NLVM 9 - 12 Manipulatives
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All Topics (Grades 9 - 12)

Virtual manipulatives for grades 9 - 12.

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.

Algebra (Grades 9 - 12)

Algebra Balance Scales icon Algebra Balance Scales – Solve simple linear equations using a balance beam representation.
Algebra Balance Scales - Negatives icon Algebra Balance Scales - Negatives – Solve simple linear equations using a balance beam representation.
Algebra Tiles icon Algebra Tiles – Visualize multiplying and factoring algebraic expressions using tiles.
Base Blocks icon Base Blocks – Illustrate addition and subtraction in a variety of bases.
Block Patterns icon Block Patterns – Analyze sequences of figures using pictures, tables, plots, and graphs.
Coin Problem icon Coin Problem – Use deduction to find the counterfeit coin.
Fifteen Puzzle icon Fifteen Puzzle – Solve this virtual version of the classical fifteen puzzle by arranging its tiles.
Function Machine icon Function Machine – Explore the concept of functions by putting values into this machine and observing its output.
Function Transformations icon Function Transformations – Explore how simple transformations affect the graph of a function.
Grapher icon Grapher – A tool for graphing and exploring functions.
Line Plotter icon Line Plotter – Practice drawing lines through a given point having a specified slope.
Pattern Blocks icon Pattern Blocks – Use six common geometric shapes to build patterns and solve problems.
Peg Puzzle icon Peg Puzzle – Win this game by moving the pegs on the left past the pegs on the right.
Pentominoes icon Pentominoes – Use the 12 pentomino combinations to solve problems.
Point Plotter icon Point Plotter – Practice plotting ordered pairs on a graph.
Polyominoes icon Polyominoes – Build and compare characteristics of biominoes, triominoes, quadrominoes, etc.
Stick or Switch icon Stick or Switch – Investigate probabilities of sticking with a decision, or switching.
Towers of Hanoi icon Towers of Hanoi – Solve the tower problem and test your theory by varying the number of disks.

Geometry (Grades 9 - 12)

Cob Web Plot icon Cob Web Plot – Change variables and observe patterns from this graphing simulation.
Fractals - Iterative icon Fractals - Iterative – Generate six different fractals.
Fractals - Koch and Sierpinski icon Fractals - Koch and Sierpinski – Change colors and pause this fractal simulation at any point.
Fractals - Mandelbrot and Julia Sets icon Fractals - Mandelbrot and Julia Sets – Investigate relationships between these two fractal sets.
Fractals - Polygonal icon Fractals - Polygonal – Change the parameters to create a new fractal.
Geoboard icon Geoboard – Use geoboards to illustrate area, perimeter, and rational number concepts.
Geoboard - Circular icon Geoboard - Circular – Use circular geoboards to illustrate angles and degrees.
Geoboard - Coordinate icon Geoboard - Coordinate – Rectangular geoboard with x and y coordinates.
Geoboard - Isometric icon Geoboard - Isometric – Use geoboard to illustrate three-dimensional shapes.
Golden Rectangle icon Golden Rectangle – Illustrates iterations of the Golden Section.
Great Circle icon Great Circle – Use a 3D globe to visualize and measure the shortest path between cities.
Pattern Blocks icon Pattern Blocks – Use six common geometric shapes to build patterns and solve problems.
Pinwheel Tiling icon Pinwheel Tiling – Construct and explore a very unusual tiling of the plane by right triangles.
Platonic Solids icon Platonic Solids – Identify characteristics of the Platonic Solids.
Platonic Solids - Duals icon Platonic Solids - Duals – Identify the duals of the platonic solids.
Platonic Solids - Slicing icon Platonic Solids - Slicing – Discover shapes and relationships between slices of the platonic solids.
Polyominoes icon Polyominoes – Build and compare characteristics of biominoes, triominoes, quadrominoes, etc.
Pythagorean Theorem icon Pythagorean Theorem – Solve two puzzles that illustrate the proof of the Pythagorean Theorem.
Right Triangle Solver icon Right Triangle Solver – Practice using the Pythagorean theorem and the definitions of the trigonometric functions to solve for unknown sides and angles of a right triangle.
Space Blocks icon Space Blocks – Create and discover patterns using three dimensional blocks.
Tangrams icon Tangrams – Use all seven Chinese puzzle pieces to make shapes and solve problems.
Tessellations icon Tessellations – Using regular and semi-regular tessellations to tile the plane.
Tight Weave icon Tight Weave – Visualize the creation of the Sierpinski Carpet, an iterative geometric pattern that resembles a woven mat.
Transformations - Composition icon Transformations - Composition – Explore the effect of applying a composition of translation, rotation, and reflection transformations to objects.
Transformations - Dilation icon Transformations - Dilation – Dynamically interact with and see the result of a dilation transformation.
Transformations - Reflection icon Transformations - Reflection – Dynamically interact with and see the result of a reflection transformation.
Transformations - Rotation icon Transformations - Rotation – Dynamically interact with and see the result of a rotation transformation.
Transformations - Translation icon Transformations - Translation – Dynamically interact with and see the result of a translation transformation.
Triangle Solver icon Triangle Solver – Practice using the law of sines and the law of cosines to solve for unknown sides and angles of a triangle.
Turtle Geometry icon Turtle Geometry – Explore numbers, shapes, and logic by programming a turtle to move.

Measurement (Grades 9 - 12)

Converting Units icon Converting Units – Use a simple system for converting units.
Fill and Pour icon Fill and Pour – Solve puzzles requiring you to fill and pour containers.
Geoboard icon Geoboard – Use geoboards to illustrate area, perimeter, and rational number concepts.
Geoboard - Circular icon Geoboard - Circular – Use circular geoboards to illustrate angles and degrees.
Great Circle icon Great Circle – Use a 3D globe to visualize and measure the shortest path between cities.
How High? icon How High? – Try your hand at the classic Piagetian conservation of volume test.
Pattern Blocks icon Pattern Blocks – Use six common geometric shapes to build patterns and solve problems.

Data Analysis & Probability (Grades 9 - 12)

Bar Chart icon Bar Chart – Create a bar chart showing quantities or percentages by labeling columns and clicking on values.
Box Model icon Box Model – Randomly selects and displays draws from a box.
Box Plot icon Box Plot – Use this tool to summarize data using a box plot graph.
Coin Tossing icon Coin Tossing – Explore probability concepts by simulating repeated coin tosses.
Hamlet Happens icon Hamlet Happens – Verify that rare events happen by drawing letters from a box.
Histogram icon Histogram – Use this tool to summarize data using a histogram graph.
Loan Calculator icon Loan Calculator – Explore how to pay off a loan, and how interest affects payment.
Pascal's Triangle icon Pascal's Triangle – Explore patterns created by selecting elements of Pascal's triangle.
Pie Chart icon Pie Chart – Explore percentages and fractions using pie charts.
Savings Calculator icon Savings Calculator – Explore how savings, with or without regular deposits, grow over time.
Scatterplot icon Scatterplot – Plot multiple data points in two dimensions and determine correlation.
Spinners icon Spinners – Work with spinners to learn about numbers and probabilities.
Stick or Switch icon Stick or Switch – Investigate probabilities of sticking with a decision, or switching.
Whammy Awards icon Whammy Awards – See how using different voting schemes can result in contradictory outcomes.
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