Math Apps & Digital Manipulatives

I Know It  I Know It is a comprehensive, interactive math practice site for students K-5.  

Mathigon – Polypad Manipulatives

Elementary and secondary teachers will love Mathigon’s Polypad, a highly interactive digital canvas with a growing collection of math manipulatives and backgrounds. Use the Question builder to overlay questions and answer checks on the canvas. Teacher-created Polypads can be shared to Google Classroom as assignments. But that’s not all! Mathigon is an incredible, award-winning resource for teachers looking for an alternative to traditional math textbooks. The site offers a wide range of free content to provide students with meaningful math experiences to develop mathematical thinking skills. The site is continually adding new content and provides a collection of tutorial webinars.

National Learning Virtual Manipulatives  

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Abacus — An electronic abacus that can be used to do arithmetic. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Algebra Balance Scales — Solve simple linear equations using a balance beam representation. Algebra (6–8), Algebra (9–12)

Algebra Balance Scales - Negatives — Solve simple linear equations using a balance beam representation. Algebra (6–8), Algebra (9–12)

Algebra Tiles — Visualize multiplying and factoring algebraic expressions using tiles. Algebra (Pre-K–2), Algebra (3–5), Algebra (6–8), Algebra (9–12)

Attribute Blocks — Learn color and shape concepts by sorting blocks. Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–5), Measurement (3–5)

Attribute Trains — Learn about shape and color patterns of by completing trains of blocks. Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–5), Measurement (3–5), Geometry (6–8), Measurement (6–8)

Bar Chart — Create a bar chart showing quantities or percentages by labeling columns and clicking on values. Number & Operations (Pre-K–2), Data Analysis & Probability (Pre-K–2), Number & Operations (3–5), Data Analysis & Probability (3–5), Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Base Blocks — Illustrate addition and subtraction in a variety of bases. Number & Operations (Pre-K–2), Number & Operations (3–5), Algebra (3–5), Number & Operations (6–8), Algebra (6–8), Algebra (9–12)

Base Blocks Addition — Use base ten blocks to model grouping in addition. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Base Blocks Decimals — Add and subtract decimal values using base blocks. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Base Blocks Subtraction — Use base ten blocks to model separation of groups in subtraction. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Block Patterns — Analyze sequences of figures using pictures, tables, plots, and graphs. Algebra (6–8), Algebra (9–12)

Box Model — Randomly selects and displays draws from a box. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Box Plot — Use this tool to summarize data using a box plot graph. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Chip Abacus — Learn about carrying and digits using chips. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Circle 0 — A puzzle involving adding positive and negative integers to sum to zero. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Circle 21 — A puzzle involving adding positive and negative integers to sum to twenty one. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Circle 3 — A puzzle involving adding positive real numbers to sum to three. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Circle 99 — A puzzle involving adding positive and negative integers to sum to ninety nine. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Cob Web Plot — Change variables and observe patterns from this graphing simulation. Geometry (6–8), Geometry (9–12)

Coin Problem — Use deduction to find the counterfeit coin. Algebra (6–8), Algebra (9–12)

Coin Tossing — Explore probability concepts by simulating repeated coin tosses. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Color Chips - Addition — Use color chips to illustrate addition of integers. Number & Operations (Pre-K–2), Number & Operations (3–5)

Color Chips - Subtraction — Use color chips to illustrate subtraction of integers. Number & Operations (3–5), Number & Operations (6–8)

Color Patterns — Arrange colors to complete a pattern. Number & Operations (Pre-K–2), Algebra (Pre-K–2), Number & Operations (3–5), Algebra (3–5)

Congruent Triangles — Build similar triangles by combining sides and angles. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8)

Converting Units — Use a simple system for converting units. Measurement (3–5), Measurement (6–8), Measurement (9–12)

Conway's Game of Life — Discover the rules that determine change in these simulations. Number & Operations (6–8), Number & Operations (9–12)

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. Number & Operations (9–12)

Diffy — Solve an interesting puzzle involving the differences of given numbers. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Dueling Calculators — Visualize a dramatic simulation of the effect of propagating rounding errors. Number & Operations (6–8), Number & Operations (9–12)

