# Top Manipulatives for Teaching Math

The Editorial Team March 3, 2023

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Learning mathematics cannot be achieved through memorization alone. Manipulatives provide a physical representation of the issue being addressed, leading to a more meaningful, hands-on experience. They’re very beneficial for real-world math problems.

Throughout history, physical objects have been used to represent abstract concepts and ideas. Ancient forms of the manipulative resembled counting systems resembling an abacus. In the early 19th century, geometric shape manipulatives transformed the way people looked at their world by introducing them to more than just numbers.

## Benefits of manipulatives in teaching math

Math is more than just words, symbols, letters and numbers – it also has practical applications. Unfortunately, there can sometimes be a lack of understanding or connection between the theoretical concepts of math and how they function in real-life scenarios. When students are presented with the opportunity to interact with math through manipulatives, they can make a connection between the problem and its practical application.

When used in teaching math, manipulatives can:

• Help students construct physical models of the problem to be solved
• Build confidence by taking abstract ideas and making them concrete
• Provide a tangible way to test a theory through trial and error
• Mimic real-world experiences, such as scale models and prototypes
• Engage and excite learners with colorful shapes and objects over monochromatic letters and numbers
• Break down complicated concepts into recognizable parts
• Increase the enjoyment of working with math, which often translates into greater proficiency
• Establish concrete understanding, which leads to stronger abstract comprehension

Manipulatives help build a foundation for understanding math concepts, allowing the students to grasp the material and develop problem solving skills. By utilizing manipulatives during math instruction, your classes will become an enjoyable atmosphere of learning and exploration.

### Ideal manipulatives for preschool and kindergarten

Math is an essential part of education, and its first building blocks are established in early childhood. For many kids, the foundation for this discipline begins with parents or caregivers who interact with them by counting fingers and toes and teaching them catchy rhymes.

Setting small items such as food onto a plate, into a bowl, or directly handing them to the child can provide an opportunity to count and practice math skills. Establishing this foundation while they are still young will ensure that their knowledge and understanding of mathematics is firmly cemented.

Manipulatives are an incredibly valuable tool for preschool- and kindergarten-aged children who aren’t yet able to communicate their ideas clearly. These objects provide a universal way of expressing and understanding concepts when words alone cannot explain them. When selecting manipulatives, look for ones that are interesting and engaging. Other suggestions::

• Easy to grasp and hold
• Large and easy to see (e.g., DUPLO bricks)
• Lacking small pieces that might get swallowed or lost
• Brightly colored
• Slightly rounded or smooth on the edges
• Made in familiar patterns and shapes (e.g., pattern blocks)

You can also create homemade manipulatives from everyday items. Make use of the following:

• Magnet balls or gems
• Uncooked pasta (you can dye it with Kool-Aid to add a classification aspect)
• Popsicle sticks
• Buttons
• Erasers
• Cotton balls
• Q-tips
• Coins
• Marshmallows (both mini and regular size)
• Marbles
• Board game pieces
• Beans
• Corn kernels

If you’re looking to kickstart your math manipulative collection, there are many places to begin your search. Thrift stores, yard sales and online third-party marketplaces can be great sources, while educational websites may also provide helpful guidance. However, always remember that when starting out, less is more.

No matter how you use them, store your manipulatives in containers that are convenient and easy to access. When storing small pieces, ensure the lids are securely fastened. This protects the contents from spilling or being accessed by unsupervised youngsters. Food storage containers are very useful and can be found in most stores, while specialty stores (like those selling gaming items) provide more specialized, creative solutions.

### Ideal manipulatives for Grades 1-3

Children at the early elementary levels come into these grades with a rudimentary knowledge of math. However, they might not have prior experience with manipulatives used specifically for mathematical purposes. Nevertheless, fine motor skills are more developed at this age, so you can use items that are more refined. These can include:

As little ones explore their world, provide them with opportunities for investigation and discovery. Math centers filled with enriching activities can promote cognitive development and engender in children a love of learning. Such experiences can also encourage the development of self-confidence as they interact with their physical surroundings.

### Ideal manipulatives for Grades 4-6

Engaging with hands-on materials isn’t just for younger grades – older students benefit from them, too! By building upon their existing base knowledge, manipulatives allow for more in-depth learning as these students focus on harder core subjects. Consider including:

• Pattern blocks for fraction skills
• Base ten blocks for volume, place value and decimals
• Rolling dice for mastering fast facts in basic math
• Protractors
• Analog clocks to explore elapsed time
• Graph paper
• Dry-erase tablets

### Ideal manipulatives for middle and high school students

At these grade levels, creative expression is often minimized in favor of achieving academic requirements. Manipulatives offer an opportunity for continued tactile learning that engages both hemispheres of the brain. With these materials in hand, students can explore and discover within an established framework.

• Balance scales to teach measurement and equality on both sides of an equation
• LEGO for area and perimeter exercises
• Algebra tiles for factoring polynomials
• Paper plates to explore the facets of the unit circle
• Transparent geometric solids for volume and measurement
• Spinners for probability, data and statistics
• Butcher paper to cover desks and tables for group collaboration exercises

## Popular math manipulatives

Manipulatives may be commonplace in the classroom setting, however they have far more applications than what we typically assume. Anything could serve this purpose and there are certain products readily available that have come to be recognized for aiding in teaching various topics. For instance, they help simplify intricate processes like basic arithmetic operations and more advanced strategies like decimal division. Furthermore, their utility is not restricted merely to children or classrooms; these resources can prove advantageous to any person regardless of age or educational environment.

