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Virtual manipulatives
Hands-on math and science models that work in the browser on a computer, tablet or phone: shade fraction bars, build numbers from blocks, move clock hands, balance equations and light up a circuit.
Numbers and operations
- Grades K to 7Interactive number lineA free interactive number line with six ranges, including negative numbers, tenths and quarters. Drag or tap to place a pointer that snaps to each tick.
- Grades 1 to 4Virtual base ten blocksFree virtual base ten blocks. Add and remove hundreds flats, tens rods and ones cubes and watch the total update. Ideal for place value and regrouping.
- Grades 2 to 5Multiplication arraysFree virtual multiplication arrays. Drag to set the rows and columns, up to 12 by 12, in dots or squares, and see the multiplication fact build itself.
- Grades 1 to 4Virtual money for counting practiceFree virtual money for counting practice. Tap US coins and bills, or UK coins and notes, to add them up, take coins back, and watch the total change.
- Grades 2 to 4Division by sharing and groupingFree division manipulative. Share up to 40 counters into equal groups one round at a time, or make groups of a size, and see the quotient and remainder.
- Kindergarten to Grade 2Even and odd numbersFree even and odd numbers tool. Pick a number from 1 to 30, pair up the counters to see if one is left over, then sort number cards into even and odd.
- Grades 4 to 7Interactive factor treeFree factor tree maker. Split a number from 4 to 200 into factor pairs until every branch is prime, and see its prime factorization with exponents.
- Kindergarten to Grade 4Interactive hundred chartFree interactive hundred chart. Color squares, skip count by 2, 3, 4, 5 and 10, find common multiples, and play hide and seek with numbers from 1 to 100.
- Grades 6 and 7Virtual integer chipsFree virtual integer chips. Add yellow positive and red negative counters, cancel zero pairs, and model adding and subtracting negative numbers.
- Grades 2 to 5Interactive multiplication chartFree interactive 12×12 multiplication chart. Tap a fact to see its array, light up squares and times tables, find turnarounds, and take a quiz.
- Kindergarten to Grade 2Virtual number bondsFree virtual number bonds. Move counters between two parts of a whole from 5 to 20, hide a part to find the missing number, and find all the bonds of 10.
- Grades 1 to 3Interactive open number lineFree open number line. Pick a start number, add or subtract with jumps of 1, 10 and 100, and see each jump drawn as a labeled arc.
- Grades 1 to 5Interactive place value chartFree place value chart with disks from millions to hundredths. Build numbers, regroup 10 disks into the next place, and read expanded and word form.
- Kindergarten to Grade 2Virtual rekenrek (20-bead rack)Free online rekenrek with two rows of 10 beads in fives. Slide beads to show numbers to 20, spot doubles and near doubles, and take the Show me challenge.
- Grades 2 to 4Rounding hillFree interactive rounding hill. Place a number between two tens or hundreds, predict which way the ball rolls, and see why halfway rounds up.
- Grades 4 to 6Interactive Sieve of EratosthenesFree interactive Sieve of Eratosthenes. Cross out multiples of 2, 3, 5 and 7 on a 1 to 100 grid, by hand or step by step, and find all 25 primes up to 100.
- Kindergarten to Grade 3Skip counting frogFree skip counting number line. A frog hops by 2s, 3s, 4s, 5s, 10s or 25s, and your child predicts each landing number before it jumps.
- Kindergarten to Grade 2Virtual ten framesFree virtual ten frames. Add red and yellow counters to one or two frames, see the split and how many more make 10 or 20, and flash amounts to subitize.
Fractions, decimals and percents
- Grades 2 to 5Virtual fraction bars and fraction circlesFree virtual fraction bars and circles. Split a whole into up to 12 equal parts, shade them, and add a second bar to compare and find equivalent fractions.
- Grades 4 to 6Adding fractions with a modelFree adding fractions model. Put two fractions on bars, split the parts until they match to find a common denominator, then combine the pieces in steps.
- Grades 3 to 5Compare fractionsFree tool for comparing fractions. Set two fractions, see them as bars or circles, pick <, = or > and use the 1/2 and 1 benchmarks to explain why.
- Grades 4 to 6Decimal grid (hundredths)Free 10 by 10 decimal grid. Tap or drag to shade hundredths and see the decimal, simplified fraction and percent, then try a shade-the-amount challenge.
