Paper folding provides elementary mathematicians with the opportunity to visualize fractional size, and once stacked, allows students to see equivalency as a way of naming the same size area using a different number of units. There are several ways to use paper folding to visualize concepts that lead to fractional understanding including: comparing halves and fourths, generating equivalent fractions, adding fractions with unlike denominators, and subtracting fractions with unlike denominators. Here are my favorite ways to use paper folding to teach fractions conceptually:

The Best Ways to Teach Fractions for Understanding Using Paper Folding

1. Comparing Halves and Fourths

This paper folding activity is best used with mathematicians in first or second grades OR mathematicians who are struggling in upper grades.

➡️ Focus: Halves and Fourths

1️⃣ Fold one rectangular paper (copy paper or colored cardstock) in half. Then, cut the paper in half along the folded line. 

2️⃣ Fold another rectangular paper in half and in half again. Then, cut the paper in fourths along the folded lines.

3️⃣ To support vocabulary development, write “one fourth of paper” on each of the four equal pieces of paper and “one half of paper” on each of the two equal pieces of paper. 

4️⃣ After preparing the halves and the fourths, have one mathematician hold one of the halves and another mathematician hold one of the fourths. 

5️⃣ Compare the pieces by holding them next to each other on on top of one another. 

6️⃣ Ask: Who has the larger number of pieces? Who piece is largest?

These can be posted in the room as a reference, helping mathematicians visualize the concept of halves and fourths as well as the relationship between the two fractional parts.

This fraction paper folding activity focuses on following standards:

→ TEKS- 1.6G Partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words.

→ TEKS- 1.6H Identify examples and non-examples of halves and fourths.

→ TEKS 2.3A Partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words.

2. Generating Equivalent Fractions with Paper Folding and Number Lines 

This paper folding activity is best used with mathematicians in third grade OR mathematicians who are struggling in upper grades.

➡️ Focus: 1/2, 2/4, 3/6, and 4/8

1️⃣ Take a paper strip. Hold it horizontally. Fold it vertically down the middle. 

Ask: How many equal parts are in the whole? Two. What fraction of the whole is one part? One half. 

2️⃣ Draw a line to show where the paper was folded and label each half 1/2, one out of 2 units.

3️⃣ Repeat procedure and fold paper strips to show thirds, fourths, and fifths. 

4️⃣ Draw a number line that is a little longer than the paper strip. Use your strip as a ruler to mark zero and 1 above the line, and 0/2 and 2/2 below the line.

5️⃣ Use the number line to generate equivalent fractions using the other paper strips. 

This fraction paper folding activity focuses on following standards:

→ TEKS 3.3F Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines.

→ TEKS 3.3G Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.

→ TEKS 4.3C Determine if two given fractions are equivalent using a variety of methods.

3. Adding Fractions with Unlike Denominators 

This paper folding activity is best used with mathematicians in fourth and fifth grad mathematicians OR mathematicians who are struggling in middle school.

We lose a lot of mathematicians when introducing addends with unlike denominators. 

➡️ Focus: 1/2 + 1/3

1️⃣ Ask: Can I add one-half plus one-third? 

2️⃣ Discuss with your partner.

3️⃣ Share out with the class. Sample answer: “I cannot add one-half plus one-third until the units are the same. We need to find like units.”

Continue below for the rest of this activity.

4️⃣ Make like units by folding paper as shown in the photograph above. 

This fraction paper folding activity focuses on following standards:

→ TEKS 4.3D Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <.

→ TEKS 4.3E Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.

→ TEKS 5.3H Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations.

4. Subtracting Fractions with Unlike Denominators 

This paper folding activity is best used with mathematicians in fourth and fifth grad mathematicians OR mathematicians who are struggling in middle school.

Just like adding fractions with unlike denominators is tricky for mathematicians, so is subtraction!

➡️ Focus: 1/2 - 1/3

1️⃣ Ask: Can I subtract one-third from one-half?

2️⃣ Discuss with your partner.

3️⃣ Share out with the class. Sample answer: “I cannot subtract until the units are the same. We need to find like units.”

4️⃣ Draw one fraction model and partition it into two equal units. Then, write one-half below one part and shade. (This makes it easier to see one-half after changing the units.

5️⃣ Draw a second fraction model and partition it into thirds with horizontal lines. Then, write one-third below one part and shade. 

6️⃣ Now make equivalent units. 

7️⃣ Ask: How many new units do we have? Six units.

8️⃣ Ask: One half is how many sixths? One-half is three-sixths. One-third is how many sixths? One-third is two-sixths.

9️⃣ Write the equation with the number missing. Cross out 2 of the 3 shaded sixths. 3/6 - 2/6 = 1/6.  So, one-half minus one-third is one-sixth!

