Just Say the Word! (Part 1)

Professional Learning, Teaching and Learning

Creating School-Wide Agreements for Common Math Vocabulary

I recently witnessed a captivating first-grade lesson. As students interacted in small groups, using various visuals and models to capture their ideas of two-digit addition, the teacher moved around the room, asking them to justify their chosen visuals, to represent the visuals with numbers, and to explain the connections between the two. Both the engagement and rigor exceeded typical expectations for first-graders.

And then it happened…the teacher brought the students back together to share their discoveries. In the midst of their eloquent descriptions and uncharacteristically sophisticated explanations, the teacher asked, “Can anyone tell us how they used the flip-flop facts as part of the process?”

Flip-flop facts? Did I hear that correctly? Did she really use “flip-flop facts” in place of “commutative property?”

We’ve all done it – we’ve lost the battle for precision by using descriptive words in place of the proper language of mathematics. We think we are being helpful. However, we are ultimately doing damage in the long run. If our young children can say “tyrannosaurus rex” and compare him to “triceratops” with great precision, why shouldn’t they be expected to use frequently-encountered academic vocabulary at all grades?

Well-Intended Mistakes: Using Imprecise Language May Lead to Misconceptions

Here are a few more examples of teacher-prompted imprecision I’ve recently witnessed:

  • Using the word “point” rather than “and” when reading a number with a decimal point
  • Using “reducing” rather than “simplifying” for equivalent fractions
  • Using “plugging in” rather than “substituting” when evaluating expressions or equations
  • Using “equals” to describe the action of finding an answer rather than as a statement of equality
  • Using “borrowing” and “carrying” rather than “grouping” and “ungrouping” for all four operations
  • Using “moving the decimal” to describe unit conversion – it’s not the decimal point that moves but, rather, the digits that move to the left or right
  • Using the word “decimal” to refer to “decimal point”
  • Using “top and bottom number” to describe “numerator and denominator” (a fraction is one number – one value, not two)
  • Using “keep-flip-change” to describe a rule for dividing fractions rather than actually developing the concept
  • Using “rounding” as a synonym for “estimating” – rounding is but one strategy for finding an estimate

School-Wide Agreements: Establishing a Common Vocabulary Across Your Campus

Well-meaning teachers across the country tend to use descriptive language in place of mathematical precision. Don’t get me wrong – using descriptions when developing the vocabulary is a great strategy. However, we must also ensure that our students internalize and use the correct terminology with increasing frequency.

One way to ensure that teachers and students alike move toward a common mathematical language is to establish school-wide agreements around vocabulary usage. One way to achieve this is to follow these steps:

  • Create grade-level lists: Using your standards or board-adopted curriculum, list the mathematical vocabulary for each grade level.
  • Select words/concepts used across grade levels: Next, look for math language that appears across grade levels and select specific words that tend to be replaced with more common vernacular, such as the terms listed above. Select between 10 and 20 words to begin with.
  • Discuss within grade levels: Ask each grade level to map out words and phrases they tend to use in place of the actual terminology. Discuss how this language might create misconceptions or misuses over time.
  • Discuss across grade levels: Share out the mapped vocabulary across grade levels and discuss why some of the non-precise terminology may become problematic later on. This may be achieved in a school-wide meeting or through a shared bulletin board where comments may be left.
  • Create an agreed-upon list of terms and definitions…and check in with one another! Once a list of agreed-upon math terms is created, post it where everyone can see it, and revisit it on occasion to ensure everyone continues to adhere to it.

Vocabulary Development in the Classroom

Tune in next week to learn classroom strategies for introducing and reinforcing school-wide agreed-upon math vocabulary. You won’t want to miss it!

For now, please join the conversation. Share your stories about math vocabulary uses and misuses in the comments section below. What have you noticed in the classroom, either from the teacher or the student perspective? How might we do better by our students? We look forward to hearing from you!

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

One more thing: Check out Peggy’s journal entry comparing  KP Ten-Frame Tiles with Base Ten Blocks. This week, she addresses the grouping nature of KP Ten-Frame Tiles while illuminating how base-ten blocks may do more damage than good when used to help children understand place value.

Just Say the Word! (Part 2)

Game Play, Professional Learning, Teaching and Learning

In my last post, I shared the dangers of using imprecise language in the classroom – inadvertent mistakes we teachers make that can lead to student misconceptions down the road. I shared one way to ensure that teachers and students alike move toward a common mathematical language: establishing school-wide agreements around vocabulary usage. This week, we turn our attention to the classroom.

