2nd Grade · 2.NBT.B.6

Column addition in 2nd grade

Column addition means writing numbers one above the other, ones under ones and tens under tens, and adding one column at a time. In 2nd grade, your child adds up to four two-digit numbers this way. Your child also learns shortcuts for adding multiple numbers, such as finding two that make a ten.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

2.NBT.B.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

What it means, in plain words

Lining up the places matters most. The ones go under the ones and the tens go under the tens, so each column holds one kind of thing. Your child adds the ones column first, then the tens column.

When the ones add up to 10 or more, every 10 ones become 1 new ten. This trade is called regrouping (many parents learned it as carrying). Your child writes what is left in the ones column and adds the new ten to the tens column. With three or four numbers, the ones can add up to 20 or more, which makes 2 new tens.

Column addition in 2nd grade also uses the fact that numbers can be added in any order. Before adding, your child can look for two numbers whose ones make 10, such as 24 and 46, and add those first. $24 + 46 = 70$ , and a round number like 70 is easy to add to.

Your child should be able to:

Line up two-digit numbers so tens sit under tens and ones under ones
Add three or four two-digit numbers, starting with the ones
Regroup 10 ones as 1 ten, or 20 ones as 2 tens
Spot two numbers whose ones make 10 and add them first

Example

What is $34 + 25 + 18$ ?

Write the numbers in a column, tens under tens and ones under ones.
Add the ones: $4 + 5 + 8 = 17$ . That is 1 ten and 7 ones.
Write 7 in the ones place and carry the 1 ten to the top of the tens column.
Add the tens: $1 + 3 + 2 + 1 = 7$ tens, which is 70.
$34 + 25 + 18 = 77$ , so the sum is seventy-seven.

Example

What is $22 + 45 + 38 + 15$ ?

Look for ones that make 10. 22 and 38 work ( $2 + 8 = 10$ ), and so do 45 and 15 ( $5 + 5 = 10$ ).
$22 + 38 = 60$
$45 + 15 = 60$
$60 + 60 = 120$ , so the sum is one hundred twenty.

