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Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.

Number & Operations (Grades Pre-K - 2)

Bar Chart icon Bar Chart – Create a bar chart showing quantities or percentages by labeling columns and clicking on values.
Base Blocks icon Base Blocks – Illustrate addition and subtraction in a variety of bases.
Base Blocks Addition icon Base Blocks Addition – Use base ten blocks to model grouping in addition.
Base Blocks Decimals icon Base Blocks Decimals – Add and subtract decimal values using base blocks.
Base Blocks Subtraction icon Base Blocks Subtraction – Use base ten blocks to model separation of groups in subtraction.
Chip Abacus icon Chip Abacus – Learn about carrying and digits using chips.
Circle 99 icon Circle 99 – A puzzle involving adding positive and negative integers to sum to ninety nine.
Color Chips - Addition icon Color Chips - Addition – Use color chips to illustrate addition of integers.
Color Patterns icon Color Patterns – Arrange colors to complete a pattern.
Diffy icon Diffy – Solve an interesting puzzle involving the differences of given numbers.
Fraction Bars icon Fraction Bars – Learn about fractions using fraction bars.
Fractions - Naming icon Fractions - Naming – Write the fraction corresponding to the highlighted portion of a shape.
Fractions - Parts of a Whole icon Fractions - Parts of a Whole – Relates parts of a whole unit to written description and fraction.
Fractions - Visualizing icon Fractions - Visualizing – Illustrate a fraction by dividing a shape and highlighting the appropriate parts.
Hundreds Chart icon Hundreds Chart – Practice counting and visualize number patterns using a hundreds chart.
Mastermind icon Mastermind – Use inference and logic to play a game and guess a hidden pattern of pegs.
Money icon Money – Learn about money by counting and making change.
Number Line Arithmetic icon Number Line Arithmetic – Illustrates arithmetic operations using a number line.
Number Line Bars icon Number Line Bars – Use bars to show addition, subtraction, multiplication, and division on a number line.
Number Line Bars - Fractions icon Number Line Bars - Fractions – Divide fractions using number line bars.
Number Line Bounce icon Number Line Bounce – Number line addition and subtraction game.
Number Patterns icon Number Patterns – Discover the pattern and complete a sequence of numbers.
Percentages icon Percentages – Discover relationships between fractions, percents, and decimals.
Pie Chart icon Pie Chart – Explore percentages and fractions using pie charts.
Place Value Number Line icon Place Value Number Line – Explore place value by placing dots on number lines.
Rectangle Division icon Rectangle Division – Visualize and practice dividing numbers by using an area representation.
Rectangle Multiplication icon Rectangle Multiplication – Visualize the multiplication of two numbers as an area.
Rectangle Multiplication of Integers icon Rectangle Multiplication of Integers – Visualize and practice multiplying integers using an area representation.
Sieve of Eratosthenes icon Sieve of Eratosthenes – Relate number patterns with visual patterns.
Spinners icon Spinners – Work with spinners to learn about numbers and probabilities.

Number & Operations (Grades 3 - 5)

