At the beginning of the school year, there is a lot of hype decorating classroom. After the new borders are up, teachers begin thinking about the students on their class list. (If they're lucky enough to have it!) There will be different levels of math understanding in the classroom, especially number sense. Pre-assessment in math is tricky. But… why is that? Teachers want to see where mathematicians are in their understanding WITHOUT having to print and pass out a daunting paper test. Listen, I get it. No one gets excited about math when a thick packet of white copy paper is placed in front of them! How can we pre-assess students’ math thinking without using a paper test? I have a fun and pain-free task that will engage your mathematicians and leave you with lots of knowledge about your students’ math thinking! Don’t worry, I’ll explain! 

Use Mystery Bags as a Quick and Effective Pre-assessment of Number Sense

I recently did this activity with first grade, second grade, third grade, and fourth grade mathematicians. I think you could do it with kindergarten and fifth grade too, you just need to alter the number of objects. More about that in a minute!

Each mathematician was given a brown bag with a quantity of objects inside of it. Mathematicians were asked to make a sign for their bag to show many objects they had. I promise I’ll explain how this simple activity will give you tons of helpful information about your students’ number sense. But, first…

1. I grabbed a pack of brown paper lunch sacks, or brown paper bags, from my local grocery store. You can find this in the aisle with Ziploc bags, usually placed towards the bottom of the shelf. 
2. I printed some simple labels to identify each bag, more for my sake. (I used letters to identify each bag since we are working with numbers.) I wanted to have a log of the contents of each bag. 
3. I grabbed a variety of objects that I use as math manipulatives in my classroom, such as colored squares and linking cubes, or connecting cubes. (Since I was doing this activity with first grade and second grade mathematicians, I counted out assortments of objects that totaled in the teens. I also repeated this activity with third grade and fourth grade mathematicians and used objects that totaled in the 20s.)

You might be wondering how long this took? I prepped the bags quickly. As a busy wife and mom to three, ain’t nobody got time to spend hours prepping lessons. I got all my supplies and just made rows of objects. I did include three colors in each bag. I’ll tell you why later.

Before I introduced the activity, we talked about how signs, posters, and billboards used to advertise something use words and pictures. Their signs could include words and pictures too!

It sounded something like this: 

Have you seen a billboard out your window? I keep seeing the one with big chicken strips on it. The picture makes me interested in trying the chicken. On the sign, there are words that tell me what it is and where to get it. The words give me more information about the picture. I see posters that get me interested in different movies at the movie theatre too. There is usually a picture from the movie and words to tell me the title of the movie and the date that it is being released.

After a few minutes of exploring their bags, mathematicians worked quickly and quietly on their sign. 

I kept thinking, “How are my students developing mathematical notation?” As I observed each mathematician diligently working, I was curious how and why they were making choices as to what to include on their sign.

Some drew pictorial representations matching the color and quantity of objects inside of their bags. This is why it’s important to have more than one color in each bag. Others drew iconic representations; instead of drawing the exact objects, they drew a shape to represent the object. Most of the mathematicians, after drawing something on their sign, added numerals to represent the quantities too. 

I asked clarifying questions to each mathematician, such as:

• “How did you lay out your objects to count?”
• “Tell us how you counted.” 

If a mathematician gave me a blank stare, I asked some closed questions, for example: 

• "Do you need a word to describe your object?"
• “Did you count by ones, such as 1, 2, 3…?”
• “Did you count how many objects you had altogether? How many objects were inside your bag?”

After one mathematician shared their poster and their math thinking with the classroom, they dumped the bag out so the others could see. Revealing the mystery for their classmates was so exciting for them! 

Now, let’s make this simple. 

Examples of Mathematical Thinking using the Mystery Bag Activity

We will take a look at a few real examples from the classroom, so you can practice looking at a mathematician's number sense. There’s a lot of good information that you can glean from this simple math investigation.

Bag E

The mathematician who received Mystery Bag E attended to the color and quantity in her bag. Her bag was filled with linking cubes that were blue, white, and green. She drew an iconic representation; instead of drawing cubes, she drew squares to represent each cube. She used different colors in an unstructured, or random, arrangement. If you look towards the top of her sign, there is a key she drew noting that there were 4 cubes in each color. Though she knew there were four in each color, she miscounted and wrote "11" to represent how many cubes were in her bag.

