students

5 Easy Ways to Build Student Engagement in Real Time

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We’ve all been there: walking into a classroom where a teacher is delivering a well-intentioned wonderfully planned direct-instruction lesson. But honestly, nobody wants to sit and listen to a teacher talk for 45 minutes straight.

Recently, I was able to visit, and guest teach, a classroom. The teacher had asked a common question: How do I incorporate more student talk and collaboration during a directed lesson, and stay on pace?

The lesson involved converting milliliters to liters. We started off the lesson with a quick video introduction supplied by the curriculum. Instead of letting it remain a passive video, we looked at how to transform direct instruction into an active, high-engagement experience using simple, fast-pasted micro-routines.

1. The Power of “Think, Pair, Share” (In Under 90 Seconds)

Student discourse and collaboration do not need to be long, drawn-out, 20-minutes projects. They can, and often should, happen in quick micro-bursts.

  • Independent Processing (Think in Your Head: Before opening the floor, pose a question and require a few quiet seconds. This processing window is non-negotiable. Whether you have multilingual learners or students with processing differences, giving them a moment to formulate an answer internally changes everything.
  • Micro-Partner Talk (Quick Pair Share): Students turn to their assigned partner for a fast, 10-20 second conversation. Because partnerships are pre-established, there is zero wasted transition time. This quick conversation allows students to practice their answer, and in some cases, have one ready to go in case they are picked to share.
  • Whole-Group Discourse (Multiple Perspectives): Bring the room back together and call on several students. Never accept just one answer; even if the first one is correct. Ask multiple students to share, sometimes they will have the same answers and other times they will not. If you hear two different answers, don’t give them the solution; turn it back to the class: “We have two different ideas/answers here. Let’s discuss which one makes sense and why.”

2. Low-Stakes “Wait and Return” for Hesitant Students

What happens when you call on a student and they freeze or don’t have an answer ready? Instead of rescuing them or moving on, use a wait and return strategy:

  • Tell the student you see them, let them know you will come back to them, and move to a few other students.
  • This gives the hesitant student a safe window to hear pees articulate their thinking. Even if the student ends up parroting a strategy or answer they just heard, they are still actively listening, processing the concept, and staying in the learning loop. This also sends a powerful, but silent, message that everyone is expected to participate and “I forgot,” doesn’t get you out of it.

3. Non-Verbal & Kinesthetic Checks (100% Participation in 5 Seconds)

If you rely solely on hand-raising, you are usually only assessing the 3-4 eager students in the class. To get an instant pulse on the entire room, build in simple physical signals:

  • Thumbs-to-Chest: Ask students to put a thumb against their chest (a private, low-stakes position) to show if they agree, disagree, need re-explaining, or have an understanding of the concept.
  • Fingers for Multiple Choice: Ask students their level of understanding with a 1, 2, or 3 (1 being little and 3 being complete). You can also ask student a question with three possible outcomes and have students hold up 1, 2, or 3 findgers on their chest on the count of three.

These quick kinesthetic movements force every single student to self-reflect and take a stand, giving you an immediate visual understanding of each student before moving to the next segment, problem, slide, etc.

4. Whiteboards as “Thinking Pads” Before Partner Talk

When students are asked to talk to a partner, they sometimes freeze because they don’t know where to start. Before opening up partner discourse, have students jot a quick diagram, record an answer, or sketch a visual model on an individual dry-erase board.

  • Having their thinking written down gives students an immediate anchor during partner talk.
  • Students can compare their processes side-by-side, spot differences in their work, and practice justifying their answers, aligning directly with Mathematical Practice 3 (Cconstruct Viable Arguments and Critique the Reasoning of Others).

5. Address Misconceptions in Real Time

When a shared misconception surfaces during partner talk or whiteboard check, address it right away. Because you took the time to engage all students throughout a lesson, you are more likely to catch the misconceptions early in order to address them immediately.

Pause the lesson, highlight the competing ideas as a whole class, and facilitate a quick 2-minute clarity check. By addressing gaps in the moment, you ensure every student moves forward on solid ground and understanding.

