and me). And it is important that children are encouraged to use their fingers to support understanding. Here are a few other counting tools.

This Montessori inspired puzzle is a great one. It connects concrete (rings), pictorial (dots), and abstract (numerals) representations for number. [Note: The pieces from puzzle linked above are a choking hazard. I wouldn’t get that one if you have children under 4 in the house. Here is an alternative with larger pieces. [2b, 2c]

A Rekenrek is a nice tool to have on hand. We have this one, however there are larger ones as well with 100 beads. You can make your own as too. Here is a great blog post by the Brown Bag Teacher about the rekenrek with directions for how to make your own. [2b, 2c]

Five frames and/or ten frames are another useful tool. Here is are some printables (5 frame, 10 frame). Children can use coins and counters on them or dry erase markers if you decide to laminate them. Here is an electronic version. [2b,2c]

GAMES

Card games are great for familiarizing children with numbers as they include both numerals and a pictorial representation. Play a version of a Memory/Concentration game, Go Fish or a game of War, which we call MORE.

In addition to playing with a standard deck of cards, you could play with the Tiny Polka Dot card deck. This awesome deck was created by educators Dan Finkel and Katherine Cook. Play card games mentioned above or they have a bunch of other games to choose from. These thoughtfully-designed cards present quantities in unique ways by varying dot size, arrangement and representation. [2b, 2c]

Bears in a cave is a fun game to play. We learned about it from this awesome math wisdom book Math Fact Fluency by Jennifer Bay-Williams and Gina Kling. This book has over 60 games and tools to support math learning. Here are the directions for Bears in a cave (or Sleeping Bears as the game is called in this book). Each player needs a five frame, a plastic cup/bowl, and 5 bears (e.g., counting bear manipulatives (ages 4+) or our favorite Teddy grahams). One person places some bears in the “cave” to sleep. The other person looks at the bears “awake”/unhidden and tries to figure out how many are sleeping/hidden. The five frame may be used to place the unhidden bears to help them determine how many sleeping/hidden bears. [2b, 2c]

Any board game with a die/number spinner is a great way to develop early number sense (e.g., Count Your Chickens, Trouble, Chutes and Ladders). For more game ideas, check out math educator Kent Haines’s www.gamesforyoungminds.com, a website full of magical games to inspire wonder and joy. [2b, 2c]

MATH ART AND CRAFTS

Make some art inspired by classic picture book 10 dots by Donald Crews. 10 dots provides a springboard of examples of things that can be made with 1-10 dots. One dot (the sun). Two dots (a foxes eyes). There is a lot you can do with 10 dots and some imagination. I cut up a bunch of black dots and keep them with our art supplies. Here are a few pieces we did in our house (a tent, flowers, and a smily face with a mustache). Check out this blog post by art teacher Jenny Knappenberger. [2b, 2c]

READ

And lastly one of our favorite ways to share math is through picture books. Here are some great ones Number sense ones. Absolutely One Thing: Featuring Charlie and Lola by Lauren Child and I Know Numbers by Taro Gomi are great for exploring how numbers are used in different ways (2a). For comparing quantities, check out our post about Lia & Luís: Who Has More? by Anna Crespo and Giovana Medeiros on www.mathbookmagic.com [2b]. CRASH! BOOM! A Math Tale is great one from the Mathical list. Children can build their own block towers like the main character [2b]. Counting Kisses by Karen Katz is a sweet bedtime read [2b].A classic that you can never can go wrong with is Anno’s Counting Book by Mitsumasa Anno [2a, 2b, 2c]. Tana Hoban’s book are always great for noticing and wondering about numbers. In particular, check out Count and See. [2b, 2c].