Bag F (note the towers the mathematician made prior to drawing)

Bag F 

The mathematician who received Mystery Bag F also attended to the color and quantity in her bag. Her bag was filled with linking cubes that were yellow, green, and red. She drew a pictorial representation and drew the two-dimensional face of a cube. She used different colors in a structured, or organized, arrangement. If you look towards the top of her sign, there is a key she drew noting that there were "14" to represent how many cubes were in her bag. 

There are a few cubes that she crossed out on her paper. She explained that when she was drawing, she got carried away and was not attending to the number in the tower. She double-checked her work and noticed the error. 

NOTE: This representation was interesting because it was the only one where the cubes are linked together to form a tower which matched how the mathematician organized her cubes to count the quantity. 

Bag B

Bag H

Both of the mathematicians who received Bag B and Bag H drew a more abstract pictorial representation, unlike the previous examples. Neither mathematician drew the unitary representation, or each object in the bag. They drew one representation of each color and wrote a number to represent the quantity. Each of them wrote the total quantity on their poster too. While their representation looked different, each of them attended to the color and quantity in their bag. 

Bag C

The mathematician who received Mystery Bag C also attended to the color and quantity in her bag. Her bag was filled with linking cubes that were blue, red, and white. She drew a pictorial representation and did not have a word for the objects in her bag. She could not explain what was in her bag nor how many was inside of it. I asked her to look at her sign to help her remember. She immediately responded, "14." 

It appeared by looking at her poster that she had 1 blue, 2 red, 3 blue, 4 red, and 5 white cubes, which would total 15 cubes. She also wrote a number expression "8 + 8." While there is no equal symbol, she wrote "16" next to the expression and then the number "14." Everything on her sign is "math" and does represent quantity and color but it is not an accurate representation. 

She used different colors in a structured or organized arrangement. If you look towards the top of her sign, there is a key she drew noting that there were "14" to represent how many cubes were in her bag. 

What did I notice about my class using this Mystery Bag activity? 

As you can see, there are varying levels of math thinking in this classroom, which is great! I am eager to build each mathematician's number sense but I need to know where to begin. This activity was a great way to pre-assess their number sense. 

So, let me give you the gist I got from these examples and several others I did not include here. Overall, I noted that: 

• Most mathematicians can count objects up to 20. 
• All mathematicians can attend to quantity using a unitary, or counting by ones approach. 
• They were paying attention to the different colors and used the colors, or smaller parts, to compose the total number. 
• Some mathematicians attended to quantity more accurately. 
• There were a couple of mathematicians who counted their quantity by twos. 
• When counting their quantity later as a class in the same way, many mathematicians dropped off after the strong 2, 4, 6, 8... thus, we will work on rote counting by twos.

This is definitely a number sense investigation that I will be using for years to come in my elementary math classroom and I might even replicate it mid-year to see how their math thinking and representing has changed over time.

Are you interested in using this fun and engaging Mystery Bag activity in your math classroom? Let me help! 

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I hope this post inspires you to ditch the thick white copy paper test and use this fun and engaging mystery bag activity to pre-assess number sense in your classroom. 

What other things do you about your mathematician's thinking at the beginning of the school year?

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Laura Williams

Have you noticed that learning teen numbers is difficult for students? There are good reasons teen numbers are so difficult! Teen numbers do not follow the typical number naming system in English. As a result, teen numbers have been dubbed "tricky teens" by teachers of yesteryear. Eleven, twelve, and thirteen are, by far, the most difficult teen numbers to master. Find out the reasons why teen numbers are tricky and read about how you can help your young mathematicians learn teen numbers with ease.

Tricky Teens are Hard for Kindergarten and First Grade Students

Here's just a few reasons why learning teen numbers in kindergarten and first grades is so challenging for young mathematicians.

1. Teen numbers are an anomaly. Their digits are not written in the order of other two-digit numbers.

The word structure does not correlate with the numerical parts. 