Academic vocabulary development often has limited utility. Our students are not likely to use words like “commutative property” and “Pythagorean Theorem” when they’re talking to their families over dinner. Math terminology tends to be used in math class and does not get a lot of mileage on the playground, in the cafeteria, or on the bus ride home.

So…it’s up to us to find ways to make it palatable, meaningful, and useful. Below you will find six tips for achieving this…strategies and activities that are supported by research and have been used in thousands of classrooms.

  1. Limit It: Students can retain only so many new words at one time. And yet we often introduce 20-30 new vocabulary words with each new math topic. Rather than holding students accountable for each word, select 5-7 high-leverage terms to concentrate on. These are the ones you will hold students accountable for using.
  2. Repeat It: Remember that mathematical terminology does not have much utility outside of math class. For any new vocabulary to stick, students should use the word(s) 5 times in the first day and 30 times in the first week.
  3. Sketch It: Helping students internalize new vocabulary requires more than memorization and spelling. Students must associate each word with its meaning. To help students access their spatial memories, ask them to focus on descriptions and drawings. One of my favorite things to do with students is to have them make vocabulary picture cards, where the pictures illustrate the word’s meaning. For example, students may write the word “parallel” by making the two large, thick “l’s” in the center. For other examples, check out the vocabulary cards on the Lone Star Learning website.
  4. See It, Say It, Draw It: This simple 3-5 minute “game” activates students’ understanding of selected vocabulary. From each math unit, introduce 5-7 high-leverage terms (see above). Each time you introduce a word, write it on a popsicle stick or strip of heavy paper and place it in a cup. This action is cumulative, so, over time, there will be dozens of strips in each cup. To play the game, pull a strip , read the word, and roll a die. If you roll a 1 or 2, students write the word. If you roll a 3 or 4, students explain (to a partner) the meaning of the word. If you roll a 5 or 6, students sketch a picture that represents the word. Students get one point for each correct response. You can also play this game in small groups –simply make a cup with strips for every 2-4 students.
  5. Math Term “Quiz”: For the quiz, have students number their papers to 5. Select a term and describe it without saying the word. Students write the words, in order, on their papers as you describe them — OR, to mix it up, you might ask students to make a quick sketch — OR you may use the agreed-upon hand gestures for each word and ask students to write the words. Make it quick and simple. Occasionally include a word from a previous unit for spiral review.
  6. Act It Out: Add one more dimension to the game above by having students create a hand gesture to represent each word. The game becomes a See It, Say It, Draw It, Act It game.

As we discussed in Part 1, mathematical precision requires a deep understanding and correct usage of appropriate terminology. Using strategies such as these, borrowed from the language acquisition world, may make all the difference as your students navigate the wonderful world of math.

What do you do in your classroom or school to help students grasp the concepts behind the words? Please continue the conversation by sharing your ideas in the comments box below.

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

 

Your (Mathematics) Back-to-School Supplies

Hands-On Math, Professional Learning, Teaching and Learning

By Kim Rimbey 

The first day of school has a magic all its own. The buzz in the air. The fresh notebooks and sharpened pencils. The energy of new beginnings. For me, that feeling never went away—after all, I’ve had a first day of school every single year since I was five. (And yes… I still treat myself to a new outfit and lunchbox. Every. Single. Year.)

That same excitement doesn’t just come from seeing familiar faces or decorating bulletin boards. It also comes from knowing you’re ready—supplies gathered, tools prepped, and ideas flowing. At KP Mathematics, we want to make sure your math toolkit sparks that same ready-to-roll confidence. Even if the school year’s already underway, it’s never too late to stock up on the essentials that help students truly see and understand the math.

This week, we’re sharing our favorite math supplies—organized by representation type, following the Lesh Translation Model for Representations—plus a few lists of can’t-live-without general supplies and my personal favorite math books.

You probably won’t need everything on this list. You may not want everything on this list. But it will help you think about what’s missing and spark ideas for setting up your classroom for student success.

Let’s dive in.

 

Physical Tools

  • KP Ten-Frame Tiles
  • Base-Ten Blocks (I use BTBs sparingly – I use KP Ten-Frame Tiles for almost all NBT standards)
  • Two-Color Counters (I call them “integer chips” for grades 6+)
  • Pattern Blocks
  • Snap Cubes
  • Unit Square Tiles (one-inch)
  • Unit Cubes (one-inch)
  • Fraction Pieces (unmarked circles, bars, squares, etc.)
  • Cuisenaire Rods
  • Algebra Tiles (grades 6+)

Visual Tools

(I like laminated class sets—they’re perfect for BTC and work beautifully next to your VNPS.)