Abacus icon Abacus – An electronic abacus that can be used to do arithmetic.
Bar Chart icon Bar Chart – Create a bar chart showing quantities or percentages by labeling columns and clicking on values.
Base Blocks icon Base Blocks – Illustrate addition and subtraction in a variety of bases.
Base Blocks Addition icon Base Blocks Addition – Use base ten blocks to model grouping in addition.
Base Blocks Decimals icon Base Blocks Decimals – Add and subtract decimal values using base blocks.
Base Blocks Subtraction icon Base Blocks Subtraction – Use base ten blocks to model separation of groups in subtraction.
Chip Abacus icon Chip Abacus – Learn about carrying and digits using chips.
Circle 0 icon Circle 0 – A puzzle involving adding positive and negative integers to sum to zero.
Circle 21 icon Circle 21 – A puzzle involving adding positive and negative integers to sum to twenty one.
Circle 3 icon Circle 3 – A puzzle involving adding positive real numbers to sum to three.
Circle 99 icon Circle 99 – A puzzle involving adding positive and negative integers to sum to ninety nine.
Color Chips - Addition icon Color Chips - Addition – Use color chips to illustrate addition of integers.
Color Chips - Subtraction icon Color Chips - Subtraction – Use color chips to illustrate subtraction of integers.
Color Patterns icon Color Patterns – Arrange colors to complete a pattern.
Diffy icon Diffy – Solve an interesting puzzle involving the differences of given numbers.
Factor Tree icon Factor Tree – Factor numbers using a tree diagram.
Fraction Bars icon Fraction Bars – Learn about fractions using fraction bars.
Fraction Pieces icon Fraction Pieces – Work with parts and wholes to learn about fractions.
Fractions - Adding icon Fractions - Adding – Illustrates what it means to find a common denominator and combine.
Fractions - Comparing icon Fractions - Comparing – Judge the size of fractions and plot them on a number line.
Fractions - Equivalent icon Fractions - Equivalent – Illustrates relationships between equivalent fractions.
Fractions - Naming icon Fractions - Naming – Write the fraction corresponding to the highlighted portion of a shape.
Fractions - Parts of a Whole icon Fractions - Parts of a Whole – Relates parts of a whole unit to written description and fraction.
Fractions - Rectangle Multiplication icon Fractions - Rectangle Multiplication – Visualize and practice multiplying fractions using an area representation.
Fractions - Visualizing icon Fractions - Visualizing – Illustrate a fraction by dividing a shape and highlighting the appropriate parts.
Grapher icon Grapher – A tool for graphing and exploring functions.
Hundreds Chart icon Hundreds Chart – Practice counting and visualize number patterns using a hundreds chart.
Mastermind icon Mastermind – Use inference and logic to play a game and guess a hidden pattern of pegs.
Money icon Money – Learn about money by counting and making change.
Number Line Arithmetic icon Number Line Arithmetic – Illustrates arithmetic operations using a number line.
Number Line Bars icon Number Line Bars – Use bars to show addition, subtraction, multiplication, and division on a number line.
Number Line Bars - Fractions icon Number Line Bars - Fractions – Divide fractions using number line bars.
Number Line Bounce icon Number Line Bounce – Number line addition and subtraction game.
Number Patterns icon Number Patterns – Discover the pattern and complete a sequence of numbers.
Number Puzzles icon Number Puzzles – Solve puzzles involving arranging numbers on a diagram so that they add up to a given value.
Peg Puzzle icon Peg Puzzle – Win this game by moving the pegs on the left past the pegs on the right.
Percent Grids icon Percent Grids – Represent, name, and explore percentages using hundreds grids.
Percentages icon Percentages – Discover relationships between fractions, percents, and decimals.
Pie Chart icon Pie Chart – Explore percentages and fractions using pie charts.
Place Value Number Line icon Place Value Number Line – Explore place value by placing dots on number lines.
Rectangle Division icon Rectangle Division – Visualize and practice dividing numbers by using an area representation.
Rectangle Multiplication icon Rectangle Multiplication – Visualize the multiplication of two numbers as an area.
Rectangle Multiplication of Integers icon Rectangle Multiplication of Integers – Visualize and practice multiplying integers using an area representation.
Sieve of Eratosthenes icon Sieve of Eratosthenes – Relate number patterns with visual patterns.
Tangrams icon Tangrams – Use all seven Chinese puzzle pieces to make shapes and solve problems.
Venn Diagrams icon Venn Diagrams – Investigate common features of sets.

Number & Operations (Grades 6 - 8)

