Math manipulatives are physical objects that allow teachers and students to demonstrate certain math concepts. And just like the name suggests, it allows students to manipulate or play around with objects. In other words, they are toys that teach math concepts in interesting ways. 1

Why do We Need Math Manipulatives?

Kids are great at learning with concrete objects—just try giving them some building blocks, and they will go to town with them. But they often find it challenging to connect numbers and abstract math symbols with the real world around them. And students can recollect concepts taught through books and lectures for a short period of time. But it is essential for the students to have a thorough understanding of the concepts taught in lower grades because the concepts taught in higher grades are mostly built upon the concepts discussed in lower grades. So, we must lay this foundation for them to help them build “number sense.” 

That’s where math manipulatives can come in handy. Math manipulatives help students gain a solid understanding of the basic concepts through hands-on experience with concrete objects. And we all know that learning with our bodies is better than learning with just our minds. That’s because learning with our body activates more senses and demands higher concentration levels. This helps kids build a solid understanding of the concepts. And thinking from their perspective, learning with manipulatives is exciting and engaging. So, it’s a win-win situation for both students and teachers.1,2

Who Would Find These Manipulatives Helpful? 

In general, manipulatives have the most remarkable effect when a student is introduced to a new concept. For students studying in kindergarten and lower grades, everything they learn is completely new to them. Math manipulatives for kindergarten students tend to be popular because young students require more attention as they are not familiar with any math concepts. 

Students in higher grades are often learning concepts that are built on the concepts they have already learned at a younger age. If they have a strong foundation, they will be capable of learning new concepts effectively even without manipulatives, thanks to the “number sense” they have built over the years. But special students with learning disabilities like dyscalculia might find it difficult to grasp new math concepts. Math manipulatives can be useful in such cases.4,5

How do Math Manipulatives Help?

It is not the use of manipulatives that helps students learn. Instead, math manipulatives act as something tangible as they think about these manipulatives while learning. By establishing this tangibility, manipulatives help students find meaning in what may look like abstract numbers and symbols to them.

For example, students may not understand the significance of the area of a shape unless they know what it means in the physical world and why it is calculated the way it is calculated. The progression from a point to a line with length to a shape with an area can be demonstrated using interlocking cubes. Hence, physical objects can give meaning to abstract symbols like +, -, ×, ÷, and so on. 2

Advantages of Using Math Manipulatives

  • Adds Fun and Excitement

Gamifying the learning process makes math more appealing to students. The fun and easy-to-learn approach reduces anxiety among students. This helps to do away with the fear and hatred of math.

  • Boosts Confidence

Using a hands-on approach allows students to feel as if they are solving real-life problems. This gives students a sense of accomplishment and encourages them to believe in their own abilities.

  • Avoids Memorization

Students need not rely on math tricks and memorization. They might end up making mistakes due to memorization, even if they are well aware of the concept. The tangibility established by manipulatives helps students solve problems using their conceptual understanding.

  • Helps in Building a Strong Number Sense

Number sense is a person’s ability to understand, relate, and connect numbers. A person is said to have number sense if he/she is comfortable with numbers and math operations. To make learning math easier, it is important for students to develop a strong number sense as they progress through grade levels. 

Points to Note While Using Math Manipulatives

  • The teacher plays a critical role when it comes to teaching concepts with math manipulatives. It is important that they provide students with clear instructions on how manipulatives should be used to achieve the desired results. 
  • The use of multiple manipulatives to teach the same concept will improve students’ understanding of the concept. This ensures that they do not limit themselves to a single line of thought. Furthermore, this also teaches them that math, as a universal language, works in multiple ways. 
  • Overcomplicating a simple concept is a bad idea. This can make it appear too overwhelming.

Examples of Manipulatives

Here are some manipulatives you can use to teach your child math.3

  • Counting chips, math counters, and pattern blocks are examples of math manipulatives for kindergarten students. These are the most basic manipulatives. As the name suggests, this helps students count things, familiarizing themselves with counting numbers. 
  • Base ten blocks, or place value blocks, are really effective for representing the place values of numbers. The unit blocks denote ones, rods denote tens, flats denote hundreds, and cubes denote thousands. This manipulative gives students an idea of the scale when comparing big and small numbers. This manipulative also helps students perform math operations like addition, subtraction, multiplication, and division. 
  • Fraction bars, or fraction tiles, can be used to represent and compare fractions. Comparison of fractions can be quite tricky for students who are new to this concept.
  • Algebra tiles are multicolored tiles used to represent variables and constants in an equation. The tiny squares represent constants, the skinny rectangular pieces represent x, and the larger squares represent the value of x2. These tiles can be flipped to get the same shape in red, which represents negative values of the same terms.
  • Abacus is an effective math manipulative that can grow with the student’s math skills. Even though the above-mentioned manipulatives serve their purpose well, their main limitation is that they are limited to introductory math instructions. The abacus, on the other hand, is more versatile and can be used for quick math calculations. 

Virtual Math Manipulatives

It might be difficult to get a hold of these manipulatives at times. Since online classes are popular these days, it is quite difficult to provide the same hands-on experience to all students. It is not practical to make all students buy these manipulatives. The problem of accessibility can be solved by using virtual math manipulatives. Any student with a web browser can make use of the virtual math manipulatives that are available online. And the best thing about virtual math manipulatives is that they can be accessed at any time from anywhere.6 

Try it out and let us know if it helped your child’s math learning. Please let us know what you think about math manipulatives in the comments section, and visit BYJU’s FutureSchool Blog to learn more about them and other math concepts.


  1. Benefits of Math Manipulatives | ETA Hand2mind. (n.d.). Retrieved June 9, 2022, from 
  2. Furner, J. M., & Worrell, N. L. (2017). The Importance of Using Manipulatives in Teaching Math Today. Transformations, 3(1). 
  3. 5 Math Manipulatives Every Teacher Should Be Using – Tanya Yero Teaching. (n.d.). Retrieved June 9, 2022, from
  4. What is the Importance of Number Sense in Math? (n.d.). Retrieved June 10, 2022, from 
  5. Benefits Of Using Manipulatives In Math – Number Dyslexia. (n.d.). Retrieved June 10, 2022, from 
  6. 7 Best Virtual Manipulatives for Online Math Learning | Oryx Learning. (n.d.). Retrieved June 10, 2022, from 

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