- Grades 4 to 6Decimal place value chartFree decimal place value chart. Put 3.457 in ones, tenths, hundredths and thousandths, then multiply or divide by 10, 100 or 1,000 and watch digits slide.
- Grades 3 to 5Equivalent fractions explorerFree equivalent fractions tool. Split every part of a fraction bar into 2 to 6 pieces and watch the name change while the shaded amount stays the same.
- Grades 5 to 7Dividing fractions: how many fit?Free visual model for dividing fractions. Lay groups of one fraction along another, count whole and part groups, then check by flip and multiply.
- Grades 5 to 6Multiplying fractions with an area modelFree area model for multiplying fractions. Shade one fraction in columns and one in rows; the overlap shows the product, with simplifying and a challenge.
- Grades 3 to 5Fraction number lineFree fraction number line. Split 0 to 1, 2 or 3 into equal parts, drag a point to see the fraction, mixed number and decimal, then place fractions.
- Grades 3 to 5Mixed number builderFree mixed number builder. Add fraction pieces to circles or bars and see them switch between an improper fraction and a mixed number as each whole fills.
- Grades 5 to 7Percent bar modelFree percent bar model. Set a whole such as $80, drag to any percent to see the part, or find what percent 30 is of 120 on a double number line.
- Grades 6 to 7Ratio table and double number lineFree ratio table. Scale 3 cups of flour to 2 eggs with ×2, ×3 and ÷2, see it on a double number line, read the unit rate and find missing values.
Geometry and measurement
- Grades 1 to 3Interactive teaching clockA free interactive clock with hands you drag. Show or hide the digital time, step by five minutes or an hour, and help children learn to tell time.
- Grades 3 to 7Virtual protractor and angle makerFree online protractor and angle maker. Drag to make any angle from 0° to 360°, see its type, estimate before revealing, and take on angle challenges.
- Grades 3 to 6Area and perimeter builderFree area and perimeter builder. Tap squares on a grid to build shapes, watch the area and perimeter change, and find same-area shapes with new perimeters.
- Grades 5 to 8Circle explorerFree circle explorer. Drag the radius to see diameter, circumference and area, and unroll the circumference to see it is a bit more than 3 diameters.
- Grades 2 to 6Virtual geoboardFree virtual geoboard. Stretch colored rubber bands around pegs to make shapes, see their area and perimeter, check Pick's theorem and try area challenges.
- Grades 1 to 4Virtual measuring jugFree virtual measuring jug. Pour water, read the level on a milliliter or cup scale, take on challenges like pouring 350 mL, and compare two jugs.
- Grades 2 to 4Virtual measuring rulerFree virtual ruler. Drag a ruler to measure a pencil, crayon and more in inches to the quarter inch or centimeters to the millimeter, then check.
- Grades 1 to 6Nets of 3D shapesFree nets of 3D shapes tool. Watch nets of a cube, prisms, a pyramid, cylinder and cone fold up, turn each solid, and count faces, edges and vertices.
- Grades 2 to 8Polygon explorerFree polygon explorer. Choose 3 to 12 sides to see each regular polygon's name, interior angles, angle sum and lines of symmetry, then try challenges.
- Grades 7 to 9Pythagorean theorem explorerFree Pythagorean theorem tool. Drag the legs of a right triangle, see squares drawn on every side with their areas, and find Pythagorean triples yourself.
- Grades 1 to 5Symmetry mirrorFree symmetry tool. Color squares on a grid and watch the mirror draw the reflection, with one or two mirror lines and a complete-the-picture game.
- Grades 1 to 6Interactive thermometerFree interactive thermometer. Drag the liquid to set a temperature, read Fahrenheit and Celsius side by side, see landmarks like freezing, and convert.
- Grades 5 to 8Transformations on a coordinate gridFree transformations tool. Translate, reflect and rotate a shape on a coordinate grid, compare vertex coordinates before and after, and match targets.
- Grades 4 to 6Volume with unit cubesFree volume tool. Build a rectangular prism from unit cubes, change its length, width and height, see the layers, and learn why volume is l × w × h.
Data, probability and algebra
- Grades 5 to 8 in the US, Years 4 to 9 in EnglandInteractive coordinate planeA free coordinate plane online. Switch between a first-quadrant grid and a four-quadrant grid, tap to place a point and read its coordinates.
