# Glossary of Math Manipulatives

This glossary of hands-on manipulatives was created to help teachers learn about and use manipulatives in their regular classroom settings. Though there are dozens of different manipulatives that can be used to educate students, the pedagogical basis for using one is the same: firsthand interaction with manipulatives helps students understand mathematics. Manipulatives provide concrete ways for students to bring meaning to abstract mathematical ideas. They help students learn new concepts and relate new concepts to what they have already learned. They assist students with solving problems. When students explore with manipulatives, they have the opportunity to see mathematical relationships. They have tactile and visual models that help develop their understanding. Without these concrete references, students are too often lost in a morass of abstract symbols for which they have no concrete connection or comprehension. Teachers need to learn how to make use of concrete manipulatives so that students learn the how and why of mathematics concepts. Students’ thinking and reasoning must be the top priorities when they are engaged in learning with manipulatives. The concrete manipulatives and the activities for which they are used are only as valuable as the students’ reflection on the mathematical concepts.

## Browse our List of Math Manipulatives by Subject

## Algebra

### Algebra Tiles

Algebra Tiles involve students in learning algebraic concepts, including adding and subtracting polynomials, factoring trinomials, the Zero Principle, and solving first and second degree equations. Each tile represents the quantities x, x2, and 1 along with their additive inverses.

### Geoboards

The double-sided Geoboard is 7.5 inch square and made of plastic. One side has a 5 &time 5 peg grid. The other has a circle with a 12-peg radius. Students stretch rubber bands from peg to peg to form geometric shapes. Geoboards can be used to study symmetry, congruency, area, and perimeter.

### XY Coordinate Pegboards

XY Coordinate Pegboards can be used to graph coordinates in one, two, or four quadrants; show translations of geometric figures; display data in various forms; and demonstrate numerous algebraic concepts and relationships.

## Counting & Sorting

### Base Ten Blocks

Base Ten Blocks are constructed in powers of ten, representing ones, tens, hundreds, and thousands. The materials include 1-centimeter unit cubes to represent ones, 10-centimeter rods to represent tens, and 10-centimeter square blocks to represent hundreds. They can be used to teach number and place value concepts, such as the use of regrouping in addition and subtraction. They can also be used to teach measurement concepts, such as area and volume. Place Value Mats serve as organizers.

### Color Cubes

Color Cubes are available in manipulate® and wood, and six different colors in a set: red, orange, yellow, green, blue, and purple. They help children through hands-on exploration of basic mathematics and geometric relationships as they stack, count, sort, and work with patterns.

### Color Tiles

Color Tiles are a collection of square tiles, one inch on a side, in four colors–red, blue, yellow, and green. The tiles have applications in all areas of the math curriculum. They are useful for counting, estimating, measuring, building understanding of place value, investigating multiplication patterns, solving problems with fractions, exploring geometric shapes, carrying out probability experiments, and more. A supply of these tiles provides versatile assistance to math instruction at all grade levels.

### Cuisenaire® Rods

Cuisenaire Rods include Rods of 10 different colors, each corresponding to a specific length. White Rods, the shortest, are 1 cm long. Orange rods, the longest, are 10 cm long. Rods allow students to explore all fundamental math concepts, including addition and patterning, multiplication, division, fractions and decimals, and data analysis.

### Rekenrek

A Rekenrek is an arithmetic frame designed to help children visualize addition and subtraction strategies. The 20-bead Rekenrek features two rows of 10 beads. Each of these sets of ten are broken into two sets of 5 beads using contrasting colors–red and white–to help children see numbers, as well as to visualize how numbers can be composed and decomposed. The Rekenrek combines features of the number line, individual counters, and base-ten models such as Base Ten Blocks. This model allows for children to think in groups of those benchmark numbers, 5 and 10.

### Snap Cubes®

Each side of a Snap Cube can be connected to another cube. Cubes can be used to teach a variety of different math concepts. Use cubes to explore number sense and operations with activities involving counting, place value, addition, and subtraction. Or use cubes to show measuring using nonstandard units. Cubes can also be used to demonstrate patterning and basic geometry.

### Two-Color Counters

These versatile Two-Color Counters are thicker than most other counters and easy for students to manipulate. They can be used to teach number and operations concepts, such as patterning, addition and subtraction, and multiplication and division. Counters can also be used to introduce students to basic ideas of probability.