In contrast, in some East Asian languages, the word for 18, for example, translates into "ten eight," and 38 translates into "three ten, eight."  

 

In the English system, teen and two-digit numbers look like two single-digit numbers written beside each other; nothing shows the 10 value for the number on the left. Young mathematicians need verbal and visual supports for understanding these number words and written numbers.

 

2. Young mathematicians may have some difficulty with transitions, such as through the teen numbers and between decades.

Often times, young mathematicians say something like “twoteen” for “twelve” or “oneteen” for “eleven”. Such mistakes are attributable to the nature of the English teen-number words, which look, for example, like 10 and 1 or 10 and 2 but do not follow that pattern when spoken. 

Young mathematicians often have less difficulty with numbers beyond 20, but can still struggle through the transitions between decades. For instance, the transition between 19 and 20, 29 and 30, and so forth. 

3. The written position of the numerals are the reverse of the oral representation. 

The written position of the numerals and the oral representation of the teen numbers do not match, which causes quite the confusion for young mathematicians. 

For example, if asked to write 17, they might write the 7 first and then put the digit 1 to the left of the 7. They write the correct numerals, but they give evidence of having difficulty in matching the sound of the number with its appearance (the word “seventeen” begins with the word and sound of “seven”, so intuitively it might seem to them that the 7 should be written first). Some students will reverse digits. For example, when identifying two-digit numbers, they will write 37 as 73. 

4. The names of the teen numbers do not correspond with their values.

When young mathematicians hear thirteen, it does not elicit them to think "1 ten, 3 ones." The teen numbers represent a particular challenge for English language learners because the difference between thirteen and thirty is not easy to hear. 

One common misconception is that teen numbers relates more to place value. Learning the numbers 11 to 19 is more about composing and decomposing numbers. 

Young mathematicians need to learn that teen numbers are composed of one group of 10 and some more, or loose, ones. 

Here's three simple ways to help your mathematicians learn teen numbers:

1. Use mathematical language interchangeably. 

When working with teen and two-digit numbers, we say 13 as "thirteen" and as "1 ten, 3 ones" and say 38 as "thirty-eight" and as "3 tens, 8 ones." 

This is especially important for teen numbers as they are exceptions to the patterns for number words. These linked words are used interchangeably and help reinforce the composition of the numbers. 

2. Provide visuals of teen numbers in both written and numeral forms and give a visual cue.

Scaffold the lesson for young mathematicians by providing them with visuals of the teen numbers in both written form and the numeral form. 

Mathematicians also need practice hearing (stress the teen of the number by putting a finger near the mouth) and saying thirteen and fourteen so that they can hear the stress on the teen part of the number.

3. Use Hiding Zero cards. 

Our visual supports for these written numbers include cards that show the decade number, or 10, and cards that are half as wide that show the single digits 1 through 9. 

The single-digit cards fit on top of the 0 on the decade-number cards to enable children to build numbers in such a way that they can still see both parts of the number they are making by flipping up the single-digit card.

Are you looking for more support for your young mathematicians mastering teen numbers?

You might be interested in using these research-based teen number toolkit that contains 10 lesson ideas, activities, printables, and much more!

The Teen Number Toolkit contains lots of printables that facilitators can use during guided math, math intervention, or tutoring. The large cards can be used for whole group lessons too!

The research-based lesson ideas from the Teen Number Toolkit can be used for guided math, math intervention, or tutoring. The Hiding Zero cards are included that were featured in this post too! 

The printable pages from the Teen Number Toolkit can be used for independent practice, in math centers or math stations, or sent home as practice. 

This post on teen numbers focuses on following standards:

→ TEKS K.2B Read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures. 

→ TEKS 1.2B Use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones;

→ CCSS K.NBT.A.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a

drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed

of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

I hope this post inspires you to help your young mathematics learn teen numbers with ease!

What has helped your mathematicians learn teen numbers?