  • Place Value Mats ([compatible with KP Ten-Frame Tiles])
  • Dollar Boards and Coin Cards (KP Math exclusive)
  • Hundreds Charts (0–99)
  • Hundreds Charts (1–100)
  • Ten Frames
  • Double Ten-Frames
  • Bar Model/Tape Diagrams
  • Number Lines
  • Open Number Lines
  • Open Arrays (multiplication & division)
  • Graph Paper
  • Coordinate Grids (first quadrant)
  • Coordinate Grids (four quadrants)
  • Various geometric figures (as per your program/textbook)

Symbolic Tools

  • Cards
  • Dice
  • Calculators
  • Numeral, Number, and Symbols Charts

Verbal Tools

  • Anchor Charts
  • Sentence Frames

Contextual Tools

  • Rulers
  • Tape Measures
  • Yard/Meter Sticks
  • Balance Scales
  • Weights
  • Measuring Cups
  • Clocks 
  • Coins & Bills
  • Word Problem Frames
  • Problem-Solving Cue Cards

Don’t Forget These Supplies

  • Building Thinking Classrooms must-haves:
    • Vertical Non-Permanent Surfaces (whiteboard surfaces)
    • Dry-Erase Markers—get lots
    • Erasers (microfiber cloths are my favorite)
    • Individual Whiteboards
  • Writing & Art Supplies:
    • Reams of blank paper
    • Construction/colored paper
    • Grid paper
    • Watercolor markers (Crayola—both fine and broad tip)
    • Colored pencils
    • Pencils in different sizes (students love choice)
    • Tape
    • Scissors
    • Glue sticks

Kim’s Favorite Books (in 2025)

KP Mathematics Tools

Back-to-school is all about possibility. A well-stocked math classroom doesn’t just make your life easier—it sets the stage for deeper learning, richer conversations, and those lightbulb moments we live for.

Here’s to a year of math magic!

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

 

Beyond the Tick Marks: Number Lines, Thinking Classrooms, and the Power of Vertical Surfaces

Hands-On Math, Professional Learning, Teaching and Learning

Why Making Math Visible Matters

By Kim Rimbey 

Math is the study of patterns.
Math is a way of thinking. Math helps us describe the world—quantitatively and abstractly.
Math has many expressions.

But here’s the thing: If we can see it, THEY can see it.

When it comes to teaching and learning math, getting the thinking out of our heads and into the world is essential. Visible thinking helps us communicate clearly, uncover misconceptions, and build shared understanding.

That’s exactly why we wrote Seeing the Math You Teach—to support teachers, parents, and students in making their math thinking visible. “Seeing = Understanding.” With the understanding that there are multiple solution paths to any problem, the book offers a variety of visual strategies that help learners represent and explain their ideas.

Number Lines: More Than Meets the Eye

While prepping for a recent conference, I took a deep dive into one of our most powerful tools: the number line.

We often start with number tracks—like snap cube trains—to help young learners count units. Then, we shift to number lines with tick marks. But this shift calls for a shift in focus, too. It’s the spaces between the tick marks that matter. That’s where the “jumps” happen. That’s where the math lives.

Rimbey, K., Basham, K, Berda, C. (2025). Seeing the Math You Teach. Corwin: Thousand Oaks, CA.

And no matter what the intervals—1s, 10s, 25s, millions, fractions—every point on a number line represents a distance from zero.

This is true even if zero isn’t shown. Even if we’re looking at just a portion of the number line, the meaning of every number still depends on how far it is from zero. And it’s true for open number lines as well. Even though the jumps may not be proportional, they still represent the distance traveled from zero. It’s all about relational thinking.

Rimbey, K., Basham, K, Berda, C. (2025). Seeing the Math You Teach. Corwin: Thousand Oaks, CA.

Quick Teacher Check-In: Do your students understand that every value on a number line—visible or open—is a measure of its position relative to zero?

As students start representing their thinking using number lines, we need to help them see what they’re showing—even when zero is nowhere in sight.

Letting Students SEE and BUILD the Math

Here’s the hard truth:

We can’t just tell students what to see. They need to explore, discuss, make mistakes, and revise.

And for that to happen, we need to create learning environments that encourage deep thinking and collaborative sense-making.