## #EarlyMath: Who has Mais/More?

These #EarlyMath posts feature books centered on big ideas featured in the math wisdom book Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know by Erikson Institute’s Early Math Collaborative. Recently, we shared The Animals Would Not Sleep by Sara Levine and Marta Alvarez Miguens from the Charlesbridge Storytelling Math series, a magical #EarlyMath book centered on Sets. In this post, we share a second magical book from the Charlesbridge Storytelling Math series that centers around the big idea of Number Sense: Developing a Meaningful Sense of Quantity.

The Book
Published in 2020, Lia & Luís: Who Has More? by Ana Crespo and Giovana Medeiros offers a fresh story for an all-too-common situation: Sibling rivalry! [At least it is in my house. So much so, I hoping it peaks at ages 11 and 9, as my two oldest are often at each others throats. I can hear you parents of teenage children laughing:)]

In the book, Lia’s braggadocious brother Luís is sure he has snagged the better snack option from their family’s Brazilian grocery store. As he holds up his bag of tapioca biscuits to Lia’s two croquettes, he boasts: “I have more!”

But Lia’s not so sure. The siblings experiment with different methods to compare their yummy Brazilian snacks. Crespo’s simple story with a hint of sassiness captures the sibling-rivalry spirit brilliantly, while Medeiros’ bright, crisp illustrations make it fun and easy for young ones to follow along with the sibling’s problem-solving process. It’s no wonder that this book won a Mathical award for 2021.

This book is great for ages 3-6.

The Math

The math in this book is early number sense, in particular the concept of more. Young children are quite versed in this concept, often negotiating and communicating their desire for more. In our house, we used the ASL sign for more before my children learned to talk. In addition to cries, smiles and giggles, this sign became a key component of early communication in our house and was one of my children’s first words.

In Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know, the Erikson Institute’s Early Math Collaborative remind us of the importance of early number sense with their second set of big ideas:

Number Sense: Developing a Meaningful Sense of Quantity

2a*: Numbers are used in many ways, some more mathematical than others.

2b: Quantity is an attribute of a set of objects and we use numbers to name specific quantities.

2c: The quantity of a small collection can be intuitively perceived without counting.

[* Erikson does not include these letter labels (a, b, c). I do it in order to refer to them later. They are not meant to denote any sort of learning progression.]

A strong number sense developed in the early years “is a key building block of learning arithmetic in the primary grades, as it connects counting to quantities, solidifies and refines the understanding of more and less and helps children estimate quantities and measurements.” (Erikson Institute, Big Ideas of Early Math, p. 30)

Lia & Luís: Who Has More? is a perfect resource for exploring and refining one’s concept of more and less while developing a meaningful sense of quantity. As they debate whether one bag of biscoito de polvilho (tapioca biscuits) is more than 2 croquettes or whether 100 biscuits is more than 2 croquettes, the siblings consider size, units, and quantity before ending up with a satisfying solution, which...SPOILER

uses a pan balance!

For more information on the math of number sense and some ways to play around with this big idea at home: check out my new post at www.fairymathmother.com. Additionally, the Charlesbridge website offers Lia & Luís: Who Has More? title activities here (be sure to select the “Downloadables” tab).

The Magic

Landon’s desire for a fair share among the siblings was strong from the beginning of this book. He sided with each sibling at different parts of the argument. His preference was for the sibling with the larger number, while disregarding the unit. For example, when Luís brags he has more because his bag bigger and Lia disagrees comparing her 2 croquettes to Luís‘ 1 bag, Landon shouts, “That’s cheating, she has TWO!” Later when Luis dumps his bag and counts individual biscuits for the win, Landon responded: “He’s cheating now. He has one hundred” and proceeded making police car sounds. He was thrilled to see it all worked out fairly in the end.

In addition to the great story, we enjoyed the Portuguese language sprinkled through the dialogue and found the pronunciation key in the back matter helpful. As I read , Landon asked: “Mom why are you not talking in English?” After I explain it was because Lia and Luís are Brazilian and speak Portuguese, Landon started saying the words along with me. His favorite is para which means stop in Portuguese.

