What Are Base Ten Blocks?

Base ten blocks are blocks in three sizes: a small cube for 1, called a unit; a stick of ten units for 10, called a rod; and a square of ten rods for 100, called a flat. On homework, children draw them as a dot for each one, a line for each ten, and a square for each hundred, so 3 lines and 4 dots is 34.

The size of each block is its value. A rod is exactly ten units long and a flat is exactly ten rods, so ten of one piece can always be traded for one of the next. That trade is what the old “carry the 1” and “borrow” stand for. Free printable base ten blocks to cut out, drawn to scale, with a place value mat and three practice sheets with answer keys, are in the printables section.

What are base ten blocks (place value blocks)?

Base ten blocks are a set of blocks in which each size is worth ten of the size before it: units for ones, rods for tens, flats for hundreds, and large cubes for thousands. “Base ten blocks”, “base 10 blocks”, and “place value blocks” are three names for the same set.

Block	Shape	Value	Other names you may hear
Unit	A small cube	1	One, cube, small cube
Rod	A stick of 10 units	10	Long, ten, ten stick
Flat	A square of 10 rods	100	Hundred, square
Cube	A block of 10 flats	1,000	Thousand, big cube

You can check the sizes by laying the pieces on each other: ten units cover a rod exactly, and ten rods cover a flat. The color of a plastic set means nothing, since sets come in different colors; only the size carries the value. The large cube for 1,000 seldom comes home in the early grades: second grade stops at 1,000 (1,200 in Texas), and ten flats show 1,000 as well as one cube does.

What grade uses base ten blocks?

Base ten blocks belong to kindergarten through second grade, with first grade as the main year. The Common Core standards do not name the blocks. They ask for “objects or drawings” and “concrete models”, which is the job the blocks do.

Grade	What children do with the blocks	Common Core	Texas (TEKS)
Kindergarten	Build 11–19 as ten ones and some more ones	K.NBT.A.1	None (first grade)
1st grade	Show tens and ones; add within 100, sometimes making a new ten	1.NBT.B.2, 1.NBT.C.4	1.2(B), 1.2(C), 1.3(A)
2nd grade	Add the flat; add and subtract within 1,000, trading tens and hundreds	2.NBT.A.1, 2.NBT.B.7	2.2(A)

Common Core kindergarten standard K.NBT.A.1 asks children to build the numbers from 11 to 19 “into ten ones and some further ones, e.g., by using objects or drawings”, which is where a rod first appears in many classrooms. A double ten frame shows the same teen numbers as one full frame and some more. First grade defines a ten as “a bundle of ten ones” (1.NBT.B.2) and asks children to add within 100 “using concrete models or drawings”, understanding that “sometimes it is necessary to compose a ten” (1.NBT.C.4). Second grade adds the hundred, “a bundle of ten tens” (2.NBT.A.1), and asks for adding and subtracting within 1,000 the same way (2.NBT.B.7).

Texas waits until first grade for the teen numbers as a ten and ones. Its first-grade standard 1.2(B) asks children to “use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way”, and second grade does the same up to 1,200 (2.2(A)). A Texas child may therefore be asked to show 34 as 2 tens and 14 ones as well as 3 tens and 4 ones.

The same split into tens and ones carries into third-grade multiplication, where an area model multiplies the tens and the ones separately: 4 × 23 is 4 × 20 plus 4 × 3.

How do you show a number with base ten blocks?

To show a number with base ten blocks, put out as many blocks of each size as its digit says: for 34, 3 rods and 4 units, with the rods on the left like the 3 in 34. These five steps build that up, a few minutes at a time, in the order children meet them in school.

1. 1

   Build a teen number

   Lay out 14 units in a row, then swap ten of them for one rod, checking that the rod is exactly as long as the ten units. Your child now has one rod and 4 units. Say it together: ten and four, fourteen.

2. 2

   Show a two-digit number

   For 34, put out 3 rods and 4 units. Put the rods on the left and the units on the right, the same order as the digits in 34. Count the rods by tens, then the units by ones: 10, 20, 30, 31, 32, 33, 34.

3. 3

   Write it down every time

   Have your child write 34 beside the blocks, then 3 tens 4 ones. Writing the number next to the blocks is what ties the blocks to the numerals, so do it on every number, not only at the end.

