Math Manipulatives: How Can They Improve Student Learning in Math?

ALI Staff | Published  April 03, 2024

Math manipulatives are a great way to make math more accessible for your students, especially if you know they may struggle with a new concept.

While the more complex tools are useful with older students, you can introduce simple math manipulatives with your youngest learners, too.

They’re a great way to start breaking down abstract concepts into more concrete ones and boost foundational skills in math.

Let’s look at why these math supports are so beneficial to students, starting with how we define math manipulatives.


An image of math manipulatives


What are math manipulatives?

Math manipulatives are objects used to support teaching math concepts in a hands-on way.

These math tools for students can be concrete, like pattern blocks, cubes, or paper geometric shapes, or virtual, like online math vocabulary cards, math apps, and math games through digital math curriculums.

Students can use these tools to visualize concepts, interact with what they’re learning, and deepen their understanding of abstract information. Manipulatives in math can also help students feel more involved in their learning if they’re able to “touch” math concepts in this way.


Strategies for Integrating Math in Play for Young Learners

Math manipulatives enhance learning by making the abstract more concrete, tapping into students’ diverse learning styles, and enhancing real-world connections. Let’s look at these benefits in a bit more detail.


Math manipulatives are student-centered.

Math manipulatives encourage students to experiment, make predictions, and find solutions through trial and error.

While the teacher may provide the tools, the activities are driven by the students.

This fosters critical thinking and strategizing. It’s also a great way to introduce more in the classroom.


Math manipulatives are hands-on learning.

Math manipulatives are hands-on learning in its most basic sense.

Students are physically doing math using the tools in front of them or manipulating what they see on their devices to reimagine concepts.

Math tools are also easily adaptable for students with additional needs and tap into both kinesthetic and visual learning styles.


Math manipulatives support real-world connections.

Manipulatives help students make connections between abstract math concepts and real-world scenarios.

Time-telling tools help students learn about the passage of time and think about concepts like travel times and managing their own time.

Measurement tools like rules or tape measures can introduce students to length, distance, and cooking recipes.


Math manipulatives build confidence.

Hands-on experiences allow students to engage with math on a deeper level. It’s more fun, too, and can build perseverance in students who may not have connected with math otherwise.

This can lead to a sense of accomplishment when students finish a difficult problem. It sets the stage for a lifelong love of learning and combats math anxiety.


Math manipulatives are a concrete representation of ideas.

Using manipulatives in math gives students a way to physically interact with mathematical ideas, even if it’s virtual over classic tools like fraction tiles and geoboards.

For example, using blocks to add or take away quantities based on a given story is a simple way to introduce addition and subtraction.


Math Manipulatives & the Concrete-Representational-Abstract (CRA) Model

Math manipulatives are integrated into each step of the CRA model in math, but they’re particularly important at the concrete level.

This instructional approach is based on the idea that concrete experiences can help students develop the skills they need to see (and manipulate) math concepts more abstractly.

The CRA model starts with the concrete stage. This is where students use physical objects or visuals to explore what they’re learning in math. From there, they transition to visual or written representations of those concrete objects.

This can look like diagrams or tallies instead of counting blocks.

The last stage is the abstract.

This is the symbol stage, where students begin using mathematical symbols and equations to solve problems. Much like math manipulatives themselves, this approach scaffolds learning and guides students from tangible experiences to more abstract thinking.


Examples of Math Manipulatives

Virtual options, printables, and DIY math manipulatives are all ways to reach students at their level. When deciding on manipulatives for math in your classroom, start with your content.

Which concepts have been challenging for students to grasp in the past?

Think about classroom objects and supports your students already enjoy. How can you incorporate engaging objects into your math instruction?

If you know a group in your classroom loves dinosaurs, for example, use your bin of plastic dinosaurs to support a counting lesson.

You’ll be able to hold your students’ attention longer and show them you prioritize their interests when planning instruction.

Here are some examples of common math manipulatives to support math instruction:

  • Counters
  • Cuisenaire Rods
  • Popsicle sticks
  • Marbles
  • Stacking toys
  • Wooden shapes
  • Pattern blocks
  • Dominoes
  • Dice
  • Spinners
  • 100s chart
  • Rekenrek/counting frame
  • Balance scales
  • Fraction tiles
  • Pizza fractions
  • Flashcards
  • Base 10 blocks
  • Geoboards
  • Magnetic whiteboards
  • Linking cubes
  • Rules
  • Measuring tape
  • Clocks
  • Play money
  • Origami
  • Abacus
  • Sand timers
  • Measuring cups/spoons
  • Virtual vocabulary cards
  • Math apps


What are the best math manipulatives?

The best math manipulatives are the tools that give students an effective way to learn a new math concept. From there, teachers can get creative with what they use to engage their students.

Keep in mind that elementary math manipulatives don’t need to be purchased at the store to work in your classroom.

Building blocks, buttons, and printable fraction bars can all be used as math manipulatives. The most important thing is tapping into your students’ learning styles and curiosities to boost engagement in math.

If you find that using Goldfish crackers is a way to get them interested in a lesson adding and subtraction, that’s a great use of your time and crackers!


Develop Your Students’ Math Skills in a Fun Way

Incorporating math manipulatives into your daily instruction is a great way to enhance your students’ math skills and make lessons more fun for them.

By giving them a chance to experience math rather than just see it on a worksheet, you’re giving them a chance to deepen their understanding of concepts that will build from one grade to the next.

Math manipulatives are a fun, interactive way to empower students to become more confident learners.

Math can be intimidating for students. Whatever we can do to create space for students to make mistakes, adjust their thinking, and pick up new skills is a powerful thing.


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