- Grades 6 to 8Algebra balance scaleA free algebra balance scale. Pick an equation, do the same thing to both sides with one tap, undo any step, and watch x end up on its own.
- Grades 6 to 9Virtual algebra tilesFree virtual algebra tiles. Use x², x and unit tiles, positive and negative, to model expressions, cancel zero pairs, combine like terms and simplify.
- Grades 1 to 4Bar graph maker for kidsFree bar graph maker for kids. Use a ready data set or your own, drag bars from 0 to 20, change the scale, and read the total, most, least and differences.
- Grades 3 to 7Function machine: guess the ruleFree function machine. Put numbers in, watch what comes out, build an input-output table, and crack the mystery rule, from +3 to two-step and square rules.
- Grades 2 to 5Line plot maker with fractionsFree line plot maker. Stack X marks above whole numbers, halves or quarters, plot a data list, and see the mode, range and total update as you go.
- Grades 7 to 9Linear graph explorer: y = mx + bFree y = mx + b graph explorer. Change the slope and intercept, see the slope triangle and table of values, and match lines in quick challenges.
- Grades 6 to 8Mean, median and mode explorerFree mean, median and mode explorer. Drag up to 15 dots on a dot plot, watch the balance point and median move, and see what an outlier does.
- Grades 4 to 8Growing pattern builderFree growing pattern builder. Make tile patterns that grow by the same amount each time, predict figure 10, and find the nth-term rule for the sequence.
- Grades 1 to 3Pictograph maker for kidsFree pictograph maker for kids. Build a picture graph with each picture worth 1, 2 or 5, use half pictures, and answer questions about the data.
- Grades 5 to 8Pie chart makerFree pie chart maker. Set up to 5 values and watch the pie draw with fractions, percents and angles, compare it with a bar chart, and try slice challenges.
- Grades 5 to 8Probability simulatorFree probability simulator. Flip a coin, roll a die or spin a spinner up to 100 times at once, and compare experimental and theoretical probability.
- Grades 9 to 11Quadratic graph explorerFree quadratic graph explorer. Change a, b and c in y = ax² + bx + c and see the parabola's vertex, axis of symmetry and roots, with vertex form alongside.
- Grades 6 to 8Spinner designerFree spinner designer. Make a spinner with 2 to 8 sections of any size, spin up to 1,000 times, and compare experimental and theoretical probability.
- Grades 6 to 8Two dice sums simulatorFree two dice simulator. Roll up to 1,000 times, watch the bar chart of sums from 2 to 12 take shape, and find every way to make a sum on the outcome grid.
Physics, Earth and space
- Grades 3 to 8Simple circuit simulatorA free simple circuit simulator for kids. Add or remove cells and bulbs, open or close the switch, and see when the bulbs light in a series circuit.
- Grades 2 to 8Color mixing simulatorA free color mixing simulator. Overlap red, green and blue spotlights, then mix cyan, magenta and yellow paint to see why light and paint mix differently.
- Grades 1 to 5Day and night simulatorA free day and night simulator. Spin the Earth, follow a person through sunrise, noon, sunset and midnight, and watch a stick's shadow change.
- Grades 1 to 6Float or sink simulatorA free float or sink simulator. Drop wood, a rock, an apple, ice and more into water, oil or salt water, predict first, and compare their densities.
- Grades 3 to 8Balanced and unbalanced forces simulatorA free forces and motion simulator for kids. Set four force arrows on a box, find the resultant force, and see if the forces are balanced or unbalanced.
- Grades 3 to 8Gravity on other planets simulatorA free gravity on other planets simulator. Weigh a mass on a spring scale on each planet and the Moon, compare jump heights, and see mass vs weight.
- Grades 3 to 8Lever and seesaw simulatorA free lever and seesaw simulator. Place weights at different distances, move the fulcrum, and balance it when weight × distance matches on each side.
- Grades 3 to 8Light reflection simulatorA free light reflection simulator. Aim a laser at a mirror, see the normal and the angles of incidence and reflection, and build a working periscope.
- Grades 1 to 4Magnets simulatorA free magnets simulator for kids. Flip two bar magnets to see poles attract and repel, then test everyday objects to sort magnetic from not magnetic.
