Comparing numbers can be difficult. Young mathematicians, especially in kindergarten, just become proficient in learning the quantity of numbers before diving into comparing those numbers. For decades, teachers have relied on the 'ole alligator analogy for teaching students to compare numbers and draw comparison symbols. You will find numerous blog posts and printables with this cute alligator, even suggesting to use him with decimals and percentages. Have you or your students become dependent on drawing teeth on comparison symbols? Students think, "Is the bigger value eating the smaller one?" or "Is it the value it already chopped on?" This becomes confusing, especially for younger students. While this can be a cute anchor chart, students are not internalizing the meaning of the comparison symbols. This misnomer is confusing children and frustrating their future teachers. I know what you are thinking, if the alligator analogy isn't the best for students to learn, what can I teach my students so they can retain the correct meaning for these symbols? Read more to find a strategy for teaching comparing numbers and correctly explaining comparison symbols. 

There's A Better Way To Compare Numbers

Thinking about how a child learns vocabulary, it's easy to roll back time and reflect on how a young child learns their name. How does a child learn their name? Parents have identified the child by their name. The parents and others around the child use their name in context. With repeated exposure to their name, the young child memorizes it. Soon they are able to repeat their name and identify themselves as such.

Children are innately logical and literal. If we say "alligator," children think of the lizard-like swamp animal, not a mathematical symbol. 

If adults call a comparison symbol an "alligator," we are mislabeling a content-specific word for students.

I truly believe this is what happened in my early education. I learned tricks in school, not actual mathematics. Eventually, there comes a point when tricks no longer suffice for students and can lead to failure in advanced mathematics, which is the WHY behind everything I do with Down River Resources.

There is a big movement, especially in upper elementary, middle, and high schools to break students away from these misrepresentations.

Trust me, I know it is not ANYONE'S intention to teach incorrectly, often times, we are victims of our own education. Educators teach the way they were taught unless they have since learned differently.

How Do I Teach Comparisons?

Use a word problem to introduce two sets of numbers. If you are comparing numbers 9 and 7, it may sound like this:

Kaila and Marco were born on the same day. Kaila has 9 birthday candles on her cake. Marco has 7 candles on her birthday cake. Use a comparsion symbol (>, <, or =) to compare 9 and 7.

Ideally, with exposure to symbols, such as in the word problem above, students memorize the meaning. Just as students hear comparative language, such as "equal to," "greater than," and "less than," they need to see the symbols that represent these phrases too.

After modeling this language and its corresponding symbols, the students should practice saying and writing them too!

If you are still stuck on the alligator so the students have a scaffold for learning the comparison symbol, I have a strategy to help. 

Sometimes before students can internalize the meaning of the symbol, it helps to actually analyze the shape of the comparison symbol.

Think about an equal symbol. 

The line segments are parallel; the bars are the same distance apart on both sides. (See the "equal to" image.)

Now, let's take a closer look at the symbols that represent inequalities. 

The segments, or bars, are tilted when using the inequalities. There is a smaller side and a larger sides.

The GREATER number is next to the wider end, while the LESSER number is next to the narrower end. 

Please note the language used in that statement above. Use GREATER instead of 'bigger,' and LESS rather than 'smaller.'

As students move into advanced mathematics, students will need to apply this skill to integers. Calling -6 'bigger' than -16 creates confusion for students.

As you can see below, EVERY grade level focuses on comparisons to some degree. 

Let's commit to focus on teaching mathematics, not just the tricks!

Math Content Standards Addressed: 

Kindergarten 
- TEKS K.2G Compare sets of objects up to at least 20 in each set using comparative language.
- TEKS K.2H Use comparative language to describe two numbers up to 20 presented as written numerals.

First Grade
- TEKS 1.2D Generate a number that is greater than or less than a given whole number up to 120.
- TEKS 1.2E Use place value to compare whole numbers up to 120 using comparative language.
- TEKS 1.2F Order whole numbers up to 120 using place value and open number lines.
- TEKS 1.2G Represent the comparison of two numbers to 100 using the symbols >, <, or =.

Second Grade

- TEKS 2.2C Generate a number that is greater than or less than a given whole number up to 1,200.
- TEKS 2.2D Use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =).

Third Grade

- TEKS 3.2D Compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =.

Fourth Grade
- TEKS 4.2 Compare and order whole numbers to 1,000,000,000 and represent comparisons using the symbols >, <, or =.
- TEKS 4.3D Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <.

Fifth Grade
- TEKS 5.2B Compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =.

