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Virtual Math Manipulatives: Free Online Tools and Teacher Guide
Updated · By Edulist · 7 sources
Keyboard and touch help
- Drag a piece from the tray onto the board, or press a tray button (Enter) to add it in the next spot.
- Tab to a piece. Arrow keys move it (Shift for bigger steps). Space adds it to the selection.
- D duplicates, R rotates, G trades up a group, B breaks a piece apart, Delete removes it.
- Ctrl+Z undoes and Ctrl+Shift+Z redoes (Cmd on a Mac).
- Drag across empty space to select several pieces. Drop pieces on the trash or back on the tray to delete them.
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How to use it
- Pick a manipulative
Use the buttons above the board to switch between base ten blocks, place value disks, ten frames, fraction tiles, number lines and the Montessori materials. Each one also has its own page with a full guide.
- Drag, tap or use the keyboard
Drag pieces from the tray onto the board, or tap a tray button (or press Enter) to drop one in the next spot. Tab to any piece and move it with the arrow keys.
- Work a task card
Every tool has 6 to 10 task cards. Pick one, follow the prompt, and the card checks itself as you work. Progress is saved on this device.
- Draw, share and print
Circle groups with the Pen, add Text labels, then press Share for a link to your exact board or Print for a one-page sheet.
Printables to go with it
What math manipulatives are for
A manipulative is any object a child can move to see how a math idea works. Ten unit cubes slide together into one rod, and "carry the one" suddenly has a meaning. Two 1/4 tiles sit exactly on top of a 1/2 tile, and equivalent fractions stop being a rule to memorize. The object carries the idea until the child can carry it without the object.
That move from objects to pictures to symbols is the core of most elementary math teaching. Teachers call it concrete, representational, abstract (CRA), or concrete, pictorial, abstract in Singapore-style programs. The What Works Clearinghouse practice guide on helping students who struggle with math rates "a well-chosen set of concrete and semi-concrete representations" as supported by strong evidence, and gives the number line its own recommendation. The National Council of Teachers of Mathematics lists "use and connect mathematical representations" as one of its eight effective teaching practices.
Virtual manipulatives are the same objects on a screen. They don't replace the feel of a real block in a young child's hand, but they bring things physical sets can't: values that update as you work, unlimited pieces, undo, a pen for drawing on the model, and a link that shows your exact board to someone else.
The virtual manipulatives on this page
Switch tools with the buttons above the board. Each tool also has its own page with a full guide, activities and printables.
| Manipulative | Best for | Grades | What it teaches |
|---|---|---|---|
| Base ten blocks | Place value to 9,999 | K–4 | Ones, tens, hundreds and thousands; regrouping in addition and subtraction |
| Place value disks | Bigger numbers and decimals | 2–5 | The same trades as blocks, with labeled disks; tenths and hundredths |
| Ten frame | Counting to 10 | Pre-K–1 | Seeing numbers as 5 and some more; partners of 10 |
| Double ten frame | Numbers to 20 | K–2 | Teen numbers as 10 and some more; the make-ten strategy |
| Fraction tiles | Fractions | 2–5 | Unit fractions, equivalence, comparing, adding with like and unlike denominators |
| Interactive number line | Operations and number sense | K–6 | Jumps for adding and subtracting; fractions, decimals and negative numbers |
| Open number line | Mental math | 1–4 | Adding and subtracting with friendly jumps of tens and ones |
| Montessori materials | Montessori math | Pre-K–3 | Golden beads, stamp game, bead chains and number rods |
How to teach with virtual manipulatives
A short routine works for almost any lesson.
- Show, then ask. Build one example on the board yourself, such as 34 with base ten blocks, and think out loud. Then give the child a similar number to build.
- Name what you see. Ask the child to say the number three ways: in words, in place value ("3 tens and 4 ones") and as a sentence ("30 + 4 = 34"). The readout next to the board shows the sentence so the child can check.
- Change one thing. Add a ten, take away a one, trade 10 ones for a ten. Ask what changed and what stayed the same.
- Write it down. Use the Text tool or paper to record the number sentence. The link between the model and the symbols is the point.