Keep It Fast, Keep It Frequent

Adding student engagement to a direct-instruction lesson doesn’t require throwing out your slides or abandoning your curriculum. By embedding 60-second processing pauses, whiteboard jots, and non-verbal signals, you transform passive listeners into active thinkers who are held accountable, and keep your lesson moving seamlessly.

What is your favorite low-prep way to get 100% student participation during a direct-instruction lesson? Share your go-to strategies in the comments below!

Offloading Cognitive Load in Division: The Power of the ‘Division Tool Box’

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Sometimes all it takes to transform a complex math standard is a fresh perspective and a small shift in approach.

Recently, I joined a 5th-grade class to model a strategy that lowers cognitive load during multi-digit division: pairing the partial quotient with a front-loaded division toolbox on a MathReps mat.

Multi-digit division can be taxing on working memory. Students must estimate, multiply, subtract, compare, and track place value all at once. By introducing a structured “Toolbox” before solving, we offload that mental friction so students can focus entirely on the division logic.

How the Division Toolbox Works

Before diving into the problem, for example, 8,275 ➗ 28, students fill out a pre-printed multiplication bank on the right side of their template:

  • Basic facts: 28 x 1, 2, 3, 4, 5
  • Tens place value: 28 x 10, 20, 30, 40, 50
  • Hundreds place values: 28 x 100, 200, 300, 400, 500
A math worksheet showing division and multiplication problems using the number 28, with calculations and steps outlined in green ink on an orange background.

Why Only Go Up to 5?

Capping the facts at 5 keeps setup quick and manageable while accomplishing several critical pedagogical goals:

  • Reinforces Place Value Patterns: students instantly see that once they know 28 x 2 = 56, then 28 x 20 = 560, and 28 x 200 = 5600 simply involves shifting the place values by factors of 10 (thus reviewing a previously learned standard).
  • Promotes Working Smarter: creating a bank of known facts up front eliminates mid-problem computational stalling.
  • Encourages Flexibility: teachers often worry that students will be limited if facts only go to 5. In practice, students quickly notice when they can combine partial quotients! For example, if a student needs 90 groups of 28, they will pull 50 (1400) and 40 (1120) from their bank, eventually combining them into 90m (2520) as their efficiency grows.

Step-by-Step: Solving 8,275 ➗ 28

With the Tool Box ready, solving becomes a low-stress series of subtractions:

  1. First Chunk: Looking at 8,275, students reference their Tool Box and select 28 x 200 = 5,600. They subtract 5,600 from 8,275, leaving 2,675.
  2. Second Chunk: From 2,675, they select 28 x 50 = 1,400. Subtracting 1,400 leaves 1,275.
  3. Third Chunk: From 1,275, they select 28 x 40 = 1,120. Subtracting 1,120 leaves 155.
  4. Final Chunk: From 155, they select 28 x 5 = 140. Subtracting 140 leaves a remainder of 15.
  5. Summing Partial Quotients: Adding 200 + 50 + 40 + 5 yields 295, with a remainder of 15 (295 (r) 15/28).

Right beside the partial quotient work, the large rectangle represents the dividend (8,275). This dual layout lets students view the same mathematical decomposition through two distinct visual lenses at once.

Setting Up Future Success

The teacher and students were receptive to the routine.

Using partial quotients in 5th grade doesn’t just make division accessible today; it builds the conceptual foundation students need for 6th grade, when they transition to standard vertical algorithms with deep place value understanding rather than blind step memorization.

Here’s the FREE template

How do you help your student manage cognitive load during multi-step math routines? Have you tried building a ‘Toolbox” first? Share your thoughts in the comments below.

A math worksheet featuring a division symbol at the top, followed by blank equations for multiplication by 1 to 5, 10 to 50, and 100 to 500, structured for student practice.

Strengthening Number Sense: The Power of Concrete Learning

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Building strong number sense in the primary grades is foundational to everything students encounter in their future mathematics journey. As instructional leaders and educators reflect on student data and classroom dynamics over time, it becomes clear how much our instructional tools and routines shape students’ deep understanding of numbers.

Looking back across our district’s journey, many of us have spent years navigating curriculum models that leaned heavily on structured, daily lesson pacing. Often, these programs moved quickly from introduction to procedural practice. While the intention was to maintain consistency across classrooms, an unintended gap formed: the crucial stage of concrete exploration was frequently bypassed.