As with all magical math books, Lia & Luís: Who Has More? has had many rereads. During one, Landon suggested:
“We should get those snacks. Let’s get a lot of those…Like one million of those (he said pointing to the biscuits) and one million of those (pointing to the croquettes).”

And so after a little research on where to buy them, we headed off to Brazilian Bowl in Chicago. On our way, Landon assured me, “Don’t worry mom, I won’t brag. If I have more.” I laughed recalling the story and Luís’s bragging.

When we got to the store they informed us, they were all out of tapioca biscuits so we substituted them with Yokitos brand cheese flavored corn chips, which Landon reports are way better than Pirate Booty and proceeded to eat the entire bag on the way home while asking: “How do they make it so good and delicious?”

By the way, I’m with Lia on the croquettes. I’m still thinking about them. So good and delicious. I’m also left wondering, How does Charlesbridge make their Storytelling Math picture books so magical? Lia & Luís: Who Has More? is another one to add to the list. And we can’t wait to share more soon from Charlesbridge. [If you have a math story to share, Charlesbridge is looking for more magic to add to their list, submissions due August 1st, 2021, see here for info]

You can purchase Lia & Luís: Who Has More? from Charlesbridge, Bookshop, Indie bound, Barnes and Noble or Amazon.

***

If you’d like to receive these magical math book posts every month, be sure to follow this blog in the side bar of this page. Thanks and see you soon!  Touch #mathbookmagic, pass it on.

## 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.

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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## Math Book Wisdom: An Early Math Resource Book

I asked my husband to snap this photograph moments after my son Landon was born. The sunrise over the Lake Michigan’s horizon reminded me of a scene from the movie Under the Tuscan Sun where Diane Lane explains that the Italian phrase “to give birth” (dare alla luce) means to “give to the light.” I wanted to capture the moment. My son arriving with the sun.

Four and half years later, a different horizon has my attention. The mathematical horizon. As the result of the pandemic, Landon does not attend preschool and found myself asking: What math does a preschooler need to know? The pandemic has many parents asking questions like this. Last summer, I started a new blog (www.fairymathmother.com) hoping to provide a place where parents could ask mathematical questions. I only received one parent question regarding the purpose of 1st grade addition strategies (e.g., doubles plus 1). To be honest, I haven’t done much with the blog. This year, I’m re-envisioning the blog and will be sharing early math experiences and resources. I will continue to post the magical math picture books Landon and I share at www.mathbookmagic.com and a broader collection of magical activities, games, art projects, and general picture books for preschool parents at www.fairymathmother.com.

The book featured in this post is a different from those I’ve shared before on www.mathbookmagic.com. This book is not a picture book or a book that I share with my children. It is more of an early math wisdom book that anchors me as I navigate these new waters of early math learning. This book helps me place my “ears to the ground, listening” to my child, so I can focus my “eyes on mathematical horizon.” [Ball, 1993]. Magical resources that illuminate the mathematical horizon are important anchors for any teaching, especially in pandemic (parent-led) teaching. The book below is a resource full of magical early math wisdom.

The Book

Published in 2014 by Pearson Education, Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know was written by The Early Math Collaborative, a division of the Erikson Institute in Chicago, IL. Launched in 2007, The Early Math Collaborative works to “increase the quality of early math education through professional development, research, and providing resources related to foundational mathematics – what it is, how it develops in children, and how best to teach it.” [Erikson Website]

In Big Ideas of Early Mathematics: What Teachers of Young Children Need to Know, the Early Math Collaborative “identifies Big Ideas and Precursor Concepts to help understand the many facets involved with early math teaching and learning. They are organized under topics that teachers of young children need to explore in order to support the development of everyday math thinking” from 3-6 years old. [From EMC website]

This book consists of 10 chapters: An introduction, conclusion and 8 content area chapters in between. Each content chapter is organized around two or three different big ideas. To ground these big ideas, each chapter includes a chart with sample activities, stories and quotes from teachers, videos of classroom scenarios, and a Finding Great Math in Great Books list.

