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1st Grade · 2nd Grade · 1.NBT.C.4 · 2.NBT.B.5

Two-digit addition in 1st and 2nd grade

Two-digit addition, also called double digit addition, means adding numbers that each have a tens digit and a ones digit, such as 36+4736 + 47. In 1st grade, your child adds within 100 with blocks and drawings. In 2nd grade, your child adds and subtracts within 100 quickly and correctly.

What the standards say

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

1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

2.NBT.B.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

What it means, in plain words

1st grade: adding within 100 with tens and ones 1.NBT.C.4

Adding within 100 means adding numbers whose total is 100 or less. Two-digit addition in 1st grade has two kinds of sum. One adds a one-digit number to a two-digit number, such as 54+354 + 3. The other adds a multiple of 10, a number made only of tens like 20 or 30, such as 26+3026 + 30.

The big idea is to add tens with tens and ones with ones. For 26+3026 + 30, only the tens change: 2 tens and 3 tens make 5 tens, so the total is 56. Sometimes the ones add up to 10 or more. Then 10 of the ones are bundled into a new ten. For 47+647 + 6, the 7 ones and 6 ones make 13 ones. That is 1 ten and 3 ones, so the total is 53.

Children show the sum with blocks or a quick drawing, with sticks for tens and dots for ones. Then they write the matching equation and say in words what they did.

Your child should be able to:

  • Add a one-digit number to a two-digit number, such as 54+354 + 3
  • Add a multiple of 10 to a two-digit number by adding only the tens
  • Bundle 10 ones into a new ten when the ones add up to 10 or more
  • Show a sum with blocks or a drawing and match it to an equation

Example

What is 38+638 + 6?

  1. 38 is 3 tens and 8 ones.
  2. Add the ones: 8 ones and 6 ones make 14 ones.
  3. 14 ones is 1 ten and 4 ones, so bundle a new ten.
  4. Now there are 4 tens and 4 ones.
  5. 38+6=4438 + 6 = 44, so the total is 44.

2nd grade: adding and subtracting within 100 with ease 2.NBT.B.5

Two-digit addition in 2nd grade uses two full two-digit numbers, and subtraction joins in. The goal for adding and subtracting within 100 is fluency, which means getting the right answer quickly, without counting on fingers.

Children learn a few strategies and pick the one that fits the numbers. One is to split both numbers into tens and ones and add each part. Another is to make a ten first. For 58+758 + 7, move 2 from the 7 to make 60, then add the 5 that is left: 65. Two-digit addition and subtraction are linked, so a subtraction can be checked by adding the answer back. In subtraction, a ten is sometimes broken into 10 ones when there are not enough ones to take away.

Your child should be able to:

  • Add two two-digit numbers with a total up to 100
  • Subtract a two-digit number from a number up to 100
  • Break a ten into 10 ones when there are not enough ones to subtract
  • Check a subtraction by adding the answer back

Example

What is 36+4736 + 47?

  1. Add the tens: 30+40=7030 + 40 = 70.
  2. Add the ones: 6+7=136 + 7 = 13.
  3. Put the parts together: 70+13=8370 + 13 = 83.
  4. The total is 83.

Example

What is 71−3471 - 34, and how can you check it?

  1. 71 has only 1 one, not enough to take away 4 ones.
  2. Break one ten into 10 ones: 71 is now 6 tens and 11 ones.
  3. Take away 3 tens and 4 ones. That leaves 3 tens and 7 ones, which is 37.
  4. Check by adding: 37+34=7137 + 34 = 71.
  5. 71−34=3771 - 34 = 37, so the answer is 37.

Where children usually get stuck

  • For 45+845 + 8, your child writes 413.

    The child adds 5 and 8, gets 13 and writes all of it in the ones place. The 10 inside 13 is a ten, and it has to join the other tens.

    What helps. Do the sum with coins: dimes for tens and pennies for ones. When there are 10 pennies or more, trade 10 of them for a dime and count again.

  • For 34+2034 + 20, your child writes 36.

    The child sees the 2 and adds it to the 4 ones. The 2 in 20 stands for 2 tens, so it belongs with the 3 tens in 34.

    What helps. Say the sum in tens out loud: 3 tens and 2 tens make how many tens? Then add the 4 ones at the end.

  • For 53−1853 - 18, your child writes 45.

    In the ones place, the child takes the smaller digit from the bigger one: 8 minus 3. Which number each digit belongs to does not matter to the child. The 3 ones in 53 are not enough to take away 8, so a ten has to be broken into ones first.

    What helps. Build 53 cents with 5 dimes and 3 pennies and try to pay 18 cents. Your child will need to trade a dime for 10 pennies, which is exactly the missing step.