- Grades 3 to 8Moon phases simulatorA free moon phases simulator. Drag the Moon around Earth, see the top view and the view from Earth side by side, and learn the eight phase names.
- Grades 4 to 9Parts of a wave diagramA free interactive parts of a wave diagram. Tap the crest, trough, wavelength and amplitude to learn what each one means, show labels, or quiz yourself.
- Grades 4 to 8Pendulum simulatorA free pendulum simulator. Change the length, mass and start angle, time 10 swings, and use the data table to find what really changes the swing time.
- Grades 3 to 8Pulley simulatorA free pulley simulator for kids. Lift a crate with 1, 2 or 4 supporting ropes and see how less effort force means pulling more rope.
- Grades 4 to 8Reasons for the seasons simulatorA free seasons simulator. Move Earth around the Sun month by month and see how the 23.5° tilt, not distance, changes day length and seasons.
- Grades 1 to 5Shadows simulatorA free shadows simulator for kids. Move a lamp closer, farther, higher or lower and watch a block's shadow change on the table and the wall.
- Grades 2 to 8Solar system diagramA free interactive solar system diagram for kids. Tap the Sun and all eight planets to learn a fact about each, show their names, or quiz yourself.
- Grades 1 to 8Sound waves simulatorA free sound waves simulator. Change frequency and amplitude, watch the wave and the air particles change, and play a quiet tone to hear the difference.
- Grades 5 to 8Speed, distance and time simulatorA free speed, distance and time simulator. Race two cars at speeds you choose, watch a distance–time graph draw live, and work out speed = distance ÷ time.
- Grades 2 to 7Water cycle diagramA free interactive water cycle diagram for kids. Tap evaporation, condensation, precipitation and collection to learn each stage, or take a quick quiz.
Life science and chemistry
- Grades 2 to 8States of matter simulationA free states of matter simulation. Heat or cool a box of particles to turn a solid into a liquid and a gas, and watch how the particles move in each.
- Grades 6 to 9Animal cell diagramA free interactive animal cell diagram. Tap the cell membrane, cytoplasm, nucleus and mitochondria to learn what each part does, or quiz yourself.
- Grades 7 to 10Build an atom simulatorA free build an atom simulator. Add protons, neutrons and electrons to make the first 20 elements, see the mass number and charge, and make ions.
- Kindergarten to Grade 4Butterfly life cycleA free interactive butterfly life cycle. Tap the egg, caterpillar, chrysalis and butterfly to learn about each stage, then put the stages in order.
- Grades 3 to 8Digestive system diagramA free interactive digestive system diagram. Tap the stomach, liver, intestines and more, then follow a bite of food from the mouth all the way through.
- Grades 3 to 8Food chain builderA free food chain builder. Pick a pond, forest, ocean or savanna, tap living things to build a chain from producer to top predator, then check it.
- Grades 1 to 5Frog life cycleA free interactive frog life cycle. Tap frogspawn, tadpole, tadpole with legs, froglet and frog to learn each stage, then put them in the right order.
- Grades 3 to 8Human body organs diagramA free interactive human body organs diagram for kids. Tap the brain, heart, lungs, liver, stomach, kidneys and intestines to learn what each one does.
- Grades 4 to 9Parts of the eyeA free interactive eye diagram. Tap the cornea, iris, pupil, lens, retina and optic nerve, and change the light to watch the pupil shrink and widen.
- Grades 4 to 8Human heart diagramA free interactive heart diagram. Tap the chambers, valves and blood vessels, press Beat to see blood flow, and follow a drop of blood through the heart.
- Grades 2 to 7Human skeleton diagramA free interactive human skeleton diagram for kids. Tap the skull, ribs, spine, pelvis, arm and leg bones to learn what each does, or take a quick quiz.
- Kindergarten to Grade 4Insect body partsA free interactive insect diagram. Tap a honeybee's head, thorax, abdomen, antennae, wings, legs and compound eyes, then sort animals into insects or not.
- Grades 2 to 7Parts of a flowerA free interactive flower diagram. Tap the petals, stamen, anther, pistil, stigma and ovary, then watch a bee pollinate the flower step by step.
- Grades K to 4Parts of a plant diagramA free interactive parts of a plant diagram for kids. Tap the flower, leaf, stem and roots to learn what each does, show labels, or take a quick quiz.