Where children usually get stuck

Your child writes 27, 6 and 41 in a column with the 6 under the 2 and gets 128 instead of 74.
The child lines the numbers up on the left, the way words line up on a page. The 6 is 6 ones, so it belongs in the ones column, under the 7.
What helps. Turn lined paper sideways so the lines make columns. Write T over the tens column and O over the ones column before writing any number.
For $18 + 27 + 38$ , your child adds the ones to get 23, writes 23 under the ones and ends up with 623 instead of 83.
The child has regrouped 1 ten before but has not met a column with 20 or more ones. 23 ones is 2 tens and 3 ones, so the 2 tens move to the tens column.
What helps. Act it out with dimes and pennies. Trade every 10 pennies for a dime, then count the dimes and the pennies that are left.
For $35 + 26 + 14$ , your child writes the carried 1 above the tens but answers 65 instead of 75.
The small carried digit sits apart from the numbers, so it gets skipped when the child adds the tens column.
What helps. Have your child add the tens out loud, starting with the carried ten: "1 ten plus 3 tens plus 2 tens plus 1 ten." Saying it first makes it hard to skip.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
What is the sum?
$\displaystyle 12 + 26 + 15 = \underline{\phantom{000}}$
A
63
B
43
C
53
D
27
Show the answer and how to solve it
The sum of $12 + 26 + 15$ is $53$ .
1. 1Look at the equation. First, add the ones digits.
2. 2 $13$ ones equals $1$ ten and $3$ ones. Write the $3$ in the ones place of the sum and regroup the $1$ ten into the tens column.
3. 3Now add the tens digits. Don't forget to include the regrouped $1$ .
4. 4Put the tens and ones together to get the sum.
Common mistake. A common mistake is forgetting to regroup. When the ones sum to $13$ , students may write only the $3$ and skip the extra ten — landing on $43$ instead of $53$ .
The idea underneath. When the ones add up to $10$ or more, regroup: combine $10$ ones into $1$ ten, then add it to the tens column.
2On level
Find the two numbers whose ones digits add to 10. Drag those cards so they are first.
Drag a card to move it, or tap a card, then tap where it should go.
36
22
14
49
Show the answer and how to solve it
The make-a-ten pair is $36$ and $14$ because their ones digits, $6$ and $4$ , add to $10$ . Putting them first gives $36 + 14 = 50$ , then $22$ and $49$ are easier to add on. Either order of the pair ( $36$ then $14$ , or $14$ then $36$ ) is correct, and the last two cards can be in either order.
1. 1Look at the ones digit (the right digit) of each card. The cards are $36$ , $22$ , $14$ , and $49$ , so the ones digits are $6$ , $2$ , $4$ , and $9$ .
2. 2Find two ones digits that add to $10$ . Check the pairs: $6 + 2 = 8$ , $6 + 4 = 10$ , $6 + 9 = 15$ , $2 + 4 = 6$ , $2 + 9 = 11$ , $4 + 9 = 13$ . Only $6 + 4 = 10$ , so the make-a-ten pair is $36$ and $14$ .
3. 3Drag $36$ and $14$ so they are first. One correct order is shown below.
4. 4Now $36$ and $14$ are first. Adding them gives $36 + 14 = 50$ , a tens number, which is easier to add the rest to.
Common mistake. A common mistake is choosing $22$ and $49$ because the numbers look easy to work with. But check the ones digits: $2 + 9 = 11$ , not $10$ , so $22$ and $49$ are not the make-a-ten pair. Always check the ones digits first.
The idea underneath. Two two-digit numbers add to a tens number (like $40$ , $50$ , or $60$ ) exactly when their ones digits add to $10$ . Finding this pair first turns a hard four-number addition into easier steps.
3On level
What is the sum?
$\displaystyle \begin{array}{r}\phantom{+}29 \\ \phantom{+}36 \\ \underline{+47}\end{array}$
A
102
B
12
C
112
D
113
Show the answer and how to solve it
The sum is $112$ . The ones column makes $22$ ( $2$ tens and $2$ ones), and the tens column makes $11$ ( $1$ hundred and $1$ ten).
1. 1Look at the addition stack. There are three two-digit numbers to add.
2. 2Add the ones column first: $9+6+7 = 22$ . That is $2$ tens and $2$ ones. Write down $2$ ones and regroup $2$ tens.
3. 3Now add the tens column. Don't forget to add the $2$ tens you just regrouped: $2+3+4+2 = 11$ . That is $1$ hundred and $1$ ten.
4. 4Put the digits together: $1$ hundred, $1$ ten, and $2$ ones. The sum is $112$ .
Common mistake. A common mistake is forgetting to compose a new hundred when the tens column reaches $10$ or more. When the tens column adds to $11$ , that means $1$ hundred and $1$ ten — not just $11$ written in the tens place.
The idea underneath. When a column totals $10$ or more, you compose a new unit one place to the left. Ten ones make one ten, and ten tens make one hundred.
4Stretch
Find the total shown by the blocks.
Show the answer and how to solve it
Answer. 205
The total is 205. There are 18 tens and 25 ones across all groups. Regrouping the 25 ones gives 2 more tens and 5 ones left, making 20 tens. Regrouping the 20 tens gives 2 hundreds and 0 tens left, so the total is 2 hundreds, 0 tens, and 5 ones, which is 205.
1. 1Look at the four groups. First, count all the long ten-rods.
2. 2Now count all the small ones-cubes across the four groups.
3. 3There are 25 ones, which is more than 10. Regroup 20 of the ones as 2 more tens. That leaves 5 ones, and the tens go from 18 to 20.
4. 4There are 20 tens, which is more than 10. Regroup 20 of the tens as 2 hundreds. That leaves 0 tens.
5. 5Put the place values together to read the total.
Common mistake. A common mistake is to write the tens count and ones count side by side. A student who counts 18 tens and 25 ones might write 1825 instead of regrouping. You must trade 10 ones for 1 ten, and 10 tens for 1 hundred, before naming the total.
The idea underneath. Whenever you have 10 of any place-value unit, you can trade them for 1 of the next higher unit. Ten ones become 1 ten, and 10 tens become 1 hundred. After every trade, count what is left in each place to read the number.