This fraction paper folding activity focuses on following standards:

→ TEKS 4.3D Compare two fractions with different numerators and different denominators and represent the comparison using the symbols >, =, or <.

→ TEKS 4.3E Represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.

→ TEKS 5.3H Represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations.

I hope this post inspires you to use paper folding to teach fractions conceptually?

How will you use paper folding in your classroom?

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Laura Williams

Reading or writing numerals has nothing to do with number concepts. Helping young mathematicians read and write the 10 single-digit numerals is similar to teaching them to read and write letters of the alphabet. Young mathematicians may be able to read and write some numerals more easily than others. For example, the numerals 1, 3, 4, 5, and 7 are often mastered before 2, 6, 8, and 9. These challenges to numeral formation, also called numeral writing or number writing, doesn’t have to be repetitious practice; it can be engaging! Here's how:

8 WAYS TO PRACTICE NUMBER WRITING:

1. Trace over pages of numerals. 

You can use dotted lines or write in a highlighter and have young mathematicians trace on top. It is through this type of practice that they train their brain how to form the numerals.

You can adding a dot for the starting point to help mathematicians remember when to begin.

This mathematician is using Numeral Tracing and Writing Pages.

2. Make numerals from clay or dough. 

This is a fun and interactive way that young mathematicians can practice number formation. 

3. Write numerals in shaving cream.

On a hard, clean surface, spray and spread shaving cream. Young mathematicians will use their pointer finger to form the numerals as directed.

4. Write them on a dry-erase board or chalkboard. 

Young mathematicians can use large or personal sized board to practice writing numbers. One of my favorite tools to use during small group instruction is a personal sized magnetic drawing board. The mathematicians love using them and I love saving paper! 

PRO TIP: I used these fun mini magnetic drawing boards from a dollar store in my small group area. No erasers needed! 

5. Write numerals in a sand tray or salt tray. 

Use a small wooden or plastic tray and fill it with sand or iodized salt. Mathematicians can use their pointer finger to write their numbers in the sand or salt. 

PRO TIP: I like using the sandwich containers from a dollar store that have a lid. We can quickly snap the lid off during use and snap it back on when not in use. {If you're like me and want to avoid a mess, only use these under supervision! Don't say I didn't warn you.}

Display cards from Numeral Writing Toolkit.

6. Write numerals on top of a zippered bag full of colored hair gel. 

PRO TIP: Use darker colored hair gel, such as green, to create a contrast between the gel and the table surface.

If you look close enough, the mathematician wrote the numeral '4' in the hair gel. Placing a white paper behind the bag creates a contrast to reveal the numeral more easily.

7. Write numbers in the air using a straight arm and point with two fingers (pointer and middle fingers placed together). 

Yes, mathematicians need to use two fingers to point! They are exercising additional muscles when performing this action since this activates the brain more! "Two fingers and straight elbows!" I often exclaim when writing numerals or letters in the air.

8. Trace numerals on sandpaper or other textured material. 

Cut out rectangles of sandpaper or other textured materials to create a mat for mathematicians to trace or write numerals.

I used some leftover clear cabinet liner with deep grooves. I placed numeral cards underneath the textured material to emphasis the correct formation.

Tracing cards from Numeral Writing Toolkit

Writing Numbers is Fun!

There are several ways to practice numeral writing to lead to students' success. Incorporating a variety of activities helps engage all of the young mathematicians in your classroom. 

If you are looking for support in this important skill, you may be interested in my numeral toolkit. 

The numeral writing activities described in this blog post, focus on following standards:

→ TEKS- K.2B

→ The student applies mathematical process standards to understand how to

represent and compare whole numbers, the relative position and magnitude of whole numbers,

and relationships within the numeration system.

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

→ CCSS K.CC.A.3

→ K.CC.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).

I hope this post inspires you to practice numeral writing in a variety of ways.

How will you practice numeral writing in your classroom?

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Laura Williams

Discourse is the mathematical communication that occurs in a classroom. Utilizing discourse in the math classroom can be challenging. You may already be thinking: How can I get my students to explain their thinking? Effective discourse happens when students articulate their own ideas and seriously consider their peers’ mathematical perspectives as a way to construct mathematical understandings.

Encouraging students to construct their own mathematical understanding through discourse is an effective way to teach mathematics, especially since the role of the teacher has transformed from being a transmitter of knowledge to one who presents worthwhile and engaging mathematical tasks.

We can find ways to encourage eager mathematicians to share their ideas and to engage with others about their ideas by following three research-based recommendations:

1. Clarify mathematicians’ ideas in a variety of ways.
2. Emphasize reasoning.
3. Encourage mathematician-to-mathematician dialogue. 

