Base Ten Blocks

What are base ten blocks?

Base ten blocks are math manipulatives that show place value. A small cube is one. A rod of ten cubes is a ten. A flat square of ten rods is a hundred, and a big cube of ten flats is a thousand. Because each block is exactly ten of the one before, children can see that the 3 in 347 means 300 and the 4 means 40, instead of just reading digits.

How to use the virtual base ten blocks

1. Build a number. Press + under each place, or type a number such as 347 and press Show. The mat puts each block in its column.
2. Read it three ways. Under the mat you see the number, the expanded form (300 + 40 + 7) and the number in words.
3. Break a block apart. Tap a hundred and it becomes ten tens; tap a ten and it becomes ten ones. This is the borrowing step in subtraction.
4. Regroup. When a column has 10 or more, press Regroup to trade ten for one block of the next place. This is the carrying step in addition.

These online base ten blocks work as digital base ten blocks on a projector or a tablet, with nothing to install. Each column holds up to 20 blocks, so children can show 2 tens and 14 ones before they regroup it as 3 tens and 4 ones.

Base ten blocks worksheets and printables

What number is shown? Each problem shows a set of blocks. Children write how many of each, then the number. Three levels match the grades: tens and ones for 1st grade (1.NBT.B.2), hundreds for 2nd grade (2.NBT.A.1) and thousands for 4th grade. Turn on regrouping and one place shows 10 to 15 blocks, so 2 tens and 14 ones must be read as 34.

Draw the blocks gives a number and an empty box; the answer key draws it in. Printable base ten blocks is a real-size sheet to cut out: one hundred flat, sixteen tens and about eighty ones at 1 cm per cube, with a 10 cm bar to check your printer kept the size. Print it on card, or in black and white for children to color. The place value mat gives a column for each place to sort the blocks into.

For counting to 100 first, use the ten frame and the hundreds chart; for writing big numbers, the place value chart.

How we tested this tool

We checked the tool by script in Google Chrome on Windows across 576 worksheets: both worksheet types, all three levels, every problem count, with and without regrouping and answers, in color and black and white, on Letter and A4. In 2,976 problems with 39,730 blocks drawn, every picture has exactly the blocks of its number, no block leaves its box or touches another block or the writing lines, the ones always sit together in rows of five, and no number repeats on a page; on the answer keys all 928 red answers match the counts and the number. On the cut-out sheet every cube is exactly 10 mm, rods 10 × 100 mm and the flat 100 × 100 mm, all at least 6 mm from the paper edge, with a 100 mm check bar. On the virtual mat we tested showing numbers from 0 to 9,999, breaking a hundred into tens and regrouping it back, the number words, and full columns. Testing caught problems we fixed: thousands sentences shrank below 3 mm (that level now uses one wide column of up to 3 problems), unit cubes fell to about 1 mm on crowded pages (the smallest is now 1.4 mm, at the thousands level), and ones were split across lines (they now stay in one group). We printed sheets to PDF with Microsoft Edge (one US Letter portrait page) and tested the page at a 375 px phone width.

Frequently asked questions