- Grades 6 to 10Interactive periodic tableA free interactive periodic table of the first 20 elements. Tap hydrogen to calcium to see each element's number, group, period and a fact, or take a quiz.
- Grades 5 to 9pH scaleA free interactive pH scale. Test household substances with litmus and universal indicator, then drag lemon juice, milk, soap and more onto the scale.
- Grades 6 to 9Plant cell diagramA free interactive plant cell diagram. Tap the cell wall, membrane, nucleus, vacuole, chloroplasts and more to learn what each part does, or quiz yourself.
- Grades 2 to 6Plant growth experimentA free plant growth experiment. Choose the light, water and soil for three pots, grow bean seedlings for 3 weeks and learn how to run a fair test.
- Grades 1 to 5Plant life cycleA free interactive plant life cycle. Tap seed, germination, seedling, adult plant, flowering and fruit to learn each stage, then put them in order.
- Grades 6 to 10Predator and prey simulationA free predator prey simulation. Change rabbit births, fox hunting, fox deaths and grass, then watch both populations rise and fall on a line graph.
- Grades 7 to 10Punnett square simulatorA free interactive Punnett square. Choose two pea plants' alleles, fill in the square, see genotype and phenotype ratios, and grow offspring to compare.
- Grades 1 to 5Tooth diagramA free interactive tooth diagram. Tap the enamel, dentin, pulp, root and crown, and switch between an incisor, a canine and a molar to compare them.
English, reading and phonics
- Grades 1 to 3Alphabetical order gameFree alphabetical order game. Sort 4 to 8 word tiles into ABC order by the first, second or third letter, with hints that show which letters to compare.
- Kindergarten to Grade 3Capital letters practiceFree capitalization practice. Tap the words that need capital letters in a lowercase passage: sentence starts, names, places, days, months and the word I.
- Kindergarten to Grade 2Compound word makerFree compound word game for kids. Join two word tiles, like sun + flower, to make real compound words with a picture and meaning. Four themed word sets.
- Kindergarten to Grade 1CVC word blendingFree CVC blending tool. Tap three letter tiles to hear each one, blend them into a word with a picture, and change one letter at a time to make new words.
- Grades 2 to 5Homophone pickerFree homophone game. Choose their, there or they're, to, too or two, your or you're and more to fill the gap in each sentence, with meanings explained.
- Grades 1 to 5Parts of speech sorterFree parts of speech game. Color each word in a sentence as a noun, verb, adjective, adverb, pronoun, preposition, conjunction or article, then check.
- Grades 1 to 5Punctuation fixerFree punctuation practice. Tap where the missing periods, question marks, commas and apostrophes go in each sentence, check, and read why each fix works.
- Kindergarten to Grade 3Sentence builderFree sentence builder for kids. Put scrambled word tiles in order, add a capital letter and the right end mark, and check it. Levels from 4 to 10 words.
- Kindergarten to Grade 2Syllable counter: clap the syllablesFree syllable counting game. Hear a word, tap Clap once for each beat, then see it split into syllables, like but-ter-fly. Three levels from 1 to 5 beats.
- Grades 1 to 5Synonym and antonym matchFree synonym and antonym game. Match each word to a word that means the same or the opposite, in rounds of four, and build a list of the pairs you learn.
- Grades 2 to 5Word builder: prefixes and suffixesFree online word builder. Add prefixes like un-, re- and dis- and suffixes like -ful, -ness and -ing to base words, with meanings and spelling rules.
- Kindergarten to Grade 1Word familiesFree word family game. Put a letter or blend in front of -at, -ig, -op, -un, -ake or -ight, read the word, and decide if it is real or a nonsense word.
Keep exploring
- Math by topicFractions, times tables, long division and more
- Math by gradeEvery skill from kindergarten to 8th grade
- English and grammarNouns, verbs, commas, spelling and more
- Reading passagesShort stories with read-aloud and questions
- Science by gradePlants, forces, matter, space and more
- Printable worksheetsPrint, or do them on a tablet with a finger or pen
- Free math games3D games where every move is a math question
- Fraction calculatorEvery step shown, from mixed numbers to simplest form
- Math 5-a-dayFive fresh warm-up questions every day
- Guides for parentsHow to help with fractions, tables, tests and more
Math, English and science that click.