Math manipulatives: What they are and how they work

Math can be a tricky subject for kids and adults. When people struggle with math — whether it’s simple numbers or complex algebra — hands-on tools like manipulatives can help. 

Math manipulatives are tangible objects that can represent numbers or shapes in math problems. They can be tools designed for the classroom, like math cubes. Or they can be everyday objects, like buttons. No matter the form, manipulatives can help make abstract math concepts easier to understand.

With manipulatives, people can touch, move, count, and see how these objects interact. They’re usually physical objects, but they can also be digital. There are benefits to both types. 

Physical manipulatives are common in classrooms. They’re often part of multisensory instruction and are great for building number sense. Plus, they can help with understanding other math topics, like geometry, fractions, algebra, and more. 

Some common examples are base 10 blocks, chip counters, pop-cubes, and geoboards. They can also be everyday household items, like dried beans, paper clips, straws, and folded paper. 

Simple objects work better than detailed or complicated ones. They’re easier to generalize and apply to concepts.¹ For example, using toy cars for a problem about cars makes it harder to generalize the learning to other types of problems. Also, simple objects cut down on distractions and misrepresentations. 

Many common physical manipulatives have digital (or virtual) versions. Digital manipulatives are helpful for repeated practice because they can be easily duplicated, removed, resized, and reshaped. They can also be moved around, like placing them on a scale to show how they’re equivalent, or on a number line to show order. 

Older students often prefer digital manipulatives because they feel they’re less stigmatizing than using objects like blocks or counters.² Many times, a combination of physical and digital manipulatives may work best. 

Using manipulatives is an evidence-based teaching strategy for anyone who struggles with math. Math manipulatives provide an opportunity for students to deepen their knowledge of math concepts and procedures, making math more engaging. They can make people feel more comfortable with math, boosting confidence and reducing anxiety. 

Hands-on learning with manipulatives combined with explicit math instruction works well for anyone needing extra support in math.² Here are some of the specific challenges manipulatives can help with.

Dyscalculia, a learning disability in math, can make numbers so abstract that it’s hard to assign values to the symbols. Both physical and digital manipulatives can help people with dyscalculia build conceptual and procedural understanding. 

For example, working with fractions can be hard for many people. Fraction strips can help with understanding that the same number (or whole strip) can be split into different equal-size parts. Fraction circles or a geoboard can help with understanding that any area can be divided into equal-size parts to show a fraction.

Dyslexia is a learning disorder that affects reading, spelling, and writing. It can also cause problems in math. Typical math lessons can be full of confusing language. It can be especially difficult for people with dyslexia to decode story problems. Having access to physical objects that represent the parts of the story can help with understanding. 

ADHD (attention-deficit hyperactivity disorder) is a common condition that makes it hard to focus attention. Passive learning, like lectures and note-taking, can be hard for people with ADHD to focus on. Working with manipulatives can make math more engaging.

For example, instead of just giving students the formula for finding the volume of prisms, teachers can give students pop-cubes. Students can use the cubes to build rectangular prisms based on specific dimensions. Having them find out how many cubes they used helps build their understanding. It shows them that the total number of cubes is the “volume” of the prism.

Working memory helps people keep track of information in the moment. Learning and thinking differences like ADHD, dyslexia, and dyscalculia can affect working memory.

The cognitive load of holding on to information while working through math problems can be tough for people who struggle with working memory. It can make it hard to store and recall information, and connect previously learned concepts to new ones. Manipulatives can help with recalling information.

For example, students may first use fraction strips when learning how to create equivalent fractions. If they forget the steps later, using the strips for just a problem or two may help them remember.

Anyone can use manipulatives to help with teaching, learning, and understanding math. Here are some tips for how to use them at home and in the classroom.

Manipulatives can help both kids and adults practice math skills at home. They’re a great supplement or alternative to using flashcards or practice worksheets. They can be more engaging — and less frustrating.

Follow these tips to get started:

• Look for manipulatives that are simple to use and gather.  

• Allow time for getting used to new manipulatives, especially digital ones. Or choose familiar manipulatives. 

• Manipulatives should be easy to count, group, split, or change in size. Try straws, paper clips, popsicle sticks, buttons, or small toy pieces like Legos.

• For parents and caregivers working with kids on their math homework, ask a teacher for suggestions. They can recommend objects that fit well with specific skills to practice. 

Educators should consider these questions before using manipulatives: 

• How many items are needed?

• How easy is it to access virtual tools? 

• Do the manipulatives represent the concept and procedure well? 

• Can students choose between physical or digital manipulatives?¹ 

Here are a few more tips for using manipulatives in the classroom: 

• Leave time to play or explore the manipulatives before the lesson. 

• Make sure the connection between the manipulatives and the math concept is explicit.

• Give clear, direct instructions on how to use the manipulatives.

• Guide students and give feedback as they work with the manipulatives.

• Work with students in small groups when possible. 

Math manipulatives are hands-on tools, like blocks, counters, or buttons, that help people understand math. They can be real objects you can touch or digital versions you move on a screen. Both can make math more concrete.

These tools can help everyone, but they’re especially useful for people with learning differences. For example, they can make numbers less confusing for people with dyscalculia.

At home, simple objects like straws, small toys, or paper clips make good manipulatives. In classrooms, teachers should make sure to give students clear steps for how to use them.

No matter the form, manipulatives can make math more hands-on and easier to understand.