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Laura Williams

Texas symbols, Texas Independence Day, Texas Week, and Texas-themed picture books! Texas history is not second nature to me, since I moved to the Lone Star state from New Mexico. One thing I quickly learned is that Texas people are proud, y'all. I can't complain about that. We do live in a pretty amazing state! The second thing I learned is that Texans are called to celebrate our state during the week that March Second falls in. Why March Second ? It's Texas Independence Day! <waving the Texas flag> Grab your favorite Texas-themed picture book to celebrate Texas Week! 

Celebrate Texas Week in Style at Your Elementary School

Did you know that teachers and pupils in every school in Texas need to observe this week?!

Texas Civil Statues (1932) say: "The spirit of Texas Week is that every citizen of our great state to exalt and extol the highest and the best cultural and spiritual value of Texas throughout Texas Week."

One great way to celebrate Texas Week is to educate your students about our state!

Here are some ways to exalt and exolt Texas for its special week:

• Play the state anthem, "Texas, Our Texas"
• Explain the symbols that represent our state
• Make a list of ways we can show "friendship" our state's motto
• Read Texas-themed books

Here are some of the best Texas-themed picture books to exalt and extol our Lone Star State:

Scroll through this post and find a new title to add to your Texas-themed collection!

Armadillo Rodeo by Jan Brett

When Bo spots what he thinks is a "rip-roarin', rootin'-tootin', shiny red armadillo," he knows what he has to do. Follow that armadillo! 

Bo leaves his mother and three brothers behind and takes off for a two-stepping, bronco-bucking adventure. Jan Brett turns her considerable talents toward the Texas countryside in this amusing story of an armadillo on his own. See more here.

I Spy in the Texas Sky by Deborah K. Thomas

In this Texas twist on the popular child's game, I Spy, the narrator spies some of the state's most famous features, such as the bluebonnet, mockingbird, Mexican free-tailed bat, prickly pear cactus, and Lone Star. Once each item is identified, a brief informational page is provided. See more here.

The Legend of the Bluebonnet by Tomie dePaola

When a killing drought threatens the existence of the tribe, a courageous little Comanche girl sacrifices her most beloved possession--and the Great Spirit's answer results not only in much needed rain but a very special gift in return. 

This old Texas tale tells the legend of the bluebonnet. It is the perfect book if you want to honor Texas' history with Native American See more here.

Indelible Ann: The Larger-Life Story of Governor Ann Richards by Meghan P. Browne & Carlynn Whitt 

This book is a new addition to my Texas picture book section! Dorothy Ann Willis hailed from a small Texas town, but early on she found her voice and the guts to use it.

During her childhood, Ann discovered a spark and passion for civic duty. It led her all the way to Washington, DC, where she, along with other girls from around the country, learned about the business of politics. Fast forward to Ann taking on the political boys' club: she became county commissioner, then state treasurer, and finally governor of Texas. Learn about the stunning life of the legendary "big mouth, big hair" governor of Texas, a woman who was inspired by Eleanor Roosevelt, and in turn became an inspiration to countless others. Maybe even a student in your class will be inspired by this story! See more here.

A Picture Book of Davy Crockett by David A. Adler

Legends say Davy Crockett weighed two hundred pounds when he was born, and leapt right out of his cradle ready to fight. Though those stories are an exaggeration, Crockett's life was anything but boring.  

Farmer, soldier, sharp-shooter and politician, he was a well-known figure in the early 1800s—and even after his death, his reputation as an American folk hero grew and grew.  Adler retells the true story of David Crockett's life—from his birth in Tennessee to his death at the Alamo, separating fact from fiction. A timeline of important dates is included. See more here.

L is for Lone Star: A Texas Alphabet by Carol Crane

There are enough special people, wildlife, and natural wonders in the Lone Star State to fill several alphabet books, but this picture book has the finest to represent Texas. With poems to engage younger readers and text to give further details for older students, this book is a fantastic tool for sharing Texan pride with the ones you love. See more here.

Susanna of the Alamo: A True Story by John Jakes

“Remember the Alamo!” is one of the most familiar battle cries in American history, yet few know about the brave woman who inspired it. Susanna Dickinson’s story reveals the crucial role she played during that turbulent period in Texas-American history. 