The Value of the Concrete-Representational-Abstract (CRA) Sequence

Diagram illustrating the CRA (Concrete-Representational-Abstract) model, showing a triangular structure divided into three levels: Concrete with objects at the bottom, Representational with drawings in the middle, and Abstract with symbols at the top, labeled with '245' for the abstract level.

True conceptual understanding begins in the concrete stage, especially when students encounter a concept for the very first time. For instance, when third graders learn multiplication, physical manipulatives (or tactile tools like playdough) allows them to feel, arrange, and internalize the meaning of equal groups.

When a curriculum moves straight to representational pictures or abstract symbols, students miss the opportunity to ground abstract math in concrete reality. Over time, this gap shows up in upper-elementary classrooms as a lack of foundational number sense and automaticity with basic operations.

What Our Pilot Classrooms Are Teaching Us

As our district pilots two new math curricula this school year, the observations from our piloting teachers have been eye-opening and deeply validating, albeit troubling.

  1. The Power of Student Discourse: The new instructional models center heavily on student talk, exploring how students arrive at answers rather than just whether an answer is correct. Teachers are seeing firsthand how dialogue exposes gaps in basic skills while simultaneously giving students the language to rebuild those foundations.
  2. Identifying the Gaps Early:Piloting teachers have noted where students need targeted backfilling in basic addition, subtraction, multiplication, and division. Recognizing these missing pieces is the first step toward addressing them systematically.
  3. Re-Evaluating “Pacing and Fidelity”: The conversation around “curriculum fidelity” is evolving. I know we all cringe when someone says “fidelity to the curriculum”. Strict adherence to a textbook’s pacing can unintentionally prevent teachers from responding to what the students in front of them actually need. Meeting students where they are conceptually must always take precedence over covering the next page.

Looking Ahead with Optimism

It takes courage for a district and its educators to pause, reflect, and acknowledge when a long-standing tool is no longer serving its students.

While transitioning to a new adoption takes time, and many of our teachers are balancing current materials for one final year, the mindset shift is beginning. Teachers across our schools, whether currently piloting or not, recognize the need to strengthen core number sense and are taking proactive steps in their daily routines to support their learners.

Our goal isn’t to look back with regret, but to use these shared observations to inform a better path forward, one that honors concrete modeling, values student discourse, and empowers teachers to make the best instructional decisions for their students.

How is your district or school balancing curriculum requirements with hands-on conceptual learning? What strategies help you integrate concrete tools into daily instruction? Let’s keep the conversation going in the comments below!

Scaffolding MathReps

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Recently, I walked into a fifth-grade classroom during their morning math block and was immediately struck by the culture of learning in the room.

A yellow sheet with a table displaying numbers, including thousands, hundreds, tens, and ones places, with calculations showing various forms of the number 276,734.60.

The teacher was guiding her students through their daily MathRep, specifically a 5th-grade decimal and place value frame focusing on expanded form, word form, and powers of ten (276,723.46).

Because they were still in the early stages of introducing this particular MathRep, the teacher introduced a simple, high-leverage tool to scaffold the routine: a large, yellow place value chart that students could use alongside their work.

What made this visit so special wasn’t the tool itself, but how the students interacted with it

Student Agency in Action

The yellow chart provided a visual representation, helping students align digits across place values, from hundred thousands down to thousandths, especially when working through the “Multiply the number by 10, 100, 1000” section.

Here’s what stood out:

  • Self-Advocacy: Some students needed the scaffold, but many did not. The students who needed it felt completely comfortable recognizing their own learning needs, and grabbing the chart without any hesitation or stigma.
  • Fading Support Over Time: The teacher reported that as the week progressed, their processing speed increased, they completed their MathRep faster, and their overall conceptual understanding grew noticeably stronger.
  • Low-Threat Confidence Building: The scaffold served as a safety net, allowing students to engage with complex 5th-grade decimal standards with low anxiety and high success.

Friday Assessments and Strategic Record-Keeping

When Friday arrived, the teacher didn’t abruptly pull the rug out from under her learners. Students were still allowed to use the yellow place value scaffold during their weekly MathReps check-in. The teacher simply noted in her grade book which students utilized the support.

