Sunday / April 21

How Do We Use Manipulatives When Building a Thinking Classroom?

Hi there, fellow educators! In the last two years many teachers around the world have begun to embark on the journey of building thinking classrooms (BTC) in mathematics and other subjects—inspired by the research and work of Dr. Peter Liljedahl in his book  Building Thinking Classrooms in Mathematics (Corwin 2020). If you are one of those teachers, you know one of the hallmarks of the BTC framework is having students work collaboratively on vertical non-permanent surfaces (VNPSs). Or perhaps you are a teacher fine-tuning your pedagogy, and your students are already working collaboratively “up at the boards.” Whether you have embarked on a full “BTC journey” or not, the question of how to effectively use manipulatives while students are working on those vertical surfaces is a natural one.

In my experience working closely with teachers during their BTC journey, integrating manipulatives is a game-changer at any grade level.

Students thrive on hands-on math experiences, and these physical tools not only enhance understanding but also enable students to express their mathematical thoughts. The challenge lies in seamlessly infusing them into problem-solving sessions, especially when students are working on vertical surfaces.

Let’s break this down into three actionable steps…

Step 1: Dive into Math Tool Adventures!

First things first, let’s introduce manipulatives as TOOLS FOR MATH even before diving into thinking tasks. Imagine the excitement when you hand out a treasure trove of math tools to your eager learners. They get to explore, experiment, and figure out which tools work best for various math adventures. Witness their playful discovery of the features of each manipulative, eagerly anticipating the cool math applications they can dive into. Next, let’s get specific! Delve into how each tool connects with different, specific math concepts. For a detailed plan to introduce manipulatives to your students, check out my previous Corwin Connect post, Managing Manipulatives During Math Class…From Playful to Purposeful.

Step 2: Sketching – An Artsy Twist to Math!

Time to put those organizational skills to good use! Before heading to the whiteboards, invite your students to SKETCH VISUAL REPRESENTATIONS of the manipulatives. Let their thinking flow as they sketch the manipulatives in simple ways, assuring them we are looking for abstract art, not realism. For our younger math artists, reassure them that they don’t need to draw the non-essential details – tallies, x’s, or circles can perfectly represent those teddy bear counters. For the older bunch, guide them on organizing their sketches, focusing on spatial positioning and the types of visuals they create (e.g., tables, charts, diagrams). And in both cases, encourage connections within and between physical, visual, and symbolic representations. Making these visual connections is like creating a roadmap from manipulatives to their VNPS. You can find more tips on connecting representations in my previous Corwin blog post, Helping Students Connect Manipulatives to Paper-Pencil Math.

Step 3: Let the BTC Math Magic Begin!

Now comes the magical part Once your students are acquainted with the manipulatives they’ll be using, they’re ready to represent them visually and symbolically on their VNPS. This is the perfect place for students to make direct connections between the concrete, pictorial, and abstract (CRA) representations. Even better, students can use all five representational types included in the Lesh Translation Model of Representations (physical, visual, symbolic, verbal, and contextual).

Here’s the process that’s being introduced in many BTC classrooms:

  • Place a desk or small table next to each VNPS and set up the manipulatives.
  • As your students stand at the VNPS, let them decide which, if any, manipulatives they want to use as their math companions.
  • Make sure students know it’s their choice – they can use these awesome tools, or, if they prefer, dive directly into the BTC process with their visual representations.
  • Support groups-of-three as they work together to connect the physical, visual, and symbolic representations.
  • Encourage discourse as students connect their physical, visual, and symbolic representations – they should be using the manipulatives as thinking tools, and their thinking is exemplified through their student-to-student conversations.
  • During the consolidation conversation, highlight ways in which students transferred their manipulatives thinking to their VNPSs. Emphasize the VNPS representations during the conversation, using the manipulatives to support the thinking as needed.

Integrating manipulatives into your thinking classroom takes a bit of preparation, but trust me, it’s worth every bit of effort!

Providing students with opportunities to strategically choose their tools and sketch their way to mathematical success sets the stage for an exciting BTC journey.

Incorporate these strategies into your repertoire, and watch the math magic unfold in your thinking classroom! Please reach out and share your math adventures at

Corwin resources that lend themselves to this conversation:

Written by

Kimberly Rimbey serves as the chief Learning officer at KP Mathematics. A lifelong teacher and learner her heart’s work centers on equipping teachers and helping them fall in love with teaching and learning over and over again. Kim’s interests include high-quality professional learning modules, building conceptual understanding through multiple representations and meaningful discourse, and building pedagogical content knowledge that goes beyond the theoretical and into the classroom. Always a teacher at heart, Kim has served in many teaching and leadership capacities within school districts, organizations, and the private sector. She is the co-inventor of KP® Ten-Frame Tiles and has authored and co-authored such publications as Mastering Math Manipulatives and Meaningful Small Groups in Math for Corwin.

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