Enter…Vertical Non-Permanent Surfaces (VNPSs)

VNPSs—think whiteboards, whiteboard cling film, windows, chart paper, etc.—are erasable vertical spaces where students stand, collaborate, and represent their thinking.

Peter Liljedahl’s Building Thinking Classrooms popularized this approach, and I’ve seen firsthand how transformative VNPSs can be.

Benefits of VNPSs

For Students 

  • Interact and record their thinking
  • Erase, rework, and revise as they learn
  • Represent ideas in multiple ways
  • See other groups’ strategies
  • Stay on their feet and activated

For Teachers 

  • Easily scan every group’s work
  • Step in briefly to nudge, hint, or extend
  • Plant seeds and move thinking forward
  • Select and sequence work to meet learning goals
  • Spotlight key ideas—like number lines and distance from zero

But What If I Don’t Have Enough Whiteboards?

Good news—VNPSs aren’t about expensive equipment. Here are some ideas for where to find inexpensive VNPSs (from the Building Thinking Classrooms update posted on June 2, 2025 – used with permission – click here to subscribe):

Your Next Steps

For Teachers

Two big ideas, two next steps:

  1. How might you talk about number lines in a way that conveys “distance from zero” as the central idea? 
  2. How might you incorporate VNPSs (or use them more intentionally) to support visible, collaborative math thinking? 
  3. Which visual do you use to support your students’ thinking? For more ideas on number lines and many other visuals, check out my newest book, Seeing the Math You Teach. 

For Leaders

Same two ideas, new lens:

  1. How might you build shared understanding during PLC/planning sessions around the idea that number lines represent distances from zero? How might you facilitate doing math together? 
  2. What barriers can you remove to ensure teachers have access to VNPSs and the tools to use them effectively? 

Final Thoughts

Let’s keep helping students see the math we teach.
Let’s help them own their thinking.
Let’s keep learning—together.

 

Interested in Workshops by Kim Rimbey?

Kim offers workshops on a variety of topics, including Building Thinking Classrooms, Ten-Frame Mathematics, Mastering Math Manipulatives, Small-Group Math Instruction, and See the Math You Teach: A New Vision for Math Teaching and Learning. View Kim’s PD Catalog to learn more.

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.

 

Seeing the Math You Teach – Part 2

Hands-On Math, Problem Solving, Professional Learning, Seeing The Math You Teach, Teaching and Learning

When You See the Math, They Will See It Too 

by Chryste Berda

If math has ever made you feel small, you’re not alone. Many of us have internalized the message, intentionally or not, that math is a fixed ability: you either have it or you don’t. But what if making math visible could be the very thing that transforms that feeling of smallness into strength? 

In my classroom, we lived by just two rules:

  1. Math makes sense.
  2. Everyone will be good at math.

I picked up these rules at a math conference years ago, and they became my mantra from that point forward. But recently, a moment reminded me that these rules are deeply connected—and that one cannot exist without the other.

When Rule #2 Is Broken

I was screening number sense for a colleague when a 9-year-old student caught my attention. She got the problem 14-9 wrong and then sighed in frustration.

“No, that’s not right, but I don’t know why this is so hard for me! I’m just not good at math.”

In that one sentence, I heard it: Rule #2 had already been broken for her. 

But here’s what I’ve learned: Everyone will be good at math only WHEN we teach it in ways that make sense. That’s Rule #1. And when we break Rule #1, we can’t keep Rule #2.

Making Math Visible Is the Key

Just the day before, I had been working with our district’s special education teaching team. The focus? Making math accessible by making it visible.  

Making math visible doesn’t just mean using manipulatives or diagrams – it means illuminating the thinking, patterns, and connections behind the math. It means helping learners see what’s going on under the surface. 

One teacher pulled me aside during that workshop. In a hushed voice, she said:  

“I’m not a math person, but I want to be—for my students. The way you’re showing us how to make the math visible? I’m actually learning the math for myself!” 

She followed up this comment by asking if we could continue to collaborate as she begins this with her students.  You see, math becomes visible not just through clear explanations, but through shared exploration – with colleagues who remind us we’re not in this alone because in Rule #2, “everyone” doesn’t just mean all students, it literally means everyone – colleagues, parents, administrators, students, – everyone! 

From Professional Learning to Classroom Confidence

This philosophy is at the heart of our book, Seeing the Math You Teach. We’ve seen how making math visible doesn’t just support student understanding–it builds teacher confidence, too.

At a recent 6th-grade professional learning community meeting, teachers tackled one of the most misunderstood standards: Mean Absolute Deviation (MAD). Before it appeared in standards, many educators had not even heard of it. And early resources? Practically nonexistent! 