This approach honors where students are in their learning journey while providing the teacher with accurate, actionable data on who has reached independent mastery and who still benefits from visual anchors.

Embrace the Scaffolds

When implementing MathReps (or any daily math routine), it’s vital to remember that our students enter the room at different entry points. Scaffolds, whether they are place value charts, dry-erase overlays, or concrete manipulatives, aren’t crutches; they are bridges to independence.

By normalizing tools and letting students drive their own support, we help them build fluency, accuracy, and, most importantly, mathematical confidence.

How do you normalize scaffolds and tools during daily math routines in your classroom? Let me know in the comments below!

Why Does This School Year Feel Harder Than Ever? (And Why You’re Not Alone)

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We are only six weeks into the school year, but if you talk to teachers in the staff room, in the hallways, or during trainings, a single overwhelming theme emerges: everyone is stressed and exhausted.

It doesn’t feel like the typical “start-of-the-year chaos” that usually settles down by mid-September. Instead, it feels like we are walking on quicksand or trying to stand on a moving plate of jello. There doesn’t seem to be solid ground anywhere.

If you are feeling overwhelmed right now, I want to say this clearly right up front: you are not alone, and it is not just you.

It’s Not One Big Thing—It’s the Stacking of Everything

When teachers ask why this year feels so heavy, there’s no single villain or easy answer. It is the cumulative weight of dozens of competing priorities, mandates, and logistical hurdles all landing on a teacher’s shoulders at the exact same time:

  • Schedules in Constant Flux: Between push-in services, IEP pull-outs, assembly schedules, and weekly collaboration meetings, finding a solid, uninterrupted 45-minute block of core instruction feels almost impossible.
  • Shifting Pedagogical Focus: Teachers are navigating shifts toward Standards-Based Learning, working alongside external consultants, and adapting to new instructional coaching models, and in some cases, all while piloting new math curricula in real time.
  • Logistical Friction: Field trips stall because of transportation shortages or budget constraints. Meanwhile, state and local clearance inspections (Williams Act) require “uncluttered classrooms”—a near-impossible demand when new curriculum adoptions arrive with multiple bulky storage bins and materials that teachers are expected to house inside their own rooms due to a lack of storage.
  • Evolving Student Behavior: While the vast majority of our students are kind and wonderful, student behaviors feel visibly heightened compared to even a decade ago. A colleague who returned to the classroom after just a three-year hiatus noted a drastic shift in student dynamics and stamina.

To be clear: this is NOT a bash on my district or its leadership. These systemic pressures are happening in school districts across the country. It is simply the reality of modern education.

We are fortunate in our district to have strong community backing, supportive parents, and incredible students. But even in a great environment, the sheer volume of daily adjustments is taking a toll.

Finding the Bright Spots

I don’t have sage advice, a magic silver bullet, or a 5-step plan to fix the system. This work is hard, and some days it feels unsustainable. It’s important to acknowledge our reality.

But I do know that even in the middle of the quicksand, there are bright spots worth holding onto:

  • A campus hosted a beautiful cultural celebration day that highlighted our diverse community.
  • I watch teachers every single week who, despite the fatigue, are actively looking to improve their craft.
  • I see educators implementing routines like MathReps and EduProtocols, finding moments of genuine student success and engagement in the middle of a chaotic day.

I See You

If you are going home at the end of the day feeling drained, second-guessing yourself, or wondering why everything feels so much harder this fall, give yourself some grace.

You are juggling a mountain of expectations while building a safe, loving environment for your students every single morning. It has to get better, right? Until it does, know that I see you, your colleagues see you, understand what you’re going through, and are walking through it right alongside you.

How is the start of the year feeling in your school or district? What bright spots are keeping you grounded right now? Let’s support each other in the comments below.

The Lasting Impressions We Leave

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Living and working in the same community for decades (yikes! Has it really been decades?) is an interesting experience.

When you stay in one school district for as long as I have, “interesting” can quickly turn into “wild,” the good kind of wild. Over the years, I’ve taught hundreds of students. As time has marched on, I’ve started seeing second-generation learners, teaching the children of former students.

Now, in my role as an instructional coach, I get to experience one of the rare, incredible highlights of a long career: coaching/teaching alongside former students who are now district teachers themselves.