This well-researched story, which we read as a family this past fall, inspired us to take a trip to the Alamo. Our young daughter's face lit up when she saw the statue of Susanna. Her role in Texas will forever be remembered through this text. See more here.

Ima & the Great Texas Ostrich Race by Margaret McManis

In 1892, ten-year-old Ima Hogg rides her pet ostrich in a race against her brothers who are on horseback on a Texas ranch. This fun picture book contains lots of facts about the real Ima, daughter of Texas Governor James Stephen Hogg.

While this might be a lesser known Texas-themed picture book, but I had the best time listening to McManis, when she came for an author's visit at a New Mexico elementary school. I remember sitting in the cafeteria, full of eager children, and thinking, "Wow! I have got to get to Texas!" McManis has the best Texas twang. We just don't have accents like that here in El Paso. See more here.

West Texas Chili Monster by Judy Cox 

Mama makes a huge pot of award-winning chili for the Texas Chili Cook-Off, but a lean, green, chili-swiggin' space alien smells the chili and heads straight for Texas, gulping down the entire entry. Read this picture book to find out what happens. See more here. 

Need some fun, standards-based Texas activities to celebrate Texas Week?

The most popular Texas-themed resource is the lapbook bundle featured on the left side of the photograph above. This bundle is loaded with an interactive lapbook, Texas symbols matching puzzles (center photograph), student printables, posters, and more!

Texas Symbols are fun to study to Texas Week! These engaging two-piece matching puzzles, featured in the center of the photograph above, will keep your sanity with simple cuts for preparation. These are available individually or in the bundle mentioned above.

Texas Emergent Readers featured on the right side of the photograph above. These unique emergent readers combine sight words and Texas history.

 

I hope this post inspires you to read a fun Texas-themed picture book during Texas Week!

What's your favorite Texas-themed picture book?

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Laura Williams

Valentine's Day is one of my favorite holidays to celebrate in the classroom. It is such a happy time to celebrate friendship. While I do enjoy celebrating holidays, there are a few things I do NOT like about celebrating the holidays: crafts are often messy, expensive, or too complicated. After my first couple of years of teaching, I hated celebrating the holidays. I bit off more than I could chew in the name of the celebration. I took a step back and decided to make things simple. I don't do glitter, paint, or more than six-step crafts! If the craft is simple and meaningful, I'm here for it. Here's a collection of my favorite crafts to use in my classroom that are SIMPLE! 

Top 3 Valentine's Day Crafts for the Classroom

Cupcakes, hearts, and love... oh my! There's so many fun, favorites in this post. Each of them is simple to create and contain several options for differentiation. 

1. Differentiated Math Cupcake Craftivity 

Your mathematicians will LOVE creating and designing these fun Valentine's Day math cupcakes!

Depending on your grade level, your mathematicians can use their scrumptious cupcake to show how they compose and decompose numbers, use addition or subtraction, or represent numbers using place value, including standard form, expanded form, and using base-ten blocks. Mathematicians can also draw pictorial models too!

There's so many ways to use this sweet cupcake for students to show their understanding of math concepts and more!

There are three suggested uses (see photograph below) for this project, but it is open-ended and can be differentiated to fit your math curricular or students' needs!

2. Love Writing Craftivity 

One thing I love about this writing craft is that it can be used for a variety of celebrations, including Valentine's Day, Mother's Day, Father's Day, or Grandparents' Day. 

It can be placed adoringly on a bulletin board to display standards-based writing activity which students will create comparisons for their love for someone special. This activity has lots of options for younger students and older students! It makes a unique gift for a someone special.

There's an English version OR a Spanish version too!

3. Valentine's Craftivity

This is by-far the most used craftivity out of the set. 

Create a Valentine's Day bulletin board and display this standards-based writing activity to display the top three things that your students love! This February bulletin board craft has options for younger students and older students!

One teacher just left some feedback that they are putting this together as a mobile and hanging them from the ceiling in the classroom. 

There is so many options with each of these fun crafts to celebrate friendship for Valentine's Day! 

I hope this post inspires you to simplify crafting for Valentine's Day!

Which craft is your favorite in this set?

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Laura Williams