## Geometry

### AngLegs®

AngLegs enable students to study polygons, perimeter, area, angle measurement, side lengths, and more. The set includes 72 snap-together AngLegs pieces (12 each of six different lengths) and two snap-on View Thru® protractors.

### Attribute Blocks

The Attribute Blocks set includes five basic shapes (triangle, square, rectangle, circle, and hexagon) displaying different attributes. The basic shapes come in three different colors, two different sizes, and two different thicknesses. Attribute Blocks can be used to teach sorting, patterns, and identifying attributes.

### Color Cubes

Color Cubes are available in manipulate® and wood, and six different colors in a set: red, orange, yellow, green, blue, and purple. They help children through hands-on exploration of basic mathematics and geometric relationships as they stack, count, sort, and work with patterns.

### Color Tiles

Color Tiles are a collection of square tiles, one inch on a side, in four colors–red, blue, yellow, and green. The tiles have applications in all areas of the math curriculum. They are useful for counting, estimating, measuring, building understanding of place value, investigating multiplication patterns, solving problems with fractions, exploring geometric shapes, carrying out probability experiments, and more. A supply of these tiles provides versatile assistance to math instruction at all grade levels.

### Geoboards

The double-sided Geoboard is 7.5 inch square and made of plastic. One side has a 5 &time 5 peg grid. The other has a circle with a 12-peg radius. Students stretch rubber bands from peg to peg to form geometric shapes. Geoboards can be used to study symmetry, congruency, area, and perimeter.

### Pattern Blocks

Pattern Blocks are a collection of six shapes in six colors—green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons. The shapes are designed so that the sides are all the same length except for the trapezoid, which has one side that is twice as long. This feature makes it possible for the shapes to nest together and provides for a wide range of explorations.

### Relational Geosolids

Relational GeoSolids are 14 three-dimensional shapes that can be used to teach about prisms, pyramids, spheres, cylinders, cones, and hemispheres. GeoSolids facilitate classroom demonstrations and experimentation. The shapes can be filled with water, sand, rice, or other materials to give students a concrete framework for the study of volume.

### Snap Cubes®

Each side of a Snap Cube can be connected to another cube. Cubes can be used to teach a variety of different math concepts. Use cubes to explore number sense and operations with activities involving counting, place value, addition, and subtraction. Or use cubes to show measuring using nonstandard units. Cubes can also be used to demonstrate patterning and basic geometry.

### Tangrams

Tangrams are ancient Chinese puzzles made of seven three- and four-sided shapes. Each set of tangrams contains four tangram puzzles in four different colors. Each puzzle consists of five triangles (two small, one medium, and two large), a square, and a parallelogram. Tangrams can be used to solve puzzles in which all seven pieces must be put together to create a specified shape. Tangram puzzles teach many geometric concepts, including symmetry, congruency, transformations, and problem solving.

### XY Coordinate Pegboards

XY Coordinate Pegboards can be used to graph coordinates in one, two, or four quadrants; show translations of geometric figures; display data in various forms; and demonstrate numerous algebraic concepts and relationships.

## Fractions, Decimals, and Percents

### Cuisenaire® Rods

Cuisenaire Rods include Rods of 10 different colors, each corresponding to a specific length. White Rods, the shortest, are 1 cm long. Orange rods, the longest, are 10 cm long. Rods allow students to explore all fundamental math concepts, including addition and patterning, multiplication, division, fractions and decimals, and data analysis.

### Deluxe Rainbow Fraction® Circles

The set consists of nine color-coded, 3 ½ inch plastic circles representing a whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths. The circles enable students to explore fractions, fractional equivalences, the fractional components of circle graphs, and more.

### Deluxe Rainbow Fraction® Squares

The set consists of nine color-coded, 10-cm plastic squares representing a whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths. The squares enable students to explore fractions, fractional equivalences, and more.

### Fraction Tower® Equivalency Cubes

Faction Tower Equivalency Cubes snap together to demonstrate fractions, decimals, and percentages. Each tower is divided into stacking cubes that represent a whole, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths. Each cube is labeled with the part of a whole that it represents. One side shows the fraction, another shows the decimal, and a third shows the percentage. The fourth side is blank. Students can turn the cubes or towers to see each of the representations of the same value. Towers, or portions of towers, can be compared with each other.

### Two-Color Counters

These versatile Two-Color Counters are thicker than most other counters and easy for students to manipulate. They can be used to teach number and operations concepts, such as patterning, addition and subtraction, and multiplication and division. Counters can also be used to introduce students to basic ideas of probability.