Factor Tree — Factor numbers using a tree diagram. Number & Operations (3–5), Number & Operations (6–8), Algebra (6–8)

Fibonacci Sequence — Explore the Fibonacci sequence and the golden ratio. Number & Operations (6–8), Number & Operations (9–12)

Fifteen Puzzle — Solve this virtual version of the classical fifteen puzzle by arranging its tiles. Algebra (Pre-K–2), Algebra (3–5), Algebra (6–8), Algebra (9–12)

Fill and Pour — Solve puzzles requiring you to fill and pour containers. Measurement (3–5), Measurement (6–8), Measurement (9–12)

Fractals - Iterative — Generate six different fractals. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Fractals - Koch and Sierpinski — Change colors and pause this fractal simulation at any point. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Fractals - Mandelbrot and Julia Sets — Investigate relationships between these two fractal sets. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Fractals - Polygonal — Change the parameters to create a new fractal. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Fraction Bars — Learn about fractions using fraction bars. Number & Operations (Pre-K–2), Number & Operations (3–5)

Fraction Pieces — Work with parts and wholes to learn about fractions. Number & Operations (3–5), Number & Operations (6–8)

Fractions - Adding — Illustrates what it means to find a common denominator and combine. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Fractions - Comparing — Judge the size of fractions and plot them on a number line. Number & Operations (3–5), Number & Operations (6–8)

Fractions - Equivalent — Illustrates relationships between equivalent fractions. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Fractions - Naming — Write the fraction corresponding to the highlighted portion of a shape. Number & Operations (Pre-K–2), Number & Operations (3–5)

Fractions - Parts of a Whole — Relates parts of a whole unit to written description and fraction. Number & Operations (Pre-K–2), Number & Operations (3–5)

Fractions - Rectangle Multiplication — Visualize and practice multiplying fractions using an area representation. Number & Operations (3–5), Number & Operations (6–8)

Fractions - Visualizing — Illustrate a fraction by dividing a shape and highlighting the appropriate parts. Number & Operations (Pre-K–2), Number & Operations (3–5)

Function Machine — Explore the concept of functions by putting values into this machine and observing its output. Number & Operations (6–8), Algebra (6–8), Number & Operations (9–12), Algebra (9–12)

Function Transformations — Explore how simple transformations affect the graph of a function. Algebra (6–8), Algebra (9–12)

Geoboard — Use geoboards to illustrate area, perimeter, and rational number concepts. Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–5), Measurement (3–5), Geometry (6–8), Measurement (6–8), Geometry (9–12), Measurement (9–12)

Geoboard - Circular — Use circular geoboards to illustrate angles and degrees. Geometry (3–5), Measurement (3–5), Geometry (6–8), Measurement (6–8), Geometry (9–12), Measurement (9–12)

Geoboard - Coordinate — Rectangular geoboard with x and y coordinates. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Geoboard - Isometric — Use geoboard to illustrate three-dimensional shapes. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Golden Rectangle — Illustrates iterations of the Golden Section. Geometry (3–5), Number & Operations (6–8), Geometry (6–8), Number & Operations (9–12), Geometry (9–12)

Grapher — A tool for graphing and exploring functions. Number & Operations (3–5), Algebra (3–5), Number & Operations (6–8), Algebra (6–8), Number & Operations (9–12), Algebra (9–12)

Great Circle — Use a 3D globe to visualize and measure the shortest path between cities. Geometry (6–8), Measurement (6–8), Geometry (9–12), Measurement (9–12)

Hamlet Happens — Verify that rare events happen by drawing letters from a box. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Histogram — Use this tool to summarize data using a histogram graph. Data Analysis & Probability (3–5), Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

How High? — Try your hand at the classic Piagetian conservation of volume test. Geometry (6–8), Measurement (6–8), Measurement (9–12)

Hundreds Chart — Practice counting and visualize number patterns using a hundreds chart. Number & Operations (Pre-K–2), Number & Operations (3–5)

