Math

Empower 4th Graders with Decimal Mastery

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Why This MathRep Matters

For 4th-grade educators who are guided by the CCSS.Math.Content.4.NF.C.6 and CCSS.Math.Content.4.NF.C.7 standards (part of the Number & Operations—Fractions domain), this MathRep is a game-changer.

  • CCSS.Math.Content.4.NF.C.6
    • Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
  • CCSS.Math.Content.4.NF.C.7
    • Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Why Teachers Love It

  • Low floor, high ceiling: Students can start with simple conversions and move toward rich reasoning and comparisons.
  • Multiple entry points: Some may begin with fraction-to-decimal conversion, while others may focus on comparing decimals; yet, both pathways are supported.
  • Discussion built in: The MathRep encourages students to explain their thinking (“I know 0.59 is less than 0.6 because …”), which deepens understanding. Using this MathRep in Snorkl can further support student reasoning.
  • Standards-aligned and ready to use: Especially helpful when you need a targeted resource for 4.NF.C.6 and 4.NF.C.7.

Ready to Get Started

Download or open the accompanying MathRep (see video) and begin your lessons with this ready-to-go template. Embed the video in your class expectation or homework link to give students a chance to revisit the concept later. Doing it on paper? Why not print out a blank template and a completed template on the back and insert it into a plastic sleeve? Students then have a reference if they get stuck.

Visit MathReps.com for free templates and more resources.

Final Takeaway

This MathRep is a powerful, standards-aligned tool for supporting 4th-graders in mastering decimal notation and comparison. By anchoring learning in discussions, visual models, and student reasoning, it simplifies complex content into manageable and engaging experiences. Add this to your toolkit and watch your students build confidence with decimals.

Let me know how it goes in your classroom – I’d love to hear your success stories and any tweaks you make!

Customize Your MathReps in Snorkl Easily

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This past summer, I’ve been sharing insights about the MathReps collection available in Snorkl. In my recent post, New MathReps Available in Snorkl Library, I provided a quick guide on how to easily navigate the platform to discover your favorite MathReps. Don’t miss the latest video that demonstrates how to seamlessly add these resources to your library and customize them to suit your specific needs.

Math Dash Chats: Boost Classroom Discourse

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Earlier this year, a simple idea sparked a solution to a common challenge in many classrooms: how to review math concepts and encourage student conversation when time is short. This led to the creation of Math Dash Chats.

Our district, like many others, was grappling with a noticeable gap in our curriculum—a lack of dedicated time for math discourse. We know that talking about math helps students solidify their understanding, but with so many standards to cover, where do you fit it in? I created Math Dash Chats for 3rd Grade, as an instructional coach who works closely with 3rd-grade teams, it felt like the perfect place to start. Since then, I’ve created sets for grades 2-6 and am excited to expand to grades 7 and 8 soon.

So, what exactly are Math Dash Chats, and how can they help your students? I’m so glad you asked!

What are Math Dash Chats?

Math Dash Chats are 36 prepared slides for your grade level (currently grades 2-6). The activity is designed to be a quick, five-minute daily review that gets students talking.

The slides are divided into six sections, five of which are based on Common Core domains like Geometry and Measurement, and the sixth is a directions section. Problems are hidden behind colorful “doors” [01:05], which you can view beforehand. Then, simply drag the questions over for a fun and engaging reveal.

How Do They Work?

The idea is simple: choose one “door” a day to discuss for about five minutes. This brief, focused discussion ensures a consistent review without taking up valuable class time. The topics covered are not just standard procedures; they encourage students to explore reasoning, number sense, and even domains like geometry or measurement that are often rushed through or left for the end of the year.

The video provides an example from the “Convince me that” category, where students are asked to prove that “4 tens is the same as 3 tens and 10 ones” [01:53]. This type of question promotes collaboration, and you might find that students want to use personal whiteboards or manipulatives to work through some of the problems together.

The Result

The response from teachers has been overwhelmingly positive. They love the ease of a no-prep, ready-to-go resource that gets students talking about math. Who doesn’t love a well-thought-out, free resource that is proven to work?

If you’re looking for a quick, impactful way to review math concepts and get your students engaged in meaningful math conversations, Math Dash Chats are for you!

Math Dash Chats Folder: Please make a copy of the desired slide deck for yourself by selecting ‘file’ > ‘make a copy’. If you receive a message that says ‘Access Denied’, it may be an issue with your district account. I’ve encountered this recently. If this happens, I suggest trying your personal account and sharing it with your district account. If that doesn’t work, contact me and we can try a few other options.

Let’s Talk Math

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My current position, Tech TOSA/Instructional Coach, affords me the opportunity to go into teachers’ classrooms and share the amazing things that are happening. So here I am sharing what this talented first-grade teacher in my district is doing.