The Best 3 Ways to Encourage Effective Discourse in Math

Think about all of the interactions among all the participants that occur throughout a math lesson--in the whole-class setting, in small groups, between pairs of children, and with the teacher. We will dive in deep today to learn the BEST three ways to encourage effective math discourse in your classroom.

Clarify mathematicians’ ideas in a variety of ways.

Clarification is important for English learners because it reinforces language and enhances comprehension. We often think of using this skill in reading, but it’s equally important in mathematics!

Here’s some practical ways to use clarification in the classroom: 

• Restate ideas as questions to verify what mathematicians did. This allow also them to confirm what you’ve heard or observed. 
• Apply precise language and make significant ideas more apparent.
• Look for opportunities to clarify questions to ensure that ALL students understand ideas and reasoning.
• Ask others to restate someone else’s ideas in their own words. This expresses ideas in a variety of ways and encourages listening to one another.
• Use teacher prompting. (See examples in the photo below.)

When we pay attention to mathematicians’ ideas, we send a message that their ideas are valued. This is the key to encouraging participation of individual mathematicians.

Emphasize reasoning.

Getting mathematicians to explain their reasoning is hard at first! Reasoning helps mathematicians understand their own thinking and the thinking of others. As they communicate about ideas, mathematicians will make connections between relational understanding and move towards mathematical proficiency.

Here’s some practical ways to use reasoning in the classroom: 

• Ask follow-up questions whether answers are correct or incorrect to place an emphasis on the reasoning process. This is to help mathematicians understand the others’ thinking.
• Follow-up on both correct and incorrect answers to reduce anxiety. We do not want students only having to explain wrong answers!
• Move mathematicians to more conceptually based explanations when able. 
• Ask mathematicians what they think of the idea proposed by another.
• Ask mathematicians if they see connections between two of their ideas OR an idea and a concept previously discussed.
• Use teacher prompting. (See examples in the photo below.)

Encourage mathematician-to-mathematician dialogue.

We wants eager mathematicians to think of themselves as capable of making sense of math. We do not want them to rely on teacher as the keeper of all knowledge. Encouraging student-to-student dialogue can help build this positive sense of self.

Here’s some practical ways to use student dialogue in the classroom:

• When mathematicians have different solutions, ask them to discuss one another’s solutions.
• Ask someone to rephrase another mathematician’s ideas or add something further to someone else’s ideas.
• Before a whole class discussion, have mathematicians practice their explanations with a peer. {This supports ALL mathematicians.}
• Use teacher prompting. (See examples in the photo below.)

Mathematicians are more likely to question one another’s ideas than the teacher’s ideas.

The value of student talk throughout a math lesson cannot be overemphasized. As mathematicians share their approaches, describe and evaluate tasks, and make conjectures, learning will occur in ways that are otherwise unlikely to take place.

Remember, whoever is talking is doing the learning. Will it be you or your mathematicians?

I hope you use the suggestions recommended in any of the three ways to encourage effective discourse in math.

How are you currently using discourse in your classroom? 

What recommendation would you like to add to your repertoire?

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Laura Williams

We want to motivate students, encourage active learning in the classroom while we develop critical-thinking, communication, and decision-making skills. Group work can be an effective method to do all of these things. When looking more specifically at the 21st Century Skills, (12 abilities that we want to instill in our students to prepare for careers in the Information Age) group work enables us to build critical thinking, creativity, collaboration, communication, flexibility, leadership, initiative, productivity, and social skills. Wow! Nine of the 12 21st Century Skills can be addressed by simply using group work in the classroom! What does productive group work look like in the classroom? What does productive group work sound like in the classroom? We will be diving into student group work! 

The Best Skills for Cooperative Learning Groups 

It is imperative that in the first weeks of school that you intentionally plan and spend time working on how to work well in groups with your students. We cannot assume that our students come into our classroom with the appropriate social skills needed for productive cooperative groups. 

You want your students to be able to:

✅ listen to each other

✅ respect each other

✅ build on each others’ ideas

Things you might see when students work well in groups:

🔎 leaning in and working in the middle of the table

🔎 sticking together

🔎 following team roles

Things you might hear when students work well in groups:

👂 equal air time

👂 silence when speaker is talking

👂 asking each other a lot of questions

Model and practice

When first starting out using groups, you must have students model the correct behaviors (listed above). Have students practice working in groups. When finished, have the classroom gathered together and label specific behaviors that were aligned to the classroom expectations. 

If you requested that all of the group members lean in, praise a group specifically for leaning in and working in the middle of the table. 

By specifically labeling the correct behaviors, you are reinforcing the specific expectations for productive group work.

How can you provide support with building on each others' ideas? 

• Begin to ask more open-ended questions that may have more than one solution.
• Give students question stems and encourage them to ask questions within their groups.
• Practice questioning between partners and groups.

Students love using these sentence stems in the classroom. 