Ladybug Leaf — Program a ladybug to hide behind a leaf. Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–5), Measurement (3–5), Geometry (6–8), Measurement (6–8)

Ladybug Mazes — Program a ladybug to move through a maze. Geometry (Pre-K–2), Measurement (Pre-K–2), Geometry (3–5), Measurement (3–5), Geometry (6–8), Measurement (6–8)

Line Plotter — Practice drawing lines through a given point having a specified slope. Algebra (6–8), Algebra (9–12)

Loan Calculator — Explore how to pay off a loan, and how interest affects payment. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Mastermind — Use inference and logic to play a game and guess a hidden pattern of pegs. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Money — Learn about money by counting and making change. Number & Operations (Pre-K–2), Measurement (Pre-K–2), Number & Operations (3–5), Measurement (3–5), Number & Operations (6–8), Measurement (6–8)

Number Line Arithmetic — Illustrates arithmetic operations using a number line. Number & Operations (Pre-K–2), Number & Operations (3–5)

Number Line Bars — Use bars to show addition, subtraction, multiplication, and division on a number line. Number & Operations (Pre-K–2), Number & Operations (3–5)

Number Line Bars - Fractions — Divide fractions using number line bars. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Number Line Bounce — Number line addition and subtraction game. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8)

Number Patterns — Discover the pattern and complete a sequence of numbers. Number & Operations (Pre-K–2), Number & Operations (3–5)

Number Puzzles — Solve puzzles involving arranging numbers on a diagram so that they add up to a given value. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Pascal's Triangle — Explore patterns created by selecting elements of Pascal's triangle. Number & Operations (6–8), Number & Operations (9–12), Data Analysis & Probability (9–12)

Pattern Blocks — Use six common geometric shapes to build patterns and solve problems. Algebra (Pre-K–2), Geometry (Pre-K–2), Measurement (Pre-K–2), Algebra (3–5), Geometry (3–5), Measurement (3–5), Algebra (6–8), Geometry (6–8), Measurement (6–8), Algebra (9–12), Geometry (9–12), Measurement (9–12)

Peg Puzzle — Win this game by moving the pegs on the left past the pegs on the right. Number & Operations (3–5), Number & Operations (6–8), Algebra (6–8), Number & Operations (9–12), Algebra (9–12)

Pentominoes — Use the 12 pentomino combinations to solve problems. Algebra (Pre-K–2), Geometry (Pre-K–2), Algebra (3–5), Geometry (3–5), Algebra (6–8), Geometry (6–8), Algebra (9–12)

Percent Grids — Represent, name, and explore percentages using hundreds grids. Number & Operations (3–5), Number & Operations (6–8)

Percentages — Discover relationships between fractions, percents, and decimals. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Pie Chart — Explore percentages and fractions using pie charts. Number & Operations (Pre-K–2), Data Analysis & Probability (Pre-K–2), Number & Operations (3–5), Data Analysis & Probability (3–5), Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Pinwheel Tiling — Construct and explore a very unusual tiling of the plane by right triangles. Geometry (9–12)

Place Value Number Line — Explore place value by placing dots on number lines. Number & Operations (Pre-K–2), Number & Operations (3–5)

Platonic Solids — Identify characteristics of the Platonic Solids. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Platonic Solids - Duals — Identify the duals of the platonic solids. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Platonic Solids - Slicing — Discover shapes and relationships between slices of the platonic solids. Geometry (6–8), Geometry (9–12)

Point Plotter — Practice plotting ordered pairs on a graph. Algebra (6–8), Algebra (9–12)

Polyominoes — Build and compare characteristics of biominoes, triominoes, quadrominoes, etc. Algebra (Pre-K–2), Algebra (3–5), Algebra (6–8), Geometry (6–8), Algebra (9–12), Geometry (9–12)

Pythagorean Theorem — Solve two puzzles that illustrate the proof of the Pythagorean Theorem. Geometry (6–8), Geometry (9–12)

Rational Numbers Triangle — Explore a triangular array that contains every positive rational number exactly once. Number & Operations (9–12)

Rectangle Division — Visualize and practice dividing numbers by using an area representation. Number & Operations (Pre-K–2), Number & Operations (3–5)