Earlier in the week, I was in my Tech TOSA role. I went into this first-grade classroom to teach a lesson on coding using Beebots. I’m sure you’ve figured out this is not what I’m here to discuss. When I walked in, I noticed this chart on her board. What struck me about it was its simplicity. As you can see, it has some basic concepts and images to accompany it. What also drew my attention was the title: Let’s Talk Math. This implies that Math is something that should be discussed. It’s not something we do in isolation or keep to ourselves. While I did not have time to discuss with the teacher what she does with this chart, I know her well enough to say that she references it consistently.

I think it’s worth noticing that this is not flashy, cutesy, or Pinteresty in any way. Too often, we teachers ‘do too much,’ as the kids would say. That isn’t to say that those who make their room match or aesthetically pleasing “do too much.” It’s just to say that if you’re not that kind of teacher—like me—that’s okay. Having something as simple as a chart on your whiteboard works just as well. The important thing here is accessibilty – both in terms of understanding and placement – is most important. If it’s in a place where students can’t see it, like being too high up, or teachers don’t reference it, it’s no good to anyone.

What is my point in all of this? I wanted to celebrate the awesomeness of what this teacher is doing and highlight its simplicity. What are some simple ways you keep your students engaged while encouraging discussions?

NOTE: You may have noticed that I use hyphens in my writing. This has been a thing for me for many years: you can find them in previous posts dating back to pre-AI. I also know that AI uses them often, and it is one of the tell-tale signs that something has been written with AI. I felt the need to point out that while I use them, they are not a result of AI, just of my own knowledge of how to use them.

Effective Place Value Techniques for Teaching Addition

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Are you looking for a way to help students truly see what’s happening when they add multi-digit numbers? One powerful approach uses place value-based strategies that build from representational thinking toward more efficient, abstract methods.

Start with Expanded Form

In the first part of the video, I model a place value strategy using expanded form. Students break apart each number into hundreds, tens, and ones, add those values separately, and then combine their sums.

This representational method supports flexible thinking and strengthens their understanding of how numbers work. It also lays a strong foundation for future strategies that depend on place value fluency.

Scaffold Toward the Algorithm

Next, I introduce a slightly more advanced approach that continues to use the Hundreds Chart as a scaffold. This visual support helps students begin to internalize regrouping and transitions them toward the traditional addition algorithm, a 4th-grade standard.

This shift is intentional. By gradually moving from expanded form to a structure that supports the algorithm, students develop a deeper understanding of why the algorithm works—not just how to use it.

Support with Consistent Structure

The real power of MathReps lies in their consistency. Each template reinforces key math skills in a familiar format, allowing students to focus on developing strategies and precision rather than navigating new instructions each time.

Whether students are practicing during warm-ups, small groups, or independent work, MathReps create a rhythm of reflection and growth with immediate feedback.

Grab the Free Templates

The MathReps template shown in the video is available for free at MathReps.com. And if you’re looking for a reusable option, check out the dry-erase Wipebook versions—perfect for centers, partner work, or teacher modeling.

One Rep at a Time

With MathReps, you’re not just assigning practice—you’re building confidence, one rep at a time.

Why Manipulatives Matter Beyond Early Grades

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In the early grades, it’s not uncommon to see math manipulatives used daily in the classroom. Teachers pull out connecting cubes, counters, base ten blocks, and more—tools that help students build a concrete understanding of math concepts. Whether they’re exploring different ways to make 10 or practicing addition, these hands-on tools support their thinking in meaningful ways.

This follows the CRA model—Concrete, Representational, Abstract. We start with the concrete, like manipulatives. Once students have a solid grasp of the concept, we move into the representational, such as drawings or visual models. Finally, we introduce the abstract, using numbers and symbols alone. For example:

  • Concrete: Use connecting cubes to model 5 + 3
  • Representational: Draw 5 circles and 3 more
  • Abstract: Solve 5 + 3 = 8

But here’s what I’ve been thinking about lately: why do we often abandon manipulatives once students move into the upper grades?

Sure, by fourth or fifth grade, many students no longer need cubes for basic addition and subtraction. At that point, they’ve likely mastered those foundational skills and can work abstractly. But what about when we introduce new, more complex concepts—like volume in upper elementary or integers in middle school?

Volume is a great example. It’s a tough concept to grasp without something physical to hold or build. Yet so often, we hand students a formula and expect them to just “get it.” What if we instead gave them time to build with cubes, experiment, and see what volume means before jumping into the numbers?

The same goes for concepts like negative numbers. A number line or clothesline math activity can help students visualize and understand the relationships between positive and negative values. Why skip that step?

All this has me wondering: Is it a time issue? A training issue? Have we simply forgotten how powerful manipulatives can be for older students, too?