Try four practice questions

Real 1st grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

  1. 1Warm-up
    Maria is adding the ones in this problem.
    First ones:
    Second ones:
    After Maria trades 10 ones for 1 ten, how many tens and ones does she have?
    A
    0 tens and 10 ones
    B
    0 tens and 0 ones
    C
    1 ten and 10 ones
    D
    1 ten and 0 ones
    Show the answer and how to solve it

    Maria has 1 ten and 0 ones. She had 10 ones in all because 5 plus 5 is 10, and trading 10 of those ones for 1 ten leaves 0 ones.

    1. 1First, look at the two groups of ones. Maria has 5 ones in the first frame and 5 ones in the second frame.
    2. 2Add the two groups of ones together to find the total.
    3. 3Maria has 10 ones in all. She trades 10 of those ones for 1 ten. After the trade, 0 ones are left along with the new ten.

    Common mistake. A common mistake is keeping all 10 ones AND adding the new ten, picking '1 ten and 10 ones'. When you trade 10 ones for 1 ten, those 10 ones go away from the count — no ones are left over.

    The idea underneath. Trading 10 ones for 1 ten doesn't change the amount, just the way it's grouped. 10 ones is the same as 1 ten and 0 ones.

  2. 2On level
    Carlos solved this addition problem. Look at the addition shown.
    16+37
    Select the statement that best describes the work.
    A
    Carlos's 43 comes from adding the tens incorrectly.
    B
    Carlos's 43 is correct.
    C
    Carlos's 43 comes from swapping the digits.
    D
    Carlos's 43 comes from forgetting to make a new ten.
    Show the answer and how to solve it

    The answer is "Carlos's 4343 comes from forgetting to make a new ten." because 16+37=5316 + 37 = 53, but Carlos wrote 4343 — exactly 1010 less. He wrote the 33 from 6+7=136 + 7 = 13 in the ones place but never added the new ten to the tens column.

    1. 1Look at Carlos's work. The space for the new ten is empty and the sum is 4343.
    2. 2Add 16+3716 + 37 correctly. Ones place: 6+7=136 + 7 = 13, so write 33 and make a new ten. Tens place: 1+3+1=51 + 3 + 1 = 5. The correct sum is 5353.
    3. 3Compare Carlos's 4343 to the correct 5353. Carlos's sum is exactly 1010 less. That fingerprint matches: the new ten was never recorded or added.
    4. 4The answer is "Carlos's 4343 comes from forgetting to make a new ten."

    Common mistake. A common mistake is choosing "is correct" without adding 16+3716 + 37 first. The displayed sum 4343 is 1010 less than the actual sum 5353 because the new ten from 6+7=136 + 7 = 13 was never added.

    The idea underneath. Each regrouping mistake leaves a different fingerprint on the answer: forgot-the-new-ten makes the sum 1010 too small; added-the-carry-twice makes it 1010 too big; reversed-the-digits flips the tens and ones. Comparing your own sum to the displayed sum tells you which mistake (if any) happened.

  3. 3On level
    Look at the addition problem shown with base-ten blocks. What is the sum?
    +
    A
    7
    B
    38
    C
    64
    D
    37
    Show the answer and how to solve it

    The sum is 37. The blocks show 3 tens and 7 ones in all.

    1. 1Look at the cyan blocks. They show 3 tens and 4 ones — that is 34.
    2. 2Look at the pink blocks. They show 3 ones.
    3. 3Add the ones to find the new ones total.
    4. 4Now there are 3 tens and 7 ones. That is 37.

    Common mistake. It is easy to count the pink ones cubes as if they were tens rods. Each pink cube is worth 1, and each tens rod is worth 10.

    The idea underneath. Each tens rod stands for 10 and each ones cube stands for 1. Add the ones together, then put them with the tens you already have.

  4. 4Stretch
    Which problem has the same answer as 45−1845 - 18 and uses a multiple of 1010?
    A
    47−20\displaystyle 47 - 20
    B
    48−20\displaystyle 48 - 20
    C
    45−20\displaystyle 45 - 20
    D
    43−20\displaystyle 43 - 20
    Show the answer and how to solve it

    The matching problem is 47−2047 - 20. Both numbers go up by 22, so the answer stays the same: 45−18=2745 - 18 = 27 and 47−20=2747 - 20 = 27.

    1. 1Look at the problem 45−1845 - 18. The second number, 1818, is close to a friendly ten (2020).
    2. 2Change 1818 into 2020 by adding 22.
    3. 3To keep the answer the same, add 22 to the first number too.
    4. 4The new problem is 47−2047 - 20. Check that both problems give the same answer:

    Common mistake. A common mistake is changing only the second number. If you turn 1818 into 2020 by adding 22, you must also turn 4545 into 4747 by adding 22. If only one number changes, the answer changes too.

    The idea underneath. Subtraction measures the gap between two numbers. If you slide both numbers by the same amount in the same direction, the gap stays the same — but the math gets easier when one number lands on a friendly ten.