Tuesday / April 23

5 Steps to Start Strong with Just-Right Math Tools

Ensuring that every classroom has the tools needed for student success is a high priority for teachers and leaders alike. That said, how does one know which tools are the “right” tools and on what to spend precious resources? And how do you ensure the investment in these tools pays off? One of the tools that can make a huge difference in student learning is manipulatives. Broadly defined, manipulatives are physical objects teachers and students can use to discover, illustrate, and model mathematical concepts. Manipulatives are critical to this sense-making process because they make mathematics tangible. They allow students to see, to touch, and to build their conceptual understanding of math. We know this is important for young learners, and it is equally important for middle-grades students as concepts get increasingly complex.

Let’s explore guidance on how to select and manage your math manipulatives, including taking inventory, prioritizing purchases, considering storage options, and getting started.

1. Make a List

Which manipulatives are most important to have on hand? If you are limited on the number of manipulatives available, here is a list of questions to ask yourself:

• What are my math goals for the year?
• What tools will best address the standards in each major chunk of math content?
• Which tools will have the most utility, based on the trajectory of concepts and skills I’ll be teaching this year?
• Are any tools redundant? For example, if two-sided counters are available, students can pretend these are bears, cars, or dinosaurs – they need not have access to specifically-molded counters.
• Does each manipulative have a distinct use? For example, unit tiles have a clear and distinct purpose in grade levels where area is emphasized; in early grades, they are simply used as counters.

2. Take Stock

Taking an inventory of the tools that you already have is a necessary first step. Equally important is taking inventory of how those tools have been used and will be used in the future. This is how you’ll decide what else you need to buy, borrow, find a virtual equivalent for, or create. As you take inventory of the math tools that are in your classroom or school, the amount of each manipulative you have at your disposal will be important. Do you need a set for each child? Or will it suffice to have enough for every pair or each small group?

Here is a general process for taking inventory:

• Pull all manipulatives off the shelves and out of the cupboards.
• Group manipulatives by domain: counting and cardinality, number and operations in base ten, fractions, measurement, geometry, statistics, expressions and equations, etc.
• Make a list of the manipulative names and quantities, organized by domain.
• Analyze by quantity, noting how many you need for each if your students will work individually, in pairs, or in small groups.
• Analyze by domain, noting when you have manipulatives that essentially serve the same purpose.
• Compare your inventory to the original list you made. Look for gaps in your list, especially noting if you have no manipulatives for an entire domain.

3. Prioritize Purchases

You may find yourself in the position of having to choose which manipulatives to purchase and how to prioritize your decisions. Here are a few questions to assist you:

• Major vs. supporting content: Does this manipulative support major content for your grade level, or is it supporting content?
• Versatility and frequency: Does this manipulative have utility across multiple standards and concepts that will be taught throughout the year, or is it limited to a small set of standards and only needed for a couple of weeks?
• Accessibility: Do you have access to this manipulative by borrowing from another classroom or checking it out from a resource library? Is there an appropriate virtual option?
• Replaceability: Are there alternatives for this manipulative?
• “On-the-cheap” options: Can you make it yourself (think “fun foam” cut on the paper cutter)? Can you purchase it at a secondhand shop or a teacher outlet? Can you find a lower-cost option? Might you find it at a “retiring teacher garage sale” or an online clearance sale? Can you substitute with everyday objects (e.g., small erasers as counters)?

4. Consider Storage and Packing Options

Here is a general rule of thumb: When manipulatives come in sets, find a way to keep them in sets. For example, if your Cuisenaire® blocks come in trays, keep them in the trays and place them in sealable bags. Place sets of fraction tiles (or circles or squares) in sealable quart bags. Drop the x-y coordinate pegboard, along with the corresponding pegs, axes, and bands, into a sealable gallon bag. This will make them easy to sort, to use, and to inventory. This also helps you transport the sets as well as to redistribute across classrooms, when necessary.

5. Start Strong

• Outline Expectations: When introducing manipulatives to your class, clearly outline the expectations, even to the point of rehearsing appropriate use. Some teachers create anchor charts that describe what appropriate use of manipulatives looks like and sounds like. Review these expectations frequently, as needed. Remind students that manipulatives are tools for thinking and learning, not toys.
• Plan for Partner Work: The simplest way to handle a shortage of tools is to have students work with partners. Ask students to work in pairs, triads, or groups of four. While one student manipulates the tools, others can represent the same problem(s) on paper, using different representations (see the Lesh Translation Model, Figure 1). [insert Figure 1.1 on the right if possible] Other approaches may include rotating students through stations or small groups, or making additional sets of manipulatives on a paper cutter or die-cut machine.
• Model During Instruction: Be sure to integrate the use of manipulatives into your teaching moves, modeling appropriate use, and engaging in “think-alouds” to demonstrate how the manipulatives impact thinking and learning. Remind students that manipulatives support both thinking and communication. Occasionally, engage students in conversations about the many tools they have at their disposal to represent mathematics in various ways.

Using tools that help students develop new ideas, communicate their thinking, and dive deeper into new ideas enhances math teaching and learning immensely. Being strategic about the tools you make available to students is an important start to a strong math program. Using these steps to take inventory and to get started will lay a foundation for successful manipulatives-based instruction in your classroom.

Sara Delano Moore lives in Kent, Ohio and serves as the Vice President for Content & Research at ORIGO Education.  A former classroom teacher and mathematics teacher educator, her work emphasizes the power of connecting multiple representations for deep learning and the importance of mathematical comprehension.  Her desert island manipulative is Cuisenaire™ Rods.

Kimberly Rimbey hails from Phoenix, AZ, where she works as the Director of Mathematics for a local school district as well as the Chief Learning Officer and CEO for her own company, KP Mathematics. She is passionate about making math meaningful for all students, especially through the use of multiple representations and communication. When working in math classrooms, her basic look-for is this: “Whoever’s doing the most talking is doing the most thinking.”

Sara and Kim are the co-authors of Mastering Math Manipulatives: Hands-On and Virtual Activities for Building and Connecting Mathematical Ideas for grades K-3 and 4-8 (Corwin, 2021).