I’d love to hear your thoughts.
Do you use manipulatives in your classroom? What grade do you teach? What concepts do you use them for?

Let’s keep the conversation going—and keep math meaningful at every grade level.

Experiencing MathReps Success at Cipriani Elementary

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A few weeks ago, I had the absolute pleasure of visiting Cipriani Elementary School in Belmont, California, and let me tell you—it was a fantastic day that filled my heart.

Throughout the day, I was met with warm smiles, welcoming teachers, and the most amazing group of students. I had the opportunity to visit several classrooms ranging from TK through fifth grade, and in each room, I was able to demonstrate MathReps and watch in amazement as students flourished in their math knowledge.

What stood out most to me during these classroom visits was the level of engagement and understanding the students displayed. They were respectful, kind, curious, and so eager to learn. It’s one thing to talk about the power of MathReps—but it’s another thing entirely to see it in action in so many classes.

The Cipriani staff was incredible. Not only were they open and receptive, but they also shared their own tips and tricks for how they modify and adapt MathReps to meet the needs of their students. I was genuinely inspired by the way they’ve made the framework their own. I came to share—but I left having learned so much from them too. That kind of collaborative energy is what makes this work so meaningful.

One of my favorite moments from the day happened in a third-grade classroom. As I was working with the students, one of them looked up at me, wheels turning in their head, and said, “Wait… your name is on the bottom of our MathReps!” The class instantly lit up with excitement. Then they asked, “Did you also make Math Dash Chats?” When I said yes, the energy doubled. That little moment of connection—of realizing that the person who created something they use every day was standing right there with them—was truly special. It reminded me that kids are paying attention, even when we don’t think they are.

Later that afternoon, I led a Math 360 professional development session with the entire staff. Thanks to our friends at Wipebook, we had large Wipebook flip charts to work with, and it made the experience even more interactive and fun. The discussions were rich and reflective, and once again, the Cipriani teachers brought their full selves to the table—asking great questions, sharing insights, and showing a genuine passion for improving math instruction.

Overall, it was such a rewarding, joy-filled day. I left Cipriani Elementary feeling deeply grateful—and even more motivated to continue visiting classrooms across the country to share the love, importance, and power of MathReps.

I am thankful to everyone at Cipriani Elementary for making me feel so welcome.

Spice Up Your Math Lessons with the Nacho Problem EduProtocol!

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Allow me to introduce you to an engaging and effective way to get your students thinking critically about math: Nacho Problem! If you’re looking for a structured-yet-flexible approach to problem-solving that promotes discussion, reasoning, and collaboration, then this EduProtocol is exactly what you need.

What is Nacho Problem?

Nacho Problem is a structured math discussion protocol that helps students develop their problem-solving and reasoning skills in a low-floor, high-ceiling way. Instead of just solving problems in isolation, students work through an incorrectly solved problem that leads to, explaining their thinking, and building deeper conceptual understanding.

It’s not just any problem—it’s “Nacho” Problem because it encourages students to engage with math differently!

How It Works

Nacho Problem follows a consistent routine that makes math discussions more meaningful and accessible for all learners. Here’s a breakdown of the process:

Launch the Problem:

  • Choose a problem that has been solved incorrectly. It can be a common misconception or a key concept.
  • Present the problem to the class and encourage students to think critically.

Think & Solve:

  • Students work independently or in pairs to solve the problem using their own methods.
  • They show their thinking through models, equations, or number lines.

Share & Compare:

  • Students explain how they solved it and compare their work with others.
  • Emphasize multiple strategies—there’s more than one way to solve a problem!

Debrief & Reflect:

  • Discuss which strategies were efficient, clear, or creative.
  • Make connections between representations and reinforce math vocabulary.

Why Use Nacho Problem?

🔹 Builds Math Confidence – Encourages all students to participate in math discussions.
🔹 Focuses Thinking – Students can critically analyze problems, looking for errors and correcting them.
🔹 Reinforces Multiple Strategies – Helps students see different ways to approach a problem.
🔹 Encourages Math Talk – Improves reasoning, justification, and communication skills.
🔹 Works with Any Grade Level – Can be adapted for K-12 by adjusting the complexity of the problem.

Hear About It In Under 2 Minutes

I recently created a video tutorial to show exactly how Nacho Problem works. Check it out here:

Try It in Your Classroom!

Want to give Nacho Problem a try? Here’s what you can do next:

Choose a problem that fits your students’ current math skills.
Use a template to help students structure their thinking.
Encourage collaboration by having students discuss and compare strategies.

You can find free templates and more math strategies at eduprotocolsplus.com and MathReps.com!

