Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.

Number & Operations (Grades Pre-K - 2)

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

Number & Operations (Grades 3 - 5)

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

Number & Operations (Grades 6 - 8)

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

Number & Operations (Grades 9 - 12)

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