A Third-Grade Classroom Reunion

This year, I have the privilege of working with a team of teachers that included one of my former 5th graders.

Part of our lesson routine involved me reading a picture book aloud to her 3rd-grade class right after recess before launching into our lesson. When I walked into her room, she had three picture books laid out on the front board.

Normally, I let the students vote on which book they want to hear. As I scanned the options, my eyes immediately zeroed in on a Skippyjon Jones book; a hilarious, animated series I have loved reading to children for years.

I turned to the class and asked, “Which book should we read today?”

Before the kids could pick, my former student stepped in and said, “Actually, there is a specific book I would like you to read.”

She turned to her 3rd graders and explained that when she was a 5th grader in my class years ago, I used to read to them all the time, and one memory she has was listening to me read Skippyjon Jones. When she was pulling books for my visit, she specifically pulled that title so her students could experience it, too.

So, I dove right into full Skippyjon Jones character mode: silly voices, animated accents, and all. The students loved it, the teacher loved it, and I had an absolute blast.

“You’re My Favorite”

After the story, we transitioned into our scheduled Snorkl lesson. As I walked around the room supporting students with their tasks, I used one of my classic, go-to phrases:

“You’re my favorite.”

Anyone who knows me knows this phrase means both everything and nothing at the same time. I’ll say it to one student, then I’ll walk away, look at the very next student, and say, “You’re my favorite,” too. To me, it simply means: You tried hard, you’re on the right track, and I see you.

As I said it to a few 3rd graders, I heard a giggle from the back of the room. I looked over at my former student and asked, “Do you remember that?”

She smiled and said, “Yep. There are a lot of things I remember.”

Learning Has to Be Fun, Too

Standing in that classroom was a powerful reminder of how teaching works.

Sometimes we get so bogged down in standards, pacing guides, data trackers, and curriculum pilots that we forget a fundamental truth: the things we do and say leave a lasting impression long after the academic content fades.

Decades later, my former student didn’t recall a specific worksheet or a test score from 5th grade. She remembered the silly character voices. She remembered the goofy phrases. She remembered that learning in our classroom was joyful, safe, and fun.

As educators, everything we do leaves a mark. In the end, my hope for all our students is that alongside mastering academics, they carry fond memories of the silly stories, the animated read-alouds, and the playful moments that made them love coming to school.

Because at the end of the day, learning has to be fun, too.

Have you had the opportunity to work with a former student? What was it like?

What are some of the fun and lasting memories you make in your classroom?

Boost Math Discourse with Math Dash Chats

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Recently, I was chatting with a teacher who is new to her grade level this year. As we talked about successes and challenges, she expressed a strong desire to get her students talking more during math.

Her classroom isn’t part of our district’s current curriculum pilot program, which means she is still relying on our outdated curriculum. As I’ve mentioned in previous posts, our older curriculum lacks built-in opportunities for mathematical discourse.

That’s when I introduced her to Math Dash Chats.

Math Dash Chats are designed as a quick, 5-minute warm-up to get students talking at the very beginning of a math block. She was eager to try it, watched the quick Math Dash Chats video walkthrough, and tested it out with her class for a few days. Shortly after, I stepped into her classroom to model a quick demo lesson.

Inside the Classroom Demo: From “Notice” to High-Level Math

During the demo lesson, the class chose to ‘open (the door) the Graphing prompt for the day.

We started with a simple, low-stakes entry point: “What do you notice?”

That single question launched a rich, student-driven discussion:

  • Students began by identifying the structural elements: the title (Number of Books Read), the data being collected, and how it was displayed along the axes.
  • As student observations deepened, one student noticed that Tuesday had the highest bar.
  • That observation naturally opened the door for a deeper comparison prompt: “How many more books were read on Tuesday than on Monday?”

In less than five minutes, the conversation moved fluidly from basic visual observation to comparative analysis, all driven by the students, with me simply guiding the conversation to ensure key mathematical concepts were highlighted.

Why Math Dash Chats Work: Low Floor, High Ceiling

The philosophy behind Math Dash Chats is simple: continuous, low-stakes exposure to standards through student talk.