Final Thoughts

Nacho Problem is a fun, engaging, and powerful way to deepen students’ understanding of math. By making math conversations routine and structured, you’ll see more confidence, curiosity, and engagement in your classroom.

Understanding Subtraction with Pictorial and Expanded Models

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Why Use Multiple Models?

By using a pictorial model alongside expanded notation, students get a visual and numeric understanding of subtraction. This helps them move beyond memorized procedures to truly grasp why and how regrouping works.

Let’s break it down step by step!

Step 1: Set Up the Problem

We’re working with 736 – 274.

  • 736 is represented using pictorial models in a place value chart:
    • 7 hundreds
    • 3 tens
    • 6 ones
  • Below, we note in the corner of each place value column what we’re subtracting: 200 + 70 + 4 = 274

Step 2: Subtract Using the Pictorial Model

Subtract the Ones (6 – 4):

  • Cross off 4 ones (I like to use x to represent 1s).
  • That leaves 2 ones.

Regroup the Tens (30 – 70):

  • Uh-oh! We don’t have enough tens to subtract 70.
  • So, we regroup 100 into 10 tens (since 100 = 10 tens).
  • Now, we have 13 tens total (13 tens = 130)
  • We subtract 70 (or 7 tens) from 13 tens, leaving 6 tens (or 60).

Subtract the Hundreds (700 – 200):

  • After regrouping, we have 600 left in the hundreds place.
  • Subtracting 200 leaves us with 400.

Final Answer: 462

Step 3: Solve Using Base 10 Expanded Notation

Now, let’s represent the numbers in expanded form:

  • 736 → 700 + 30 + 6
  • 274 → 200 + 70 + 4

Subtracting step-by-step:

  • 6 – 4 = 2
  • 30 – 70 (not possible, so we regroup from the hundreds)
    • Moving 100 over to the 10s place, making it 130 – 70 = 60
  • 600 – 200 = 400

Final Answer: 462

The Power of Dual Modeling

Using both pictorial and expanded form models side by side helps students see:
✏️ Why we “regroup” in subtraction
✏️ How place value plays a role in regrouping
✏️ That both methods lead to the same solution, reinforcing accuracy

When students see and practice both models together, they build deeper number sense and mathematical confidence!

Try This in Your Classroom!

You can grab a free MathReps template at MathReps.com and start using this strategy with your students today!

💡 Bonus Resource: Wipebook offers workbooks with four MathReps for second grade, providing structured practice all year long. Check them out!

Watch the Full Tutorial Video

Effective MathReps for Addition with Regrouping

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Today, we’re diving into second-grade math with a MathRep that focuses on addition with regrouping.

In our previous posts, we explored using MathReps for addition and subtraction without regrouping. Now, we’re taking it a step further and tackling regrouping, helping students make the jump from pictorial models to expanded notation and the base 10 system.

So, buckle in—let’s get started!

Step-by-Step Guide: Regrouping with MathReps

Set Up the Numbers

For this example, we’re adding 682 + 234, and we’ll use a pictorial model to visually represent the numbers before transitioning into the expanded form.

Solve Using a Pictorial Model

1️⃣ Start with the Ones Place:

  • 2 + 4 = 6
  • No regrouping needed here, so we write 6 in the ones place.

2️⃣ Move to the Tens Place:

  • We add 8 tens + 3 tens = 11 tens, which equals 110.
  • Since 10 tens = 100, we regroup by circling ten tens and moving them into the hundreds place.
  • This leaves 1 ten (10) in the tens place.

3️⃣ Move to the Hundreds Place:

  • We now have 6 hundreds + 2 hundreds + 1 regrouped hundred = 9 hundreds.

Bringing it all together:
916

Transition to the Base 10 Model (Expanded Notation)

Now, let’s break it down using expanded form:

  • 682 → 600 + 80 + 2
  • 234 → 200 + 30 + 4

Adding the place values:

  • Ones: 2 + 4 = 6
  • Tens: 80 + 30 = 110 → Regroup into 100 + 10
  • Hundreds: 600 + 200 + 100 = 900

Total: 916

Alternative Thinking: Flexible Number Sense

Instead of regrouping immediately, students can leave the tens as 110 and think of the sum as:

800 + 110 + 6 = 916

This approach challenges students to see numbers flexibly before applying the standard algorithm, deepening their conceptual understanding.

Why This Works

MathReps provide a structured, visual approach that helps students bridge the gap between pictorial models and formal mathematical notation. By working through regrouping in different ways, students develop number flexibility and problem-solving confidence.

Get Your Free MathReps!

Want to try this in your classroom? Download your free MathRep template at MathReps.com and explore even more math resources.

💡 Bonus Resource: Check out Wipebook for workbooks featuring MathReps—each workbook includes four MathReps to last the entire year!

Watch the Tutorial Video