Rectangle Multiplication — Visualize the multiplication of two numbers as an area. Number & Operations (Pre-K–2), Number & Operations (3–5)

Rectangle Multiplication of Integers — Visualize and practice multiplying integers using an area representation. Number & Operations (Pre-K–2), Number & Operations (3–5)

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. Geometry (9–12)

Savings Calculator — Explore how savings, with or without regular deposits, grow over time. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Scatterplot — Plot multiple data points in two dimensions and determine correlation. Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Sieve of Eratosthenes — Relate number patterns with visual patterns. Number & Operations (Pre-K–2), Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Space Blocks — Create and discover patterns using three dimensional blocks. Geometry (Pre-K–2), Algebra (3–5), Geometry (3–5), Algebra (6–8), Geometry (6–8), Geometry (9–12)

Spinners — Work with spinners to learn about numbers and probabilities. Number & Operations (Pre-K–2), Data Analysis & Probability (Pre-K–2), Data Analysis & Probability (3–5), Number & Operations (6–8), Data Analysis & Probability (6–8), Data Analysis & Probability (9–12)

Stick or Switch — Investigate probabilities of sticking with a decision, or switching. Algebra (6–8), Data Analysis & Probability (6–8), Algebra (9–12), Data Analysis & Probability (9–12)

Tangrams — Use all seven Chinese puzzle pieces to make shapes and solve problems. Geometry (Pre-K–2), Number & Operations (3–5), Geometry (3–5), Measurement (3–5), Number & Operations (6–8), Geometry (6–8), Measurement (6–8), Geometry (9–12)

Tessellations — Using regular and semi-regular tessellations to tile the plane. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Tight Weave — Visualize the creation of the Sierpinski Carpet, an iterative geometric pattern that resembles a woven mat. Number & Operations (6–8), Geometry (6–8), Number & Operations (9–12), Geometry (9–12)

Time - Analog and Digital Clocks — Interactively set the time on a digital and analog clocks. Measurement (Pre-K–2), Measurement (3–5)

Time - Match Clocks — Answer questions asking you to show a given time on digital and analog clocks. Measurement (Pre-K–2), Measurement (3–5)

Time - What Time Will It Be? — Answer questions asking you to indicate what time it will be before or after a given time period. Measurement (Pre-K–2), Measurement (3–5), Measurement (6–8)

Towers of Hanoi — Solve the tower problem and test your theory by varying the number of disks. Algebra (3–5), Algebra (6–8), Algebra (9–12)

Transformations - Composition — Explore the effect of applying a composition of translation, rotation, and reflection transformations to objects. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Transformations - Dilation — Dynamically interact with and see the result of a dilation transformation. Geometry (3–5), Geometry (6–8), Geometry (9–12)

Transformations - Reflection — Dynamically interact with and see the result of a reflection transformation. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Transformations - Rotation — Dynamically interact with and see the result of a rotation transformation. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Transformations - Translation — Dynamically interact with and see the result of a translation transformation. Geometry (Pre-K–2), Geometry (3–5), Geometry (6–8), Geometry (9–12)

Triangle Solver — Practice using the law of sines and the law of cosines to solve for unknown sides and angles of a triangle. Geometry (9–12)

Triominoes — Manipulate the puzzle pieces and find multiple solutions. Algebra (Pre-K–2), Geometry (Pre-K–2), Algebra (3–5), Geometry (3–5), Algebra (6–8), Geometry (6–8)

Turtle Geometry — Explore numbers, shapes, and logic by programming a turtle to move. Geometry (Pre-K–2), Geometry (3–5), Number & Operations (6–8), Geometry (6–8), Number & Operations (9–12), Geometry (9–12)

Turtle Rectangles — Change variables to observe differences in spiral designs. Algebra (Pre-K–2), Algebra (3–5)

Venn Diagrams — Investigate common features of sets. Number & Operations (3–5), Number & Operations (6–8), Number & Operations (9–12)

Whammy Awards — See how using different voting schemes can result in contradictory outcomes. Data Analysis & Probability (9–12)