I hope this post inspires you to use math language when teaching students how to compare numbers, if you want to download some free mats to use when comparing numbers, you can find them here.

Were you taught the alligator analogy?

Make sure to pin and save this post for future reference.

Why You Need to Ditch the Alligator When Comparing Numbers Strategy

Read more »

Laura Williams

One of the best things about teaching history during Women's History Month is the accessibility of quality children's literature or picture books! Students are much more likely to learn about the important events, people, and places which make our world unique through an accessible text. Throughout our history women have made valuable contributions. No matter what their role, women's experiences remain an important and sometimes overlooked aspect of our history. I've included some historical texts and a few inspirations book for young girls. These picture books value the diverse experience of women and provide inspiration for the young girl sitting in our classroom or being raised within our home.

Finding the Best Picture Books for Women's History Month

This post contains affiliate links for Amazon. I only recommend items that I own and use to my Valued Partners. By purchasing an item on the Amazon site using these links, I will receive a very small commission on your purchase that allows me to maintain this website. Thank you for your continued support!

Girls come in all different colors and sizes. They delight and amaze us. They're full of surprises. Girls can do anything they want to do. And if YOU are a girl . . . You can do these things too! 

- Girls Can Do Anything

Shaking Things Up: 14 Young Women Who Changed the World

Shaking Things Up introduces fourteen revolutionary young women—each paired with a noteworthy female artist—to the next generation of activists, trail-blazers, and rabble-rousers. This book has beautiful illustrations and is sure to inspire your budding artists too!

In this book of poems, you will find Mary Anning, who was just thirteen when she unearthed a prehistoric fossil. You’ll meet Ruby Bridges, the brave six year old who helped end segregation in the South. And Maya Lin, who at twenty-one won a competition to create a war memorial, and then had to appear before Congress to defend her right to create.

And those are just a few of the young women included in this book. Readers will also hear about Molly Williams, Annette Kellerman, Nellie Bly, Pura Belprè, Frida Kahlo, Jacqueline and Eileen Nearne, Frances Moore Lappé, Mae Jemison, Angela Zhang, and Malala Yousafzai—all whose stories will enthrall and inspire. This poetry collection was written, illustrated, edited, and designed by women and includes an author’s note, a timeline, and additional resources.

With artwork by notable artists including Selina Alko, Sophie Blackall, Lisa Brown, Hadley Hooper, Emily Winfield Martin, Oge Mora, Julie Morstad, Sara Palacios, LeUyen Pham, Erin Robinson, Isabel Roxas, Shadra Strickland, and Melissa Sweet.

This book is best suited for upper elementary students.

She Persisted: 13 American Women Who Changed the World

Chelsea Clinton introduces eager students who are ready to take on the world to thirteen inspirational women who never took no for an answer, and who always, inevitably and without fail, persisted.

Throughout American history, there have always been women who have spoken out for what's right, even when they have to fight to be heard. In She Persisted, Chelsea Clinton celebrates thirteen American women who helped shape our country through their tenacity, sometimes through speaking out, sometimes by staying seated, sometimes by captivating an audience. They all certainly persisted.

This book features: Harriet Tubman, Helen Keller, Clara Lemlich, Nellie Bly, Virginia Apgar, Maria Tallchief, Claudette Colvin, Ruby Bridges, Margaret Chase Smith, Sally Ride, Florence Griffith Joyner, Oprah Winfrey, Sonia Sotomayor—and one special cameo.

Dear Girl, 

Dear Girl, is a remarkable love letter written for the special girl in your life; a gentle reminder that she’s powerful, strong, and holds a valuable place in the world.

Through this charming text and stunning illustrations, any girl reading this book will feel that she's great just the way she is—whether she enjoys jumping in a muddy puddle, has a face full of freckles, or dances on table tops.

Dear Girl, encourages girls to always be themselves and to love who they are—inside and out.

I love text letter written inside of  book jacket. This surely gives you the sentiment that is beautifully captured within the pages of this text:

Dear Girl,
This book is for you.
Wonderful, smart, beautiful you.
If you ever need a reminder, just turn to any page in this book and know that you are special and you are loved.
—Amy and Paris

If you are a mother, aunt, grandmother, or someone special to a lucky girl, this book is the perfect gift!

Girls Can Do Anything

This enchanting book is all about the things girls can do. Whether she dreams of being a vet that heals people's pets, a firefighter that braves the flames, an astronaut floating in deep, dark space, or a fearless jungle explorer, there's nothing that a girl can't do. Girls Can Do Anything!