## Measurement

### Bucket Balance

The Bucket Balance features removable 1/2- liter buckets. The buckets are clear to help students see what they are measuring. Measure 16"L x 5.75"W x 5"H. The balance helps students explore the measurement of mass with accuracy to 1 gram.

### Color Tiles

Color Tiles are a collection of square tiles, one inch on a side, in four colors–red, blue, yellow, and green. The tiles have applications in all areas of the math curriculum. They are useful for counting, estimating, measuring, building understanding of place value, investigating multiplication patterns, solving problems with fractions, exploring geometric shapes, carrying out probability experiments, and more. A supply of these tiles provides versatile assistance to math instruction at all grade levels.

### Snap Cubes®

Each side of a Snap Cube can be connected to another cube. Cubes can be used to teach a variety of different math concepts. Use cubes to explore number sense and operations with activities involving counting, place value, addition, and subtraction. Or use cubes to show measuring using nonstandard units. Cubes can also be used to demonstrate patterning and basic geometry.

## Operations

### Base Ten Blocks

Base Ten Blocks are constructed in powers of ten, representing ones, tens, hundreds, and thousands. The materials include 1-centimeter unit cubes to represent ones, 10-centimeter rods to represent tens, and 10-centimeter square blocks to represent hundreds. They can be used to teach number and place value concepts, such as the use of regrouping in addition and subtraction. They can also be used to teach measurement concepts, such as area and volume. Place Value Mats serve as organizers.

### Cuisenaire® Rods

Cuisenaire Rods include Rods of 10 different colors, each corresponding to a specific length. White Rods, the shortest, are 1 cm long. Orange rods, the longest, are 10 cm long. Rods allow students to explore all fundamental math concepts, including addition and patterning, multiplication, division, fractions and decimals, and data analysis.

### Rekenrek

A Rekenrek is an arithmetic frame designed to help children visualize addition and subtraction strategies. The 20-bead Rekenrek features two rows of 10 beads. Each of these sets of ten are broken into two sets of 5 beads using contrasting colors–red and white–to help children see numbers, as well as to visualize how numbers can be composed and decomposed. The Rekenrek combines features of the number line, individual counters, and base-ten models such as Base Ten Blocks. This model allows for children to think in groups of those benchmark numbers, 5 and 10.

### Snap Cubes®

### Two-Color Counters

These versatile Two-Color Counters are thicker than most other counters and easy for students to manipulate. They can be used to teach number and operations concepts, such as patterning, addition and subtraction, and multiplication and division. Counters can also be used to introduce students to basic ideas of probability.

## Patterns & Attributes

### Attribute Blocks

The Attribute Blocks set includes five basic shapes (triangle, square, rectangle, circle, and hexagon) displaying different attributes. The basic shapes come in three different colors, two different sizes, and two different thicknesses. Attribute Blocks can be used to teach sorting, patterns, and identifying attributes.

### Color Cubes

Color Cubes are available in manipulate® and wood, and six different colors in a set: red, orange, yellow, green, blue, and purple. They help children through hands-on exploration of basic mathematics and geometric relationships as they stack, count, sort, and work with patterns.

### Color Tiles

### Cuisenaire® Rods

### Pattern Blocks

Pattern Blocks are a collection of six shapes in six colors—green triangles, orange squares, blue parallelograms, tan rhombuses, red trapezoids, and yellow hexagons. The shapes are designed so that the sides are all the same length except for the trapezoid, which has one side that is twice as long. This feature makes it possible for the shapes to nest together and provides for a wide range of explorations.

### Snap Cubes®

### Two-Color Counters

## Place Value

### Base Ten Blocks

Base Ten Blocks are constructed in powers of ten, representing ones, tens, hundreds, and thousands. The materials include 1-centimeter unit cubes to represent ones, 10-centimeter rods to represent tens, and 10-centimeter square blocks to represent hundreds. They can be used to teach number and place value concepts, such as the use of regrouping in addition and subtraction. They can also be used to teach measurement concepts, such as area and volume. Place Value Mats serve as organizers.

### Color Tiles

### Cuisenaire® Rods

### Snap Cubes®

## Probability

### Two-Color Counters

## Time

### Geared Clocks

These Geared Clocks are made of plastic and have hidden gears that reflect accurate hour and minute hands are color-coded to match hour and minute markings on the clock face. Clocks allow children to explore telling time on analog clocks and calculating elapsed time.