Because the prompts are open-ended, or lead to discover discussions, every student can access the conversation regardless of their current skill level:

  • Low Floor: Every student can share an initial observation during a “Notice & Wonder” prompts. Other prompts lead to reminders about things like conversions.
  • High Ceiling: The conversation can easily be pushed toward complex comparisons, justification (Convince Me That), or reasoning (Which One Doesn’t Belong).

By creating a safe, low-risk environment at the start of every math block, students build confidence using academic math language long before they encounter complex problem-solving later in the lesson.

Get Started in Your Classroom

Math Dash Chats are currently available for Grades 2 through 6, featuring 36 weeks of structured, ready-to-use slides per grade level. You can access and copy the entire collection for free in this Google Drive folder. (If you teach a different grade level and would like to see this series expanded, let me know!)

Have you tried Math Dash Chats with your students yet? What kinds of mathematical conversations are popping up in your classroom? Share your experiences in the comments below!

Math Curricula, Jelly Donuts, and the Search for What Our Students Deserve

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Eleven years ago, I wrote a blog post comparing math curricula to jelly doughnuts (go read it; it’s good and accurate).

At the time, it felt like every program hitting the market was either completely overstuffed with too much in the lessons to get through in a single block, or so loaded down with extra bells, whistles, and deep-fried decorations that the core mathematics got lost under all the glaze. Not to mention teachers having to sift through a plethora of books, online resources, and boxes of extra-help materials.

Looking back at that post today, I realized a hard truth: after evaluating those programs over a decade ago, our district didn’t adopt either. Instead, we relied on a supplementary program for over 11 years. The consequence? Years of students moving through our system with significant, systemic gaps in their mathematical understanding and skills.

This school year, however, brings fresh hope. We have officially kicked off a new math curriculum piloting process, and the landscape feels noticeably different.

Pilot #1: Innovamat (Building Thinking Classrooms & True Spiral Design)

We are currently piloting our first of two programs: Innovamat. Centered around Peter Liljedahl’s Building Thinking Classrooms framework, this program places rich student discourse and active problem-solving at the center of every lesson.

What excites me most about Innovamat is how pared-down and intentional it is, paired with its true spiral curriculum design. Rather than teaching concepts in isolated, multi-week blocks, Innovamat continuously revisits core mathematical ideas throughout the year, building upon itself. Curriculum creators seem to have finally realized how unwieldy and unrealistic past iterations were for everyday classroom execution. Innovamat certainly took note of others’ pitfalls.

Innovamat strips away the extra noise and focuses on the absolute essentials and deep understanding:

  • Manageable Lessons: The pacing is realistic, allowing teachers to complete an entire lesson within a standard math block.
  • Cohesive & Spiraled Structure: Concepts are continuously revisited in light, intentional touchpoints, preventing the “teach it once and forget it” phenomenon while keeping learning connected.
  • Focus on Discourse: Students are standing, talking, and working through math concepts together rather than passively sitting through lectures.

That isn’t to say it is without challenges. Because our students have spent years in a system that lacked deep, conceptual discourse, accessing some of the task-based material requires scaffolding and persistence. But because the core design is clean and intentionally spiraled, I am hopeful that our students will begin closing those foundational skill gaps quickly.

Pilot #2: Savvas enVision Math (Topical Architecture)

Later this fall, we will pivot to pilot our second curriculum option: Savvas enVision Math.

This second program also integrates elements of Building Thinking Classrooms and emphasizes student discourse, but it takes a more traditional, topical approach. Instruction is structured in distinct units focused on specific domains before moving to the next.

Savvas enVision also brings back a few more traditional support structures: multiple books to navigate, margin notes and guides for teachers, and built-in accessibility prompts designed to help teachers differentiate on the fly for all learners. There is more of the traditional teacher-led lesson design.

Comparing these two structural philosophies side-by-side will be an incredible learning experience for our district:

  1. Do our students benefit more from a true spiral design, like Innovamat, that offers continuous spaced practice, or from a topical approach, like enVision?
  2. Do we thrive with a streamlined, ultra-focused layout, or do we need the additional embedded teacher margin notes and resource options offered by a traditional publisher?

Hope on the Horizon

It is encouraging to see curriculum publishers finally listening to teachers and creating programs that prioritize student thinking over fluff.