4. 4

   Show a number with a zero

   Build 40 as 4 rods and no units, then 306 as 3 flats, no rods, and 6 units. Point to the empty place and say that the zero in the number means none of that size.

5. 5

   Show it another way

   Build 34 as 2 rods and 14 units, then trade ten of the units for a rod. Your child sees that 2 tens and 14 ones and 3 tens and 4 ones are the same 34, which is the trade that regrouping uses.

Step 3 is the step that makes the blocks work, because the written number is what your child keeps when the blocks are put away. Writing 34 as 30 + 4 is expanded form, the written record of the same blocks; practicing it is place value work.

How do base ten blocks show regrouping (carrying and borrowing)?

With base ten blocks, regrouping is a trade: ten units become one rod when adding, and one rod becomes ten units when subtracting. Here are two problems, each done the way most parents learned it and then with blocks.

Adding: 46 + 37

• The old way: 6 + 7 is 13, so write the 3 and carry the 1. Then 4 + 3 + 1 is 8, for 83.
• With blocks: 4 rods and 6 units, plus 3 rods and 7 units, make 7 rods and 13 units. Trade ten of the units for a rod: 8 rods and 3 units, which is 83. The carried 1 is that rod.

Subtracting: 52 − 27

• The old way: you cannot take 7 from 2, so borrow from the 5. The 5 becomes 4 and the 2 becomes 12. Then 12 − 7 is 5 and 4 − 2 is 2, for 25.
• With blocks: start with 5 rods and 2 units. There are not enough units to take away 7, so trade one rod for ten units: 4 rods and 12 units. Take away 2 rods and 7 units, and 2 rods and 5 units are left, which is 25. The borrow is that trade.

The written method is not wrong, and schools have not dropped it. The blocks show the reason behind each mark, and the Common Core asks second graders to “relate the strategy to a written method” (2.NBT.B.7). The standards never say “carry” or “borrow”: they say a child will sometimes need to “compose or decompose tens or hundreds”, and homework says “trade” or “regroup”, the words for what happens to the blocks. The written method itself, the standard algorithm, is still required in fourth grade, as new math explained for parents sets out.

Why do schools use base ten blocks?

Schools use base ten blocks because the sizes are true to the numbers, so a child can see that ten ones make a ten before writing it. The US Department of Education’s What Works Clearinghouse rates teaching with “a well-chosen set of concrete and semi-concrete representations” as having strong evidence, in its 2021 practice guide on helping children who struggle with math. The guide asks for representations that are proportional, where “the representation for ones should be one-tenth the size of the representation for tens”. It names base 10 blocks as its example and warns that otherwise “the concept of place value would be harder for students to grasp”. Coins fail that test: a dime is worth ten pennies but is smaller than one.

The blocks help when each step is tied to the written number. In a 1990 study by Karen Fuson and Diane Briars, first and second graders did each step of a problem with blocks and “immediately recorded” it in numerals. Second graders in 42 classes in a large urban school district learned to add numbers of at least four digits.

The wider evidence is real and conditional. A meta-analysis of 55 studies by Carbonneau, Marley, and Selig (2013) found effects in favor of manipulatives, moderate to large on remembering what was taught and small on problem solving and transfer. The size of the effect also varied with how the lessons were taught and how the studies were run.

The blocks are a stage, not the goal. Children move from blocks to quick drawings to numbers alone. The What Works Clearinghouse advises fading the blocks only once a child is accurate without them, and bringing them back when a child is stuck. A hundreds chart shows the same tens and ones another way, as rows of ten. A ten frame shows a single ten as a full frame of ten boxes, and a number line shows a number as a distance from 0.

What if you do not have base ten blocks at home?

Without base ten blocks at home, print them, draw them, or bundle ordinary things in tens. Four options, best first:

1. Print them. The cut-out blocks on this page are drawn to scale, so a printed rod covers ten printed units exactly. Print at 100%, not “fit to page”.
2. Draw them. Use the quick drawings school uses: a dot or small square for each one, a line for each ten, and a large square for each hundred. The Common Core writers’ progressions document describes these drawings as showing “a ten as a single unit rather than as 10 separate ones”. A child who draws 3 lines and 4 dots for 34 is doing it right.
3. Bundle real things. Ten straws in a hair tie or ten pennies in a cup make a ten, the same bundles used for counting by tens to 100. A bundle can be opened and a rod cannot, so a bundle shows the trade even more plainly.
4. Use virtual blocks. Free online versions do the same job, as long as your child still says and writes the number after building it.

