Virtual Base Ten Blocks
Build numbers with unit cubes, ten rods, hundred flats and thousand cubes on a place value mat. Break and trade blocks to see regrouping, then model addition with carrying and subtraction with borrowing, one step at a time.
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Drag a block onto the column to its right to break it into ten smaller blocks. Press ▲ Trade 10 when a column has ten or more to bundle them into one bigger block.
How to use the Virtual Base Ten Blocks
- Build a number: type it and press Build, or drag blocks from the tray onto the mat.
- Regroup: drag a rod onto the ones column to break it into 10 units, or press ▲ Trade 10 in a column that has ten or more blocks.
- Add: open Addition, enter two numbers and press Start problem. Green blocks are the first addend, orange the second. Trade 10 wherever a column reaches ten.
- Subtract: open Subtraction, enter the numbers and press Start problem. Tap blocks to take them away and break a bigger block when a column runs short.
- Stuck? Press Show next step to see the next move, and read the total, expanded form and words under the mat.
Base ten block values
| Block | Also called | Value | Made of | Place value column |
|---|---|---|---|---|
| Unit | One, small cube | 1 | — | Ones |
| Rod | Long, ten stick | 10 | 10 units in a row | Tens |
| Flat | Hundred square | 100 | 10 rods side by side | Hundreds |
| Cube | Block, thousand cube | 1,000 | 10 flats stacked | Thousands |
Worked examples
Addition with regrouping: 367 + 458. Put both numbers on the mat. The ones column has 7 + 8 = 15 units, so trade 10 units for 1 rod, leaving 5 units. The tens column now has 6 + 5 + 1 = 12 rods, so trade 10 rods for 1 flat, leaving 2 rods. The hundreds column has 3 + 4 + 1 = 8 flats. The mat reads 8 flats, 2 rods, 5 units: 825.
Subtraction across a zero: 403 − 156. Build 403: 4 flats, 0 rods, 3 units. You need to take away 6 units but have only 3, and there are no rods to break. Break a flat into 10 rods (3 flats, 10 rods), then break a rod into 10 units (9 rods, 13 units). Now take away 6 units (7 left), 5 rods (4 left) and 1 flat (2 left): 247.
Teaching tips
- Say the trade out loud: "ten ones make one ten." Children who hear and see the exchange learn why we carry and borrow instead of memorizing a rule.
- Ask for a number in a non-standard way, such as 52 made with no rods larger than 4, to practice flexible thinking (4 rods and 12 units).
- Connect the mat to the written algorithm: after each trade, write the small carried or borrowed digit above the column on paper.
- Turn off the thousands column for first and second graders to keep the mat simple.
Frequently asked questions
What are base ten blocks?
Base ten blocks are math manipulatives that show place value with size. A unit cube is 1, a rod of ten units is 10, a flat of ten rods is 100 and a large cube of ten flats is 1,000. Because each block is exactly ten of the next smaller one, they make regrouping visible.
How do you show regrouping with base ten blocks?
Whenever a column holds ten or more blocks, trade ten of them for one block of the next place: 10 units for 1 rod, 10 rods for 1 flat, 10 flats for 1 cube. Going the other way, break one block into ten of the next smaller block. Either way the total value stays the same.
How do I model addition with carrying?
Build both addends on the mat (they appear in two colors), so each column shows the combined blocks. Starting with the ones, if a column has ten or more blocks, trade ten for one block in the next column to the left. That trade is the carry. When every column has nine or fewer blocks, the mat shows the sum.
How do I model subtraction with borrowing?
Build only the first number, then take away the second number column by column starting with the ones. If a column does not have enough blocks, break one block from the column to its left into ten. That break is the borrow, also called regrouping or decomposing. The blocks left over show the difference.
Can a number be shown in more than one way?
Yes. 243 is 2 flats, 4 rods and 3 units, but it is also 2 flats, 3 rods and 13 units, or 24 rods and 3 units. The mat accepts any arrangement and the total stays correct, which helps children see that regrouping changes the form but not the value.
What grade levels use base ten blocks?
They are most common from kindergarten through about grade 4, for counting, place value, two- and three-digit addition and subtraction, and an introduction to multiplication. Older students also use them to understand decimals by letting the flat stand for one whole.
Does this work on tablets and Chromebooks?
Yes. Blocks can be dragged with a finger, mouse or trackpad, and every action also has a button, so it works with a keyboard too. Your mat is saved in your browser so it is still there after a refresh.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.