This book was written for early math teachers (ages 3-6 years old). However, as a preschool parent, this book is a valuable resource for mathematizing conversations, play, and activities at home.

The Math

The waters of early math learning are deeper and more curious than reciting the number sequence: 1, 2, 3… . Below in the table of contents you can see the broad range of content areas in early math.

Preface

Introduction

Chapter 1   SETS:  Using Attributes to Make Collections

Chapter 2   NUMBER SENSE:  Developing a Meaningful Sense of Quantity

Chapter 3  COUNTING:  More than Just 1, 2, 3

Chapter 4  NUMBER OPERATIONS: Every Operation Tells a Story

Chapter 5  PATTERN:  Recognizing Repetition and Regularity

Chapter 6  MEASUREMENT:  Making Fair Comparisons

Chapter 7  DATA ANALYSIS: Asking Questions and Finding Answers

Chapter 8  SPATIAL RELATIONSHIPS:  Mapping the World Around Us

Chapter 9  SHAPE: Developing Definitions

Conclusion

Appendix A  Big Ideas Charts

There are two or three Big Ideas in each chapter. These Big Ideas provide the reader with a clear view on the mathematic horizon of each content area. For example, in Chapter 1: Sets, the big ideas include:

Big Idea 1: Attributes can be used to sort collections into sets

Big Idea 2: The same collection can be sorted in different ways

Big Idea 3: Sets can be compared and ordered

A list of every Big Idea included in the book can be found here on Erikson’s website along with blog posts and picture book recommendations related to each big idea.

The Magic/Wisdom

As I’m not explicitly sharing this book with my children, I can’t share the “magic” as defined here. So instead I will share what I call the wisdom of this book.

This book provides a clear lens into the Big Ideas of preschool math. The Big Ideas give me a view of the mathematical horizon so that I can recognize these ideas and precursors of these ideas in conversations with my son. They inspire my choice of activities, games and projects.

This book provides activities and books focused on these big ideas of early math. I don’t need to go through Pinterest and collect 100s of activities. I don’t need to search the internet. Everything I need is in this book. I still generate my own questions and may add my own twist to activities (which I will share on fairymathbookmagic.com), but they are anchored in ideas from the book.

This book is informed by research and classroom experiences. The authors incorporated the most current research from the fields of cognitive science and mathematics education to create a set of 26 Big Ideas that lay the foundation for early math learning and thinking. Then, the authors collaborated with more than 400 preschool, kindergarten and Head Start teachers from the Chicago area to understand how to make these Big Ideas clear to students. Quotes from teachers of young children, called Teacher Talk,” provide reflections on personal experiences in understanding and implementing the Big Ideas in the classroom. The book also points out common misconceptions (or if you prefer knowledge in transition). Embedded videos are included on a CD-Rom. These wonderful videos offer lovely ideas and images of how to help young children develop mathematical understanding around Big Ideas.

I am so grateful for this magical wisdom book. We will be connecting back to this post and these Big Ideas as we share our magical math books this year. Our first magical book post will be in a few weeks. The book focuses on the Big Ideas of Sets and is part of the new Storytelling Math series from Charlesbridge. The Storytelling Math series is one magical set of books. [See what I did there? A set:) of books.]

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## Math Book Magic Holiday List (2020)

For those still out searching for gifts, here some magical math books featured on our blog this year and toy/game pairings. Enjoy! Note: The Amazon Affiliate links are given in this post when you click on the title of the book. If in the future our site collects any money from these Affiliate links, all proceeds go to buying magical math books to share with others. *Support your local bookshops at BookShop.org . All the books below can be found there.

