Math Manipulatives Explained: Benefits, Examples, and Why They Are Essential

All About Learning Press is dedicated to offering excellent, research-based instruction in all our materials. So, when All About Math was being developed, we knew it had to have manipulatives.

What are Math Manipulatives?

A manipulative is defined as any object that enables a student to work hands-on to discover the answer to a problem or to understand a concept. Our All About Reading and All About Spelling letter tiles are manipulatives, for example. Math manipulatives are hands-on objects used specifically for mathematics.

Math Manipulatives Support Multisensory Learning

Math manipulatives are vital to Multisensory Teaching because they allow students to touch, move, and see concrete representations of abstract mathematical concepts. For example, story problems are notoriously challenging for many students, but when a child can move objects around to show what is happening in each step of the story problem, they become clear and easy to solve.

Without math manipulatives, math learning often becomes overly dependent on hearing a teacher’s explanation of concepts. The teacher may point to a drawing while explaining, but the instruction remains predominantly auditory. With math manipulatives, the teacher’s explanations become supplemental to moving, building, and seeing the mathematics in action. Simultaneous Multisensory Instruction is engaged, teaching is more efficient, and learning is much easier.

Why Math Manipulatives Work: 10 Proven Benefits for Learning¹

More Fun! Even our AALP team members enjoyed lining up counting bears and building towers with the connecting cubes when we first received samples of the All About Math Manipulatives Kit!
More Engaging! Children are more actively participating in learning as they build, move, connect, and employ the objects. Active learning with manipulatives increases engagement.
More Motivation! When students have fun and are actively engaged in their learning, they are more motivated to continue. Children often choose to play with math manipulatives even after the lesson is over.
More Confidence! Students given the chance to work with manipulatives and reflect on their experiences have reduced math anxiety and are more confident in their math abilities.
More Retention! Hands-on math manipulatives aid both short-term and long-term retention, making learning more effective.
More Number Sense! Using manipulatives leads to better number sense, which is understanding quantities, more and less, number comparisons, and so on.
More Problem Solving! Manipulatives allow children to more easily visualize mathematical concepts, helping them develop more flexibility in their problem-solving strategies.
More Mathematical Reasoning! When children use manipulatives, their reasoning skills improve as they think more critically and ask higher-order questions, showing deeper learning.
More Abstract Thinking! Physical manipulatives are concrete representations of the abstract concepts involved in mathematics. Being able to see and touch these concrete objects helps students digest complexities with less effort.
More Learning! Extensive research spanning decades shows that math manipulatives improve learning outcomes.

Can I Use Household Items Instead of Math Manipulatives?

Household items like blocks, pennies, straws, rubber bands, index cards, and buttons make great manipulatives for things like counting, lower addition and subtraction, and even simple multiplication and division. It is even possible to make manipulatives to show things like place value by gluing ten dried beans to popsicle sticks to represent groups of ten.

However, while homemade math manipulatives can often save some money over purchasing them, the money saved is greatly offset by the time that must be spent. Also, if you must purchase materials to use in making manipulatives because you don’t have the items on hand, you lose out on both money and time saved. Purchased math manipulatives are likely to hold up better over long periods of use and many children, and if you purchase the exact manipulatives the lesson plans call for, you will not have to worry about rewriting or adapting lessons.

The All About Math Manipulatives Kit

The best math manipulatives for All About Math are found in our carefully chosen selection available in our Manipulatives Kit. Here is the list of math manipulatives included in our kit:

Two-Color Counters

These are disks that are red on one side and yellow on the other and are extremely versatile for mathematical learning. The two-color counters in our kit are made of a foam material that keeps them from sliding around and makes them easier to handle. The All About Math Manipulatives Kit includes 50 two-color counters, and they are used in all five levels.

One of my favorite uses of these is to show all the ways possible to compose a number. You start with 5 red disks and 0 yellow ones to show 5+0. Then, you turn over one disk so that it goes from red to yellow, and you show 4+1. Turn another to show 3+2, then 2+3, 1+4, and 0+5.

Connecting Cubes

These interlocking cubes connect on all six sides, allowing for a variety of building options. Our connecting cubes are a nice three-quarter-inch size and include 100 cubes, 10 each in 10 different colors. These are used in all levels of All About Math.

The connecting cubes are great for helping students visualize composing and decomposing tens (also known as regrouping) when adding and subtracting two-digit numbers. Loose cubes are brought together to make a tower of ten to compose, and a tower of ten cubes is broken apart to decompose.

Counting Bears

These cute, inch-tall teddy bears are fun and motivating for children. Our kit includes 40 of them—10 each of 4 different colors—and they will be enjoyed by All About Math Level 1 and Level 2 students.

As the name implies, these bears are useful for learning counting, but also so much more. They are teaching tools for sorting, sequencing, pattern recognition, addition and subtraction, and other concepts. Plus, they make great game pieces for math games!

Base-10 Blocks

Our manipulatives kit includes a set of base-10 blocks. There are 100 small unit cubes, 50 long tens rods, 10 square hundreds flats, and 1 large thousands cube. This set makes the relationship between ones, tens, hundreds, and thousands so concretely clear and will benefit students in all levels of All About Math.

The base-10 blocks are helpful for adding and subtracting multi-digit numbers with composing and decomposing (regrouping) and for learning decimals. They are essential for a deep understanding of our base-10 number system.