Using Accountable Talk in the Math Classroom

Supporting language and vocabulary development is crucial in the math classroom. Educators need to explicitly teach and pay attention to the quality of talk in the classroom. English Language Learners will be supported, as well as ALL learners. This resource will help you keep mathematicians engaged in math conversations as they become proficient in "speaking math."

I hope this post inspires you to incorporate group work in your classroom. If you are interested in using my math sentence starters for questioning in group work, you can find them in my TpT shop!

What would you add to this list? What do you find the most difficult part to practice? 

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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?

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Laura Williams

One of my favorite things to do is walk into a bookstore. It doesn't matter if it is a big box bookstore or the Friends of the Library resell shop in town. I love books... especially children's picture books. Before I started teaching, I would buy any and all books. I have had to be more strategic as the years have passed and the space to shelve these books shrinks. My focus has been building a collection of diverse and rigorous books which I can use to teach mathematics. I buy math picture books now! I have four favorites that I use for teaching place value! I hope this list helps you as you grow your math picture book library!

The Best Picture Books for Place Value

Picture books provide an opportunity to open mathematical discussions with children. This list will help you find the best picture books to use with your classroom to facilitate their learning of place value. Each of these titles specifically teach mathematical concepts about place value and were written to inform the reader about them. This is not an exhaustive list of books that can be used to teach this skill, but a solid start of titles that I actually own and use!

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!

Count to a Million

Count to a Million

Popular children's author, Jerry Pallotta, hits it out of the ballpark again with this title, Count to a Million! If you can count to ten, you can count to one million! That's a pretty bold statement! Although some may have their doubts, readers will find themselves counting higher than they ever thought possible, inspiring even the most reluctant math student, as they build confidence and have fun.

Earth Day-Hooray!

Earth Day-Hooray!

I can't get enough of the MathStart books by Stuart J. Murphy! Earth Day–Hooray! is one of his most popular children’s books too!  Earth Day-Hooray! is a story about Ryan, Luke, and Carly.  These friends need to collect and recycle 5,000 cans if they want to make enough money to plant flowers in the park.  This story is a two-for-one lesson about recycling and the math skill of place value.  Your students will be counting by groups of hundreds, tens, and ones as you read this title to them!

How Much is a Million?

How Much is a Million?

How Much is a Million? by David M. Schwartz is a great story about large numbers.  Ever wonder just what a million of something actually means? How about a billion? Or a trillion? Marvelosissimo, the mathematical magician, can teach you! Say that two times fast! How Much is a Million? breaks down complex numbers down to size in a fun and humorous way that helps children conceptualize a difficult mathematical concept.

Math Fables: Lessons That Count

Math Fables:  Lessons That Count

Math Fables: Lessons That Count by Greg Tang is an amazing resource for teaching children their math skills, in particular place value!  Through these “fables” about concepts that are relevant to the very youngest math learners, including sharing, teamwork, etc., Tang encourages children to see the basics of addition and subtraction in entirely new ways. Fresh, fun, and most of all, inspiring, this title is perfect for launching young readers on the road to math success!

Click Here to Join!

Don't Judge a Book by Its Cover!

Other Place Value Titles on my Personal Wish List

Place Value by David A. Adler (Popular Author)- This is a newly released book!

You had better not monkey around when it comes to place value. The monkeys in this book can tell you why! As they bake the biggest banana cupcake ever, they need to get the amounts in the recipe correct. There’s a big difference between 216 eggs and 621 eggs. Place value is the key to keeping the numbers straight. Using humorous art, easy-to-follow charts and clear explanations, this book presents the basic facts about place value while inserting some amusing monkey business.

Sir Cumference and All the King's Tens: A Math Adventure by Cindy Neuschwander  

Join Sir Cumference and the gang for more wordplay, puns, and problem solving in the clever math adventure about place-value and counting by tens. Sir Cumference and Lady Di planned a surprise birthday party for King Arthur, but they didn’t expect so many guests to show up. How many lunches will they need? And with more guests arriving by the minute, what about dinner? Sir Cumference and Lady Di count guests by tens, hundreds, and even thousands to help young readers learn place-value. Fans will love this new installment of the Sir Cumference series that makes math fun and accessible for all.

A Million Dots by Andrew Clements

It's a long way to 

a million, right?

Of course it is.

But do you really know 

what a million looks like? 

If you'd like to see -- actually see, right now, with your own eyes -- what a million looks like, just open this book. 

Be prepared to learn some interesting things along the way. Like how many shoe boxes it would take to make a stack to Mount Everest. And be prepared to do some number wondering of your own. But, most of all, be prepared to be amazed. Because a million is a LOT of dots.

I hope this post inspires you to use picture books as you teach place value.

What are some of the math picture books you use in your classroom?

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Laura Williams