[Age 4-6] My Shape is Sam by Amanda Jackson and Lydia Nichols’s sweet story follows Sam’s journey to becoming the shape that suits him best. Is it a circle? A square? Or some shape in between? Read more here. Pair this with Hexagon or Rectangle puzzles from Talking Math with your Kids (if you can’t get your hands on them as they just came out in limited quantities, more coming in 2021). Talking Math with your Kids site also has beautiful wooden tiling shapes from pattern blocks to turtles. Lastly, here’s another shape toy recommendation by the inventor of the Hexagon or Rectangle puzzle, math educator Christopher Danielson.

[Ages 3-6] 1-2-3 Peas is a counting book from 1-100 by Keith Baker. Peas are scattered in lively scenes in and around the numerals for each number. There are different groupings and different costumes on many of the peas (the Peatles and Pea-oyncé even make appearances).   Read more here. Pair with the Tiny Polka Dots I game.

[Ages 3-6] Let’s Count Goats was written by author and educator Mem Fox and illustrated by Jan Thomas. This humorous and fun rhyming book invites children to identify and count a whole host of goats ranging in size, silliness, and profession. The question, Can we count the____goats? is posed throughout the book. Read more here. Pair with Tiny Polka Dots game or this cute adoptable goat from FAO Schwartz.

[Ages 4-8] Dozens of Doughnuts by Carrie Finison and Brianne Farley is a rhyming picture book about a doughnut-making bear named LouAnn. Each time Louann bakes a new batch of “One dozen doughnuts hot from the pan. Toasty, and hot, and ALL for–“. … We sit at edge of the page turn only to find out … they are NOT ALL for LouAnn. Friend after friend come by and LouAnn shares her doughnuts. The more friends that come, the more doughnut-sharing must be done, every time, leaving poor LouAnn with none! Read more here. Pair with these stackable donuts for the littles ones, this tic-tac-doughnut game, or a dozen of these or these sweet treats from Melissa and Doug.

[Ages 6-10] The Boy Who Dreamed of Infinity: A Tale of the Genius Ramanujan by Amy Alznauer and Daniel Miyares tells the story of Indian mathematician Ramanujan as a boy through young adulthood.  In addition to introducing different mathematical objects and problems, The Boy Who Dreamed of Infinity is the story of a child and young adult tirelessly persevering to do what he loved, share his ideas, and to be heard and understood.  Read more here. Pair this beautiful book with these equally beautiful and wonderful coloring books from Alex Bellos and Edmund Harriss here and here.

[Ages 8+] The Original Area Mazes: 100 Addictive Puzzles to Solve with Simple Math―and Clever Logic!  features area mazes puzzles created by Ryoichi Murakami and Japanese puzzle master Naoki Inaba. These puzzles have a sudoko puzzle feel. However, in addition to using logical thinking, Area Maze puzzles require two mathematical ideas over and over. The first idea is the area of a rectangle is length times width. The second idea involves the relationship between factors and multiples. More here. This book pairs nicely with the Prime Climb game.

[Ages 6+] Lastly, Counting on Katherine: How Katherine Saved Apollo 13, written by Helaine Becker and illustrated by Tiemdow Phumiruk tells the story of Katherine Johnson, the mathematical genius who made sure that Apollo 13 returned home safely. Read more here and here. Even though this book appeared at the end of 2019, we read it again this summer during our physically distanced backyard Math Club and it pairs nicely our favorite Melissa and Doug floor puzzles. Also, get your #mathgals t-shirts here.

And if you are still unsure, here are some more lists:

• Math Book Magic Holiday 2019 list
• Here‘s a recent list of mathy book recommendations from Christopher Danielson
• Children’s book author and librarian Betsy Bird’s list of top 2020 Math Pictures here
• Here’s a great list of Stem Toys from Art of Problem Solving

Alright… I think that is enough lists for one list:)

Happy New Year all. More math book magic in 2021!

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## My Shape is Sam

Recently, Kaitlyn Leann Sanchez shared via Twitter how she planned to read My Shape is Sam to celebrate #MathStorytellingday (September 25). As soon as I heard the title and saw the cover art, I knew I needed to get my hands on this book!