So the PLC team used page 195 from our book to understand MAD together.  In those quiet moments of collaboration – around a whiteboard, over a problem, inside a question – something shifted. Confidence took root. You could feel the shift in the conversation as the process was illuminated and the math became visible—for them. 

Seeing the Math You Teach Pages

Rimbey, K., Basham, K, Berda, C. (2025). Seeing the Math You Teach. Corwin: Thousand Oaks, CA.

And when they brought that same resource into their classrooms, it became an anchor chart — a living tool for students. The color coding and step-by-step clarity in the resource helped illuminate the process behind MAD and made it visible to every student, much in the same way that it had become visible for the teachers. That’s the power of making math visible. It builds what I like to call mathematical swagger—for teachers and students.

Everyone Means Everyone 

Let’s stop pretending there’s such a thing as a “math person.” Confidence in math doesn’t come from talent—it comes from clarity. From ideas being made visible. From sense-making being prioritized. And it doesn’t happen alone. It happens in community, through collaboration and exploration, with people who remind us we’re not in this alone. Because when you see the math, they will see it too.  

Make Math Visible for Someone This Week

Take one small step this week to make math more visible—for a student, a colleague, or even yourself. Use a model. Ask a clarifying question. Share your own learning journey. Pull out that anchor chart one more time.

And if you’re ready to dig deeper, invite a colleague to co-plan with you or explore a page from Seeing the Math You Teach together. Learning is meant to be visible—and shared.

Math makes sense. And everyone will be good at math–because of you.

Chryste Berda - Chryste is energized by sharing her passion for learning with her colleagues as the district math coordinator and as a Regional VP for the Arizona Association of Teachers of Mathematics. She is intensely curious about students’ thinking and spends much of her time listening to students explain their ideas.

 

Seeing the Math You Teach – Part 3

Hands-On Math, Professional Learning, Teaching and Learning

Math Makes Sense

By Katie Basham

I wish I had known that when I was a young, impressionable student. Maybe some kids knew it—maybe they even believed it—but I certainly didn’t. I was the kid counting on my fingers, skip-counting under my breath, and hoping no one would notice. I thought of these methods as “less-than” strategies and felt a pit in my stomach at the thought of others noticing me using them.

Everyone Can Be Good at Math

Also true. And I wish my teachers had known that, too. Maybe then I would’ve felt proud of my own strategies, instead of ashamed. Because here’s the truth: success doesn’t belong to a select few. It’s not limited. There’s enough of it for every single student to feel it, own it, and believe in it.

These two beliefs—math makes sense and everyone can be good at math—are the foundation of Seeing the Math You Teach. Success shouldn’t be reserved for an elite few. All students can succeed when they understand that math is really about visualizing and explaining abstract thinking. Because when students can see the math, they can understand it….and, when they understand it? It makes sense.

What a privilege we have as educators.
 It’s no longer our job to bestow knowledge from on high. Our mission is to create learning environments where students use concrete materials, build visual representations, and gradually progress to symbolic understanding. This book is designed to empower you—to help you see and understand the math you teach, so you can help your students do the same.

Take rounding, for example.
 I recently asked a respected educator how he would explain it. Here’s how the conversation went:

Me: “What does it mean to round a number?”
Him: “Five or more, raise the score. Four or less, let it rest.”
Me: “But what does that mean?”
Him: “It means if the number ends in a five…”

As you can see, we weren’t quite getting to the heart of it.

“Rounding” isn’t really something you do, like an action—it’s more about understanding where a number falls in relation to benchmarks or friendly numbers. In other words, rounding is determining which number a given value is closest to.

  • What number is nineteen closer to?
  • What number is 18.34 closer to?
  • THAT’S what rounding is.

Rimbey, K., Basham, K, Berda, C. (2025). Seeing the Math You Teach. Corwin: Thousand Oaks, CA.

The student who can show rounding on a number line isn’t just repeating a rhyme—they’re seeing the math. They’re understanding the concept. And that, at its core, is what this book is about.

We want you—and your students—to experience success.

Because: Math Makes Sense & Everyone Can Be Good at Math!

Interested in Workshops by Kim Rimbey?

Kim offers workshops on a variety of topics, including Building Thinking Classrooms, Ten-Frame Mathematics, Mastering Math Manipulatives, Small-Group Math Instruction, and See the Math You Teach: A New Vision for Math Teaching and Learning. View Kim’s PD Catalog to learn more.