Abacus icon Abacus – An electronic abacus that can be used to do arithmetic.
Base Blocks icon Base Blocks – Illustrate addition and subtraction in a variety of bases.
Base Blocks Addition icon Base Blocks Addition – Use base ten blocks to model grouping in addition.
Base Blocks Decimals icon Base Blocks Decimals – Add and subtract decimal values using base blocks.
Base Blocks Subtraction icon Base Blocks Subtraction – Use base ten blocks to model separation of groups in subtraction.
Chip Abacus icon Chip Abacus – Learn about carrying and digits using chips.
Circle 0 icon Circle 0 – A puzzle involving adding positive and negative integers to sum to zero.
Circle 21 icon Circle 21 – A puzzle involving adding positive and negative integers to sum to twenty one.
Circle 3 icon Circle 3 – A puzzle involving adding positive real numbers to sum to three.
Circle 99 icon Circle 99 – A puzzle involving adding positive and negative integers to sum to ninety nine.
Color Chips - Subtraction icon Color Chips - Subtraction – Use color chips to illustrate subtraction of integers.
Conway's Game of Life icon Conway's Game of Life – Discover the rules that determine change in these simulations.
Diffy icon Diffy – Solve an interesting puzzle involving the differences of given numbers.
Dueling Calculators icon Dueling Calculators – Visualize a dramatic simulation of the effect of propagating rounding errors.
Factor Tree icon Factor Tree – Factor numbers using a tree diagram.
Fibonacci Sequence icon Fibonacci Sequence – Explore the Fibonacci sequence and the golden ratio.
Fraction Pieces icon Fraction Pieces – Work with parts and wholes to learn about fractions.
Fractions - Adding icon Fractions - Adding – Illustrates what it means to find a common denominator and combine.
Fractions - Comparing icon Fractions - Comparing – Judge the size of fractions and plot them on a number line.
Fractions - Equivalent icon Fractions - Equivalent – Illustrates relationships between equivalent fractions.
Fractions - Rectangle Multiplication icon Fractions - Rectangle Multiplication – Visualize and practice multiplying fractions using an area representation.
Function Machine icon Function Machine – Explore the concept of functions by putting values into this machine and observing its output.
Golden Rectangle icon Golden Rectangle – Illustrates iterations of the Golden Section.
Grapher icon Grapher – A tool for graphing and exploring functions.
Mastermind icon Mastermind – Use inference and logic to play a game and guess a hidden pattern of pegs.
Money icon Money – Learn about money by counting and making change.
Number Line Bars - Fractions icon Number Line Bars - Fractions – Divide fractions using number line bars.
Number Line Bounce icon Number Line Bounce – Number line addition and subtraction game.
Number Puzzles icon Number Puzzles – Solve puzzles involving arranging numbers on a diagram so that they add up to a given value.
Pascal's Triangle icon Pascal's Triangle – Explore patterns created by selecting elements of Pascal's triangle.
Peg Puzzle icon Peg Puzzle – Win this game by moving the pegs on the left past the pegs on the right.
Percent Grids icon Percent Grids – Represent, name, and explore percentages using hundreds grids.
Percentages icon Percentages – Discover relationships between fractions, percents, and decimals.
Sieve of Eratosthenes icon Sieve of Eratosthenes – Relate number patterns with visual patterns.
Spinners icon Spinners – Work with spinners to learn about numbers and probabilities.
Tangrams icon Tangrams – Use all seven Chinese puzzle pieces to make shapes and solve problems.
Tight Weave icon Tight Weave – Visualize the creation of the Sierpinski Carpet, an iterative geometric pattern that resembles a woven mat.
Turtle Geometry icon Turtle Geometry – Explore numbers, shapes, and logic by programming a turtle to move.
Venn Diagrams icon Venn Diagrams – Investigate common features of sets.

Number & Operations (Grades 9 - 12)

Abacus icon Abacus – An electronic abacus that can be used to do arithmetic.
Circle 0 icon Circle 0 – A puzzle involving adding positive and negative integers to sum to zero.
Circle 21 icon Circle 21 – A puzzle involving adding positive and negative integers to sum to twenty one.
Circle 3 icon Circle 3 – A puzzle involving adding positive real numbers to sum to three.
Circle 99 icon Circle 99 – A puzzle involving adding positive and negative integers to sum to ninety nine.
Conway's Game of Life icon Conway's Game of Life – Discover the rules that determine change in these simulations.
Counting All Pairs icon Counting All Pairs – Create a path that sets up a one-to-one correspondence between the counting numbers and infinite sets of ordered pairs of integers.
Diffy icon Diffy – Solve an interesting puzzle involving the differences of given numbers.
Dueling Calculators icon Dueling Calculators – Visualize a dramatic simulation of the effect of propagating rounding errors.
Fibonacci Sequence icon Fibonacci Sequence – Explore the Fibonacci sequence and the golden ratio.
Fractions - Adding icon Fractions - Adding – Illustrates what it means to find a common denominator and combine.
Fractions - Equivalent icon Fractions - Equivalent – Illustrates relationships between equivalent fractions.
Function Machine icon Function Machine – Explore the concept of functions by putting values into this machine and observing its output.
Golden Rectangle icon Golden Rectangle – Illustrates iterations of the Golden Section.
Grapher icon Grapher – A tool for graphing and exploring functions.
Mastermind icon Mastermind – Use inference and logic to play a game and guess a hidden pattern of pegs.
Number Puzzles icon Number Puzzles – Solve puzzles involving arranging numbers on a diagram so that they add up to a given value.
Pascal's Triangle icon Pascal's Triangle – Explore patterns created by selecting elements of Pascal's triangle.
Peg Puzzle icon Peg Puzzle – Win this game by moving the pegs on the left past the pegs on the right.
Percentages icon Percentages – Discover relationships between fractions, percents, and decimals.
Rational Numbers Triangle icon Rational Numbers Triangle – Explore a triangular array that contains every positive rational number exactly once.
Sieve of Eratosthenes icon Sieve of Eratosthenes – Relate number patterns with visual patterns.
Tight Weave icon Tight Weave – Visualize the creation of the Sierpinski Carpet, an iterative geometric pattern that resembles a woven mat.
Turtle Geometry icon Turtle Geometry – Explore numbers, shapes, and logic by programming a turtle to move.
Venn Diagrams icon Venn Diagrams – Investigate common features of sets.
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