Fraction Tiles

This set includes 51 tiles, representing 1 whole, 2 halves, 3 thirds, 4 quarters, 5 fifths, 6 sixths, 8 eighths, 10 tenths, and 12 twelfths. Finding equivalent fractions is so easy with this manipulative. The fraction tiles are used in All About Math Levels 3, 4, and 5.

In addition to finding equivalent fractions, this set can also be used for adding and subtracting fractions, understanding and using mixed numbers, dividing fractions, ratios, and more.

Ruler and Protractor

These simple tools are indispensable for measuring length and angles. The 12-inch ruler includes both centimeters and inches. The protractor measures angles from 1° to 180°. The ruler is used in Level 2, and the protractor is used in Levels 4 and 5.

Dry-Erase Pocket

While not technically a manipulative, the dry-erase pocket allows you to reuse any page again and again. One is included in the All About Math Manipulatives Kit and is used throughout all the levels to enhance learning and allow for repeated review and gameplay.

Storage Bin

The All About Math Manipulatives Kit comes packaged in a convenient storage bin with a locking lid.

Manipulatives alone aren’t enough.

As wonderful as the above examples of math manipulatives are, they won’t teach your child very much by themselves. Sure, playing with the fraction tiles may help a student understand equivalent fractions with no other input, but without explicit teaching, a child won’t know how or why to use equivalent fractions to find common denominators for addition and subtraction.

That’s where the All About Math program comes in. Each lesson directs how to use the manipulatives to teach both simple and complex mathematical skills and concepts. You’ll find scripting so you will know exactly what to say for your child to understand what the manipulatives are representing, how to use them, and how they relate to the real-world application of the math involved. All About Math will give you complete confidence in how to make good use of these essential learning tools.

Frequently Asked Questions about Math Manipulatives

What if I am not sure about using math manipulatives?

All About Math’s lesson plans will give you the confidence to use math manipulatives effectively! The lessons are scripted with plenty of illustrations so that you will know exactly what to say and what your child should do to achieve the utmost benefit from the manipulatives.

Aren’t math manipulatives a distraction?

No. Working with hands-on math manipulatives may take more of your lesson time than simply writing equations and answers on a whiteboard or worksheet, but please do not make the mistake of assuming that the time is wasted with the manipulatives. They take more time because there is deeper, more valuable learning in moving, building, connecting, and manipulating those objects. Allow your child the time.

Do older students still need math manipulatives?

Yes. Almost everyone agrees with the necessity of math manipulatives for kindergarteners, but many assume that manipulatives are less important as children age. This is not the case! Research has shown that even college calculus students benefit from hands-on learning with manipulatives.² Manipulatives continue to be important for deep understanding as math concepts become more complex at higher levels.

What if my child always wants to use the math manipulatives and never wants to do math without them?

It is important to allow students to use manipulatives as long as they find them helpful or beneficial. Children will naturally rely less and less on math manipulatives as their confidence and ability improve, but the exact timing for this transition will vary depending on many factors, such as the child’s age, development, complexity of the math, the child’s comfort with math, and much more.

Extensive academic research establishes that there is no age or level when students are harmed by using manipulatives. Research shows that even high school algebra students and college calculus students have improved learning when they use hands-on manipulatives!²

Also, All About Math carefully and gently moves children from using manipulatives to using drawings to doing math abstractly. It is important that your student makes the decision about when to stop using manipulatives based on his individual level of comfort with the mathematical concepts involved.

What if my child doesn’t want to use math manipulatives?

If your child does not want to use manipulatives when the lesson instruction directs him to, have him demonstrate his understanding of the method by using the manipulatives to work through 2 or 3 problems. Then, allow him to do the remaining work in whatever method he wants. It is important that your child show that he knows how to use the manipulatives, even if he doesn’t need them, because later lessons or levels will build up to more complex concepts, and he is likely to need the manipulatives then.

The All About Math Manipulatives Kit is a fun, engaging, and highly effective toolkit for your child’s mathematical learning! Which manipulative is your child’s favorite? Which do you like best?

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¹Belenky, Daniel M. and Nokes, Timothy J. (2009). “Examining the Role of Manipulatives and Metacognition on Engagement, Learning, and Transfer,”. The Journal of Problem Solving: Vol. 2: Iss. 2, Article 6. DOI: 10.7771/1932-6246.1061. https://docs.lib.purdue.edu/jps/vol2/iss2/6

Boggan, Matthew; Harper, Sallie; Whitmire, Anna (2010). “Using Manipulatives to Teach Elementary Mathematics” Journal of Instructional Pedagogies: Vol 3. https://eric.ed.gov/?id=EJ1096945

Carbonneau, Kira & Marley, Scott & Selig, James. (2012). A Meta-Analysis of the Efficacy of Teaching Mathematics With Concrete Manipulatives. Journal of Educational Psychology. 105. 10.1037/a0031084 https://bit.ly/3CNHwPv

D’Angelo, F., & Iliev, N. (2012). Teaching Mathematics to Young Children through the Use of Concrete and Virtual Manipulatives. https://eric.ed.gov/?id=ED534228

Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 18(1), 37–54. https://doi.org/10.1016/S0193-3973(97)90013-7