### Base Ten Blocks

Base ten blocks are a super useful tool for understanding place value, number sense, and regrouping. Most common sets feature light blue small cubes, rods representing 10 conjoined cubes, one square that’s equal to 100 cubes, and one large cube for 1,000 cubes. Some companies have created multiple color sets as well.

### Fractions

#### Fraction bars/tiles

These hands-on pieces help learners explore the concept of parts of a whole. They’re packaged in a set of color-coded pieces; within the set are pieces representing wholes, halves, thirds, fourths, fifths, sixths, eighths, tenths and twelfths. The set comes with a tray and a booklet that contains recommended activities. You can buy them from Learning Resources or make them yourself.

### Counters

#### Cuisenaire Rods

These rods offer a unique way to learn essential math concepts! Coming in 10 distinct colors, with every hue corresponding to a number between 1-10, these rods can assist with adding, subtracting, multiplying, and dividing. They form a staircase-like pattern when assembled- making them an engaging tool for mastering fundamental math skills.

#### Animal-shape counters

From an array of animals ranging from bears to chickens, these plastic toys can be found in most educational or children’s toy sections. Whether you are looking for a tiny monkey or a gigantic cow, with the selection of varying shapes and sizes, there’s something for everyone!

#### Circle counters

Versatile and brightly colored, basic counters are a great choice for bingo chips and more. These primary-hued pegs, made of transparent plastic, come in two-sided circles that are red on one side, yellow on the other — ideal for counting activities.

#### Rekenrek

Very similar to the abacus, this Dutch version contains strings attached to wood with a variety of beads hanging on the strings. Learners can move themleft and right as they tick off a counting sequence.

### Algebra tiles

#### Plastic, magnetic or foam tiles

Algebra tiles look similar to base ten blocks, only they don’t have markings that help with basic counting. These tiles depict various components of algebraic equations and are labeled as unit, x, y, xy, x² and y² pieces.

### Shapes and geometry

#### Geoboards

Create your own designs with a standard square pegboard! Featuring either single or two-sided styles, this pegboard provides a fun and easy way to explore angles, fractions, symmetry, shape recognition and construction. With thin pegs arranged in a variety of arrays, simply stretch rubber bands across the pegs to create your own masterpieces!

#### Tangrams

Tangrams, commonly known as pattern blocks, feature six distinct shapes representing one of six colors. It entertains learners with cards that contain colorful designs, which must be replicated using the pieces in a set.

#### Anglegs

Plane geometry never tasted so sweet! These innovative new manipulatives, which snap together like popsicle sticks held by a brass pin, give students a fun way to explore different aspects of planes, angles, and shapes. With six unique lengths available, they bring an exciting element to mathematics lessons!

### Math cubes

#### Unifix cubes

These interlocking counting cubes, the gold standard in math manipulatives, are ideal for instruction in counting, patterns, and basic operations. Offering fantastic versatility, they come in ten distinct colors and can be purchased from almost any store.

### Money

#### Plastic, wooden or paper coins

Adding coins to learning activities can enhance the enthusiasm and focus of learners. Blank coins come in various sizes and colors, manufactured or printed – either plastic or wooden discs that last even longer. They provide a creative way to test the knowledge of students, making learning an enjoyable and participatory experience!

#### Play money

Pretend money is usually constructed from thin plastic or laminated paper, however, you could always use board game currency. Generally, pretend money is smaller in size than real cash; however, a typical set includes notes of one, five, ten, twenty and hundred dollar denominations.

### Basic math

#### Dice

Dice come in many shapes and colors, from a typical six-sided cube with numbers one through six, to those with more variety. You can use these adaptable objects for common arithmetic such as adding, subtracting, multiplying and dividing; or for other activities where you need a decision-maker.

#### Dominoes

Dominoes are an excellent way to explore basic math, probability, and estimation. This classic game has 28 tiles featuring combinations of blanks and dots from one to six, similar to dice but with two combinations per tile face. Problem-solving and calculation challenges make dominoes engaging and provide multiple learning opportunities for young minds – making it a perfect fit for classroom curriculum.

#### Rulers

A standard ruler displays inches, centimeters and millimeters, but you can use a yard/meter stick and even a ruler with only 6 inches in length. They’re useful for number line counting, skip counting, and all basic math functions.

#### Abacus

The abacus has been used for centuries and remains a popular method of counting today. Originating with the ancient Romans, this counting frame comes in multiple styles and designs. With a wooden frame holding parallel rods, movable counting objects are strung on the rod and can slide back and forth.

## Mastering math with manipulatives

Despite textbook writers’ best efforts, teaching abstract math concepts without manipulatives is a tough task. Most students have difficulty comprehending this type of two-dimensional, text-based learning. Although some may easily process it, the majority prefer to engage with math through physical interaction. For these reasons, using manipulatives in lessons can significantly help learners better understand complicated mathematics topics.

Using math manipulatives offers students a comprehensive, multi-sensory experience that provides an opportunity for creative exploration. Furthermore, it allows students to personalize their education in mathematics, fostering self-confidence and mastery not achievable through traditional textbook practices.

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