On her Math is Everywhere blog, Kaitlyn shares what she loves about the book:

My Shape is Sam is a powerful book about self-discovery and self-acceptance through the eyes of a square named Sam. It has the feel of an inspirational movie and the fun of a day-in-the-life of a kid. … I truly believe this is going to be a classic of our time, reminding us all to accept ourselves for who we are, even if it doesn’t fit what’s expected.”

Thanks Kaitlyn for spreading the word about this book. We thought it was special too!

The Book

Written By Amanda Jackson and illustrated by Lydia Nichols, My Shape is Sam tells the story of a square named Sam who longs to be more like a circle. Especially because circles can roll! How fun would that be?!

This sweet story follows Sam’s journey to becoming the shape that suits him best. Is it a circle? A square? Or some shape in between? Nichols’s bright, cheerful illustrations are the perfect complement to Jackson’s heart-warming story. Published in September 2019 by Page Street Kids, My Shape is Sam is a perfect fit for ages 3-6.

Math

This story and accompanying illustrations provide opportunities to children to notice shapes. The illustrations are full of triangles, rectangles, and lots of squares and circles. I like how the book focuses on two shapes (squares and circles) and the ways in which they are and are not similar.

The book is a great introduction to investigating the properties and defining characteristics of a particular shape. In other words, noticing what makes a square a square and a circle a circle.

Below is a page describing what makes Sam a square.

[Aside on four “even sides”: I prefer “four equal” sides” or to be pedantic, “four equal length sides”. However, I recognize “even sides” is a familiar way to describe the sides of a square and I do appreciate that this language is coupled with the rulers in the illustration which imply equality.]

And here is a description of the characteristics of circles.

At the end, the book introduces a new shape called a SAM providing an opportunity to observe and compare the characteristics of a SAM to a circle and a square.

I can’t leave the Math section without a nod to why the title of this book hooked me immediately. And that has to do with a special Hierarchy of Hexagon Activity designed by math educator Christopher Danielson. Danielson was brainstorming ways to help his students (prospective teachers) distinguish between properties and defining characteristics of a shape. He wanted to problematize the situation and for him that involved placing the students in a situation where they had to classify and compare a less familiar set of shapes (as opposed to classify and compare quadrilaterals for example). He choose the set of hexagons below.

After his students cut these shapes out, he asked them to choose one that seemed special to them for some reason, and to identify what property or properties made the hexagon special. The activity engaged the students in the mathematical processes of defining and comparing shapes. They even chose names for their shapes. Here is the hierachy of hexagons his class came up with based on the shapes above.

Perhaps you see from this hierarchy why I thought of this when I saw My Shape is Sam. Check out Stacy, Mercedes, Norm and Bob! I love the idea of students naming shapes and sharing their definitions of said shapes. It’s a great opportunity to engage in the mathematical process of defining.

If you are interested in what shape was a Stacy or a Bob, you can read more about the development of the Hierarchy of Hexagons Activity here, here and here. You can also go to this Desmos teaching activity and try a related activity out in your classroom.

The Magic

So the title was definitely a magical hook for me, but what about my children? Would they think the book was magical?

I shared the book with my 4 year old son, Landon. He was a huge fan of the spread below. He loved identifying all the things Sam was a part of (a building, a truck, a train and a bridge).

The most magical part of our sharing was at the end of the book. I won’t share what shape a Sam is exactly, as I don’t want to spoil the surprise. But the last page, has an image of Sam’s new shape and the words: My Shape is Sam. As we read that page, I asked:

“What shape is a Landon?”

“This one!” He said using using his hands to trace around his body and said, “But he doesn’t have arms (pointing to Sam).” Then, pointing to Sam’s “sides” in the picture he counted, “One, two, three, four.” Then turned to me, asking: “Count me!”