While closing an 11-year gap in math understanding won’t happen overnight, placing student discourse, collaboration, and manageable lesson design at the center of instruction is the exact shift our students deserve. I look forward to sharing our findings as we move through both pilots this year!

Are you using either of these programs? What has your experience been?

5 High-Leverage Ways to Build Deep Place Value Understanding in Grades 2–6

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As elementary teachers begin the new school year, place value is almost always the starting line. It is the foundation of our Base-10 system, grounding everything from multi-digit addition and subtraction to decimals, multiplication, and scientific notation.

Unfortunately, place value can be reduced to a passive exercise in memorizing column labels: ones, tens, hundreds, thousands. But true place value understanding isn’t about naming columns; it’s about understanding the multiplicative relationships, flexibility, and magnitude of numbers. And this is where I geek out. I love this stuff!

So if you are looking to start your math block with deep conceptual understanding rather than rote procedure, here are 5 high-leverage ways to introduce and reinforce place value in your classroom this year.

1. Hook Students with a “Notice & Wonder” Prompt

Instead of lecturing on place value positions, start with a simple prompt that sparks curiosity and math discourse. Display a place value chart with a number like 2,488 written across it. Ask students: “What do you notice? What do you wonder?”

Guide the conversation to the two 8s. Ask students: “What is the difference between these two identical digits?”

This opens the door for students to discover the core rule of our Base-10 system themselves: where a digit sits determines its value. They quickly see that the 8 in the tens place (80) is 10 times greater than the 8 in the ones place (8). This sets a strong foundation for understanding the 10x and 1/10 relationships across grade levels.

2. Play Strategic Digit-Placement Games

Turn place value into an active strategy game! Give pairs of students a sheet with blank spaces representing a multi-digit number (e.g., four blank spaces for a 4-digit number: _ _ _ _).

Students take turns rolling a standard die (or a 0–9 digit spinner) and deciding where to place the rolled digit in their blank spaces. The goal? Create the largest possible number.

This simple game forces high-level strategic reasoning:

  • “I rolled a 5. Should I put it in the thousands place, or risk holding out for a 6?”
  • “If I put a 1 in the thousands place, my entire number loses its value.”

After playing, have students read their final numbers aloud to their partners and compare them using <, >, or = signs.

3. Connect Concrete Manipulatives Directly to Charts

Building numbers with base-10 blocks, place value disks, or interlocking cubes is essential, but the physical building alone isn’t enough. The magic happens when students connect the concrete blocks to the representational (pictorial) to the abstract chart.

Have students physically build a number using base-10 blocks inside or right above a place value mat. Then have students draw the blocks. This allows students to begin moving away from concrete representations toward the representational. Moving fluidly between concrete blocks, pictorial drawings, and abstract numbers ensures students understand the base-10 number system.

4. Interactive Notebook Anchors

Give students a permanent, easy-to-reference tool by incorporating half-page place value anchors into their interactive notebooks.

Combine a traditional place value chart with an open number line directly underneath it. When students write a number like 3,450, have them plot it on the open number line between 3,000 and 4,000. Seeing the number simultaneously on a chart and a number line builds a dual mental model, helping students understand both the structural breakdown of the digits and the relative magnitude of its position on the number line.

5. Integrate Daily Flexible Decomposing (Place Value MathReps)

Place value shouldn’t be taught for three weeks at the beginning of the year and then shelved. To build automaticity, embed flexible number sense into your daily warm-up routine using a MathRep. (There are lots to choose from. Be sure to check them out at MathReps.com)

Challenge students to decompose numbers in non-standard ways:

  • Standard Form: 1,200
  • Expanded Form: 1,000 + 200
  • Flexible Form: 12 hundreds or 120 tens

When students realize that numbers can be broken apart flexibly without losing their total value, mental math and complex multi-digit computation become infinitely easier.

Which Approach Will You Use First?

Building a deep understanding of our Base-10 system during the first weeks of school sets the tone for the entire math year. Whether through strategic games, rich discourse, or visual anchors, giving students multiple access points ensures no one gets left behind.

Which of these 5 strategies are you planning to try with your students this week, or when you return to school? Let me know in the comments below!