- Fade the model. Turn on Hide value and let the child predict before checking. Later, ask them to sketch the model on paper instead of building it.
Tips for classrooms
- Project it. Every tool works on an interactive whiteboard or projector. Use the zoom buttons to enlarge pieces for the back row.
- Use task cards as stations. Each tool has 6 to 10 cards that check themselves, so a small group can work while you teach another.
- Collect work with links. Students press Share and paste the link into your learning platform. The link rebuilds the board, pen marks included, without accounts or student data.
- Print for the folder. Print makes a one-page sheet with the board, the value and the task, with a line for name and date.
- Keyboard and screen readers. Every tool can be used without a mouse: Tab to the tray or a piece, Enter to add, arrows to move, Delete to remove. Readouts and changes are announced.
Tips for parents
- Five minutes is enough. A short session of building numbers and talking about them does more than a long worksheet.
- Ask, don't tell. "How do you know?" and "Can you show me another way?" are the best questions.
- Follow the school's tool. If your child's class uses number disks or a particular model, use the same one here so home and school match.
- Mix in real objects. Coins, buttons, pasta and LEGO bricks are manipulatives too. Count them into a ten frame drawn on paper.
Virtual vs. physical manipulatives
| Physical | Virtual | |
|---|---|---|
| First introduction for ages 3 to 6 | Best | Good with an adult |
| Supply | Limited by the set | Unlimited |
| Values and number sentences | You work them out | Shown as you go (or hidden) |
| Breaking a ten into ones | Trade with a bank | One tap, with an animation |
| Undo, draw, label | No | Yes |
| Sharing and printing | Photo | Link, print, SVG |
| Cost | Sets cost money | Free |
Most teachers use both: real objects for the first lessons, then virtual ones for practice, homework, whole-class demonstrations and anything that needs more pieces than the bin holds.
How to choose a math curriculum that uses manipulatives
Some programs are built around manipulatives from the start. RightStart Mathematics uses an abacus grouped in fives and tens. Math-U-See teaches with its own color-coded blocks. Singapore-style programs move from concrete objects to bar-model pictures to symbols. When you compare programs, look at how they use objects in the first lessons on each topic and how soon they move to pictures, then to written work. The best homeschool math curriculum guide compares the main options, and many families use scholarships or ESA funds to pay for them.
Printables pair well with every tool here: a place value chart, a fraction chart, printable number lines and a hundreds chart.
Sources
- What Works Clearinghouse: Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades (2021)
- What Works Clearinghouse practice guide, full PDF
- NCTM: Principles to Actions, effective mathematics teaching practices
- NCTM: Virtual Place Value (Teaching Children Mathematics, 2013)
- National Center on Intensive Intervention: Using base ten blocks virtually
- PaTTAN: Concrete-Representational-Abstract instructional approach
- Common Core State Standards for Mathematics
Questions
What are examples of math manipulatives?
Base ten blocks, place value disks, ten frames with counters, fraction tiles and circles, number lines, pattern blocks, geoboards, Cuisenaire rods, rekenreks, algebra tiles and the Montessori materials such as golden beads and number rods. Anything a child can move to model a number or shape counts.
Are virtual manipulatives as effective as physical ones?
Research supports both as part of a sequence that moves from objects to pictures to symbols. Physical pieces are best for a first introduction with young children. Virtual pieces add instant values, unlimited supply, undo, sharing and printing, and they let you do things plastic can't, like breaking a ten rod into ten ones.
Do I need an account or an app?
No. Everything runs in the browser on Chromebooks, iPads, laptops and phones. There's no sign-in, and task progress is saved only on your device.
Can students share their work with a teacher?
Yes. Share makes a link that rebuilds the exact board, including pen marks and labels. Students can paste it into an assignment, and the teacher sees the same board. Print and SVG make a picture of the board.
Which manipulative should I start with?
For counting and numbers to 20, start with the ten frame. For place value, use base ten blocks, then place value disks. For fractions, use fraction tiles. For adding and subtracting strategies, use the number lines. Montessori families can start with number rods and golden beads.
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