One size definitely does not fit all in this book: charming depictions of girls being scruffy or fancy, neat or messy, and everything in between are explored and celebrated, because each girl is unique and unlike all others. 

Empower young girls everywhere and let them know that being told "you're such a girl" is the greatest compliment of all!

One of my favorite things about this book is that girls of every walk of life are represented. There's a girl in a wheelchair and girls of color in this text. If representation matters to you when selecting a text this book surely fits the bill. 

Girl, You're Amazing!

An upbeat, rhyming tribute to girls offers readers encouragement to build confidence and self-esteem while whimsical paintings celebrate the many things that girls of every age can do.

Girl, You're Amazing! has you chanting that beautiful sentence to your favorite girl all day long!

This book also celebrates diversity. If you are looking for a book that celebrates the uniqueness of all girls, this book is for you! The illustrator aims for inclusion in her hip gouaches, which feature girls of all races and appearances. Asymmetrical faces, fashionably mismatched patterns, and a quirky palette of colors adorn each unique page.

Another great thing about this text is that it has a companion, Boy, You're Amazing! With all this girl talk, we need to remember that EACH child is unique and special no matter their gender!

I hope this post inspires you to find the perfect picture book to celebrate girls and women this March and beyond! I look forward to adding to this list as I find more books that celebrate girls.

What is your favorite female picture book?

Make sure to pin and save this post for future reference.

Read more »

Laura Williams

STAAR testing season is right around the corner! The best STAAR test prep strategy is high-quality instruction throughout the school year, but many teachers like to add a test prep session to their schedule for good measure! {Whatever helps, right?!} Whether you test prep throughout the school year or in the final weeks before the STAAR test, or other standards-based assessment, you can gamify your test prep materials to improve student motivation and engagement! Do your students want to learn? Are your students making the effort to learn? Are they enjoying the process and doing well? Are your students motivated to learn or are they dragging their heels? Gamifying test prep might be just what your students need, especially if you are reading this right around Spring Break?! Continuing reading to find a simple way to increase motivation and engagement during test prep!

How To Increase Motivation and Engagement During Test Prep

Test Prep Games are Good for the Brain

This post contains affiliate links for Amazon. I only recommend items that I own and use to my Valued Partners. By purchasing an item on the Amazon site using these links, I will receive a very small commission on your purchase that allows me to maintain this website. Thank you for your continued support!

The social component of working on a game in a group leads to LOADS of benefits on brain function including:

- Activate neurotransmission
- Increase brain plasticity
- Rewires
- Mitigates brain inflammation
- Mitigates deleterious effects of oxidative stress



These are just the benefits of the social components of gamifying educational content.

Adding learning games in your classroom will boost intrinsic and extrinsic motivation, engagement, and learning outcomes for learner!

With so many benefits, what are you waiting for friend?

My favorite way of gamifying the classroom is by simply adding a popular game to test prep sessions.  

Want to do it too?

Here's How To Test Prep with Ease:

Collect a game or gameboard. Goodwill and Savers are the best cost-savings options. I often find games on clearance too!

Use word problems or sample test questions as the educational basis of the game. You can use questions from worksheets, released test questions, or specific game cards to practice heavily-tested standards. (In Texas, we call these the readiness standards.)

Rigorous game cards

The class can be divided into two teams. The team can work together to solve the problem.

If the team gets the problem correct, the team has a turn to play the game. Students within each team can take turns being the “player” for their team by following the game’s instructions.

If the team does not get the problem correct, they forfeit their turn. {You can also create a “Steal” option. The other team can generate a solution for an extra turn. You can give teams a couple extra chances to use through the game, three strikes, etc.}

Connect Four Shots

Are you ready to try this strategy, but need test-like questions to minimize your prep time?

I'll keep you afloat with my math test prep bundles that are just waiting for you to print. These will surely add some challenge into your math test prep sessions. They can be used during testing season or throughout the year for a spiral review. The bundles come with printable game boards OR you can add your own physical game too. 

I hope this post inspires you to gamify your test prep sessions, if you need Connect Four Shots,
you can find it here.

The rigorous test prep bundles can be found in my TpT shop:

Third Grade Math Test Prep Bundle

Fourth Grade Math Test Prep Bundle

Fifth Grade Math Test Bundle

What are some other ways you have motivated and engaged your students during test prep sessions?

Make sure to pin and save this post for future reference.

Read more »

Laura Williams