Free printable base ten blocks and worksheets

Our free base ten blocks printables come as five PDFs: two to keep and use, and three practice sheets with answer keys, in the order a child uses them. Every sheet prints in black and white, with no account and no email.

• Base Ten Blocks, 5 pages. Flats, rods, and units to cut out, each piece an outline with its squares drawn inside, so a rod shows its ten units. Print this one if you have no blocks at home, on card if you can.
• Base Ten Mat, 3 pages. A tens-and-ones mat, and a hundreds-tens-ones mat that prints sideways because a flat is ten units wide. Each column has a line under it for the digit. Print this one for plastic or paper blocks alike.
• What Number Is It?, 6 pages. Pictures of blocks, and your child writes the number: teens and two-digit numbers, numbers with no tens or no ones, blocks drawn out of order, and three-digit numbers with zeros. Print this one once your child can build two-digit numbers.
• Show the Number, 6 pages. A number to draw in quick drawings and to write as tens and ones, two-digit and then three-digit. The sheet asks for the fewest blocks, so every number has one right answer. Print this one after What Number Is It?.
• Regrouping, 6 pages. Two-digit additions where your child trades ten units for a rod, then two-digit subtractions where your child trades a rod for ten units. Some problems need no trade. Print this one once your child can trade ten units for a rod and back.

The cut-out blocks and the mats are drawn at 1 cm a unit, so print them at 100%. The practice sheets draw the blocks smaller to fit the page, and still to scale: a rod is always ten units and a flat ten rods. The problems are not numbered, and each key matches its answers by position. Every PDF ends with a page of instructions for grown-ups.

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Free printable base ten blocks and worksheets

Five free PDFs in black and white, with no account and no email, in teaching order: the cut-out blocks and the mat, then What Number Is It?, Show the Number, and Regrouping. Start with the one your child can already do. The three practice sheets each have an answer key, and every PDF ends with a page of instructions for grown-ups on why, what for, and how to use it.

1. 1Base Ten Blocks (PDF)370 pieces · 5 pagesDownload
2. 2Base Ten Mat (PDF)2 mats · 3 pagesDownload
3. 3Base Ten Blocks: What Number Is It? (PDF)29 numbers to write · answer key included · 6 pagesDownload
4. 4Base Ten Blocks: Show the Number (PDF)24 numbers to write · answer key included · 6 pagesDownload
5. 5Base Ten Blocks: Regrouping (PDF)24 numbers to write · answer key included · 6 pagesDownload

Base ten block games and activities

Base ten block games need only the blocks, printed or plastic, and a die, and each one ends with your child saying and writing the number.

• Race to a flat. Take turns rolling and taking that many units. Whenever you have ten units, trade them for a rod. The first to trade ten rods for a flat wins.
• Race to zero. Each player starts with a flat. Roll and give back that many units, trading the flat for ten rods, or a rod for ten units, when you have to. This is the subtraction version.
• Grab and say. Your child grabs a handful of rods and units, sorts them, and says and writes the number.
• Show me. Say a number and your child builds it. Then say “one more ten” or “one ten fewer” and your child changes the blocks to match.

Race to a flat is a board game without the board.

Common mistakes with base ten blocks

The common mistakes with base ten blocks happen on the table, where you can see them, and each one below has a fix you can make on the spot.

• Counting pieces. Three rods and 2 units is 5 pieces but 32. Have your child count the rods by tens first: 10, 20, 30, then 31, 32.
• Counting a rod as one. Lay ten units along a rod so your child sees it is ten.
• Reading in the order the pile lies. A flat, a unit, and a rod scattered on the table is still 111. Sort the blocks biggest first, left to right, before reading.
• Writing 3 rods and 14 units as 314. No place can hold more than 9. Trade ten of the units for a rod first: 4 rods and 4 units, 44.
• Dropping the zero. Three flats and 6 units is 306, not 36. Point to the empty place and write a 0 for it.
• Subtracting the smaller digit in each column. The Common Core progressions document names the error 82 − 45 = 43, where a child takes 2 from 5 instead of trading. Build 82 and try to take away 5 units, and the missing trade shows.
• Using the blocks without writing anything down. This one is a grown-up’s mistake. Have your child write the number after every build.