Base Ten Blocks: Free Virtual Blocks and Place Value Mat

What base ten blocks teach

Base ten blocks make the hardest idea in early math visible: the same digit means a different amount depending on where it sits. In 243 the 2 means two hundred, and a child who has held two flats knows that is far more than two cubes. The blocks are built to scale, so the relationships are physical. A rod is exactly ten unit cubes long, a flat is ten rods side by side, and a thousand cube is ten flats stacked. Nothing has to be taken on faith.

The virtual set on this page keeps those proportions. A rod is drawn ten units tall, a flat is ten rods wide, and the front face of the thousand cube is the same size as a flat. The place value mat sorts blocks into Thousands, Hundreds, Tens and Ones columns, and the readout shows the number, the expanded form and the count in each column as you work.

How to use base ten blocks

Start with building and naming. Show a number with blocks, then say it in three ways: "Two hundred forty-three. Two hundreds, four tens and three ones. 200 plus 40 plus 3." The board's readout does the third one for you, so a child can check their own work.

Then move to regrouping, which is where base ten blocks earn their keep.

1. Trade up when adding. Put 27 and 15 on the mat together. The ones column now has 12 cubes. Ten of them become one rod, which moves to the tens column. The answer, 42, is now easy to read.
2. Break down when subtracting. Show 52 and try to take away 17. There are only 2 ones, so break a rod into 10 cubes. Now there are 12 ones, and taking away 7 is possible.
3. Write it down. After each trade, write what happened. The little 1 a child writes above the tens column in the standard algorithm is the rod they just made.

On this board, a rod dropped into the ones column breaks into 10 cubes automatically, the same way a ten has to become ones before it can live in the ones place. The value never changes when you trade or break, and the readout shows that.

Regrouping with base ten blocks: why the trade matters

Children who learn "carry the one" as a rule often can't say what the one is. The trade answers that question. Ten cubes slide together into a rod on screen, so the child sees that the carried 1 is one ten made from ten ones. Subtraction works the same way in reverse: "borrowing" is breaking one ten into ten ones.

This is also why the Common Core standards for 1st and 2nd grade name the trade directly. First graders learn that 10 ones make a ten and that a two-digit number is tens and ones (1.NBT.B.2). Second graders extend that to hundreds and use place value to add and subtract within 1,000, "composing or decomposing tens or hundreds" as needed (2.NBT.A.1 and 2.NBT.B.7).

Base ten blocks by grade

Activities to try

The task cards beside the board check themselves as children work. These ideas go further.

• Fewest blocks. Build a number any way you like, then trade until you have the fewest blocks. The fewest-blocks version is the standard way to write the number.
• Many ways to make a number. Show 34 as 3 tens and 4 ones, then 2 tens and 14 ones, then 34 ones. Ask what stays the same.
• 10 more, 10 less. Show 46. Add a rod. What changed? Only the tens digit. Do the same with 100 more.
• Mystery number. Turn on Hide value, build a number, and ask a partner to say it. Then show the value to check.
• The zero is a placeholder. Build 306 and notice the empty tens column. That empty column is the 0.
• Race to 100. Roll a die, add that many cubes, and trade whenever you can. The first player to trade up to a flat wins.

Tips for teachers and parents

• Name the blocks by value. Say "a ten" as well as "a rod". The goal is the number, not the plastic.
• Count by the block, not the cube. If a child counts every square on a flat, stop and ask how many rods make it. Counting by 100s and 10s is the skill.
• Use the mat. The columns keep hundreds, tens and ones apart, just like the digits in a written number, and the counts at the bottom turn red when a column needs a trade.
• Pair the board with paper. Write each number sentence as the child builds it. That link between blocks and symbols is what makes the blocks pay off later, an approach the What Works Clearinghouse practice guide calls moving from concrete to semi-concrete to abstract representations.
• Keep real blocks if you have them. For a first introduction, real blocks in the hand are hard to beat. Use this board for practice, sharing work, homework help and anything that needs more blocks than the bag holds.

What makes these virtual blocks different

This board includes the parts teachers ask for: a place value mat with column counts, trading with an animation that shows the ten forming, auto-break when a rod lands in the ones column, a running expanded form, pen and text labels, undo and redo, share links that rebuild the board, a printable snapshot, keyboard controls, and ten task cards that check themselves. Use a current browser on a computer, tablet or phone, with no account and no ads.

For practice on paper, print the base ten blocks worksheets or a hundreds, tens and ones chart. Ready for bigger numbers or decimals? Place value disks go to the millions and down to thousandths without huge blocks. Families following Montessori can use the same ideas with golden beads.

Choosing an activity

Grade bands describe possible curriculum connections, not an assessment of an individual learner. Start with an example the learner can explain, then change one feature at a time. The activity suggestions here are editorial teaching ideas, not results from a classroom trial of this software. Use the model alongside written work and physical materials when useful. The linked standards describe learning objectives; they do not endorse Edulist or require this particular tool.