I was a bit confused and asked. “Your sides?” To which he replied, “My body.”

I began counting body parts and that seemed to satisfy him. Two eyes. Two arms. One nose. One belly. Ten toes. Landon each of my counts with a “That’s right” or “Yes,” and we continued. Then I begin to get silly and miscount, counting three knees and four ears. He erupted into giggles. It was a magical moment, silly moment.

Then, Landon proceeded to tell me that he is going to “read” the book to me and as he makes his way through the pages I notice one more magical detail.

“Look, Landon, what shape are the pages of the book?”

” A Sam!”

“Yep. A Sam! How cool is that!?!”

“Very cool.”

Very cool indeed.

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## Math Book Magic Dreams

In the past 3 years, I’ve shared many math books with my children. We’ve found magic in 48 of these books. I’ve learned much from these amazing authors and illustrators and watching my children interact with their books. In addition to writing this blog, I’ve been writing picture book manuscripts and dreaming of publishing magical math books of my own.

Anyone that has written for children knows, it actually is harder than it seems. Author Anna Dewdney had this to say.

“…The irony is it would be easier to be a hand surgeon than to be a published children’s book author. It is less competitive. People have memories of children’s books. They do look deceptively simple. Of course, everybody has stories that resonate with them. It is so tempting to think all you have to do is write down the short story and there you are. They are very complicated books. You are working with a very tight format and they become like haiku. Until people have tried and tried to get published, they just don’t understand. One of my editor friends says for every 15,000 manuscripts on an editor’s desk, one will get published.” —Anna Dewdney, author of the  Llama Llama series and Grumpy Gloria. Source

Despite these odds, I continue to dream, write, submit, revise, read, and repeat. And in this post, I share my writing for the first time on this blog.

Last month I wrote a short piece for the #FallWritingFrenzy contest hosted by picture book author, agent, and math teacher Kaitlyn Leann Sanchez and children’s book author and artist, Lydia Lukidis. The Rules: Choose an inspiration photo from a set of fall-themed photos, write a piece inspired by the photo (200 words or less), and post your submission to your blog. Below is my inspiration image and my piece, Shape Makers. Instead of adding illustration notes, I’ve included an image slideshow to illustrate some of the wonder that inspired this piece.

Shape Makers

By Kelly Darke

The world’s full of shape makers.

Some make leaf shapes.
Thumb-like lobe shapes. Pointed, edge shapes. Dreamy, drip shapes.

Some make web shapes.
Triangle net shapes. Silken circle shapes. Funnel mesh shapes.

Some make nest shapes. Some dome shapes. Some underground home shapes.

Some make sticky shapes or sipping shapes or show-off shapes.

Some make rainbow shapes. Some shadow shapes. Some snowflake shapes.

And at night, as the moon rises and all is quiet and still, some shape makers make shimmering shapes in the stars.

What shapes will you make?

[Photos in the slideshow are courtesy of Pixabay with the exception of the rainbow (MARTIJN HARLEMAN/SPACEGALLERY) and the worm tunnels which are a screenshot from the video below).] Also, here are a few links regarding these shape wonders:

Worms at work

Thanks for taking the time to read my writing. And good luck to any #FallWritingFrenzy participants here! I look forward to reading your submissions.

Interested in reading more about magical math picture books? Follow this blog by clicking the button in sidebar or follow me on twitter @KellyDarkeMath for more magical math book recommendations. Next post features a rhyming picture book that sits in intersection of math, magic, and doughnuts. Coming soon!

If you’d like to receive these magical math book posts every month, be sure to follow this blog in the side bar of this page. Thanks and see you soon!  Touch #mathbookmagic, pass it on.

## Question: What’s the Deal with All These Addition Strategies?

A 1st grade parent asks: What is the deal with all these addition strategies? It seems a bit much right? Can’t students just memorize their facts? What’s the point? In this series of 3 videos, I respond.