2nd Grade · 2.NBT.B.7

Three-digit subtraction in 2nd grade

Three-digit subtraction means taking one three-digit number away from another, such as $652 - 318$ . In 2nd grade, your child learns three-digit addition and subtraction together, adding and subtracting within 1000 with blocks, drawings and written steps.

What the standard says

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

2.NBT.B.7 Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

What it means, in plain words

Three-digit addition and subtraction follow one rule: hundreds go with hundreds, tens with tens and ones with ones. Base-ten blocks make this easy to see. A flat square is a hundred, a rod is a ten and a small cube is a one.

Sometimes a place does not have enough. In $652 - 318$ , there are 2 ones and your child needs to take away 8. So your child trades 1 ten for 10 ones. Now there are 4 tens and 12 ones, and $12 - 8 = 4$ . This trade is called regrouping, or breaking apart a ten. The same trade works with a hundred: 1 hundred becomes 10 tens.

In addition, the trade goes the other way: 10 ones become 1 new ten, and 10 tens become 1 new hundred. Your child also learns that addition checks subtraction. If $652 - 318 = 334$ , then $334 + 318$ has to equal 652, and it does.

Your child should be able to:

Add and subtract three-digit numbers place by place, with blocks, a drawing or written steps
Trade 1 ten for 10 ones, or 1 hundred for 10 tens, when a place runs short
Make a new ten or a new hundred when a place adds up to 10 or more
Check a subtraction by adding the answer back

Example

What is $652 - 318$ ?

Ones: 2 ones are not enough to take away 8. Trade 1 ten for 10 ones, so there are 4 tens and 12 ones.
$12 - 8 = 4$ ones.
Tens: $4 - 1 = 3$ tens.
Hundreds: $6 - 3 = 3$ hundreds.
$652 - 318 = 334$ , so the difference (the answer to the subtraction) is three hundred thirty-four.

Example

What is $246 + 187$ ?

Ones: $6 + 7 = 13$ . That is 1 ten and 3 ones, so write 3 and move the ten to the tens.
Tens: $4 + 8 + 1 = 13$ tens. That is 1 hundred and 3 tens, so write 3 and move the hundred to the hundreds.
Hundreds: $2 + 1 + 1 = 4$ hundreds.
$246 + 187 = 433$ , so the sum is four hundred thirty-three.

Where children usually get stuck

For $524 - 167$ , your child writes 443 instead of 357.
In each column, the child takes the smaller digit from the bigger one, whichever is on top. The top number is what you start with, so 4 ones minus 7 ones needs a trade first.
What helps. Build 524 with base-ten blocks or with dollar bills, dimes and pennies. Then take 167 away for real. When the pennies run out, your child has to trade a dime.
For $403 - 158$ , your child crosses out the 0, writes 9 above it, leaves the 4 alone and gets 345 instead of 245.
The child copies a step without seeing why it works. There are no tens to trade, so 1 hundred must first become 10 tens, and then 1 of those tens becomes 10 ones. That leaves 3 hundreds and 9 tens.
What helps. Show 4 flats and 3 small cubes with blocks or a drawing. Ask your child to get more ones. The only way is to break a flat into 10 rods and then a rod into 10 cubes.
For $247 + 386$ , your child writes 51213.
Each column was added correctly, but every column total got written down in full. A place holds only one digit, so 13 ones has to become 1 ten and 3 ones, and the answer is 633.
What helps. Before writing anything, have your child say each column total as tens and ones: "13 ones is 1 ten and 3 ones." Then write the 3 and move the ten.

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
$\displaystyle 23 + 14 = 37$
Which model matches the equation above?
A
B
C
D
Show the answer and how to solve it
The correct model has block groups that match $23$ , $+$ , $14$ , $=$ , $37$ — that is, $2$ rods and $3$ cubes; then a plus sign; then $1$ rod and $4$ cubes; then equals; then $3$ rods and $7$ cubes.
1. 1Look at the equation.
2. 2Break each number into tens and ones to know what the blocks should look like.
3. 3Find the model whose three groups match all three numbers and uses a plus sign. The matching model has 2 rods and 3 cubes; then a plus sign; then 1 rod and 4 cubes; then an equals sign; then 3 rods and 7 cubes.
4. 4The other models do not match: one has the wrong result (4 tens instead of 3 tens in the last group), one has the wrong number of tens in the first group (1 rod instead of 2), and one uses a minus sign instead of a plus sign.
Common mistake. A common mistake is checking only the first two block groups (the addends) and not checking the result group. Always check all three groups AND the operator sign between them.
The idea underneath. A base-ten block model represents a complete computation: blocks for each number AND the symbol between them. To match an equation, all three block groups and the operation symbol must match — not just the first one or two parts.
2On level
Maya used a number line to add two numbers. Her work is shown below. Select the statement that best describes her work.
A
Maya's 557 is 100 more than the correct sum because the first jump was too far.
B
Maya's 557 is the correct sum.
C
Maya's 557 is 5 less than the correct sum because she forgot the last small jump.
D
Maya's 557 is 10 less than the correct sum because the tens jump was too small.
Show the answer and how to solve it
Maya's work is correct. $312 + 245 = 557$ , and all three landings on her number line are accurate.
1. 1Look at Maya's number line. She starts at 312. Her jumps are +200, +40, and +5, which add up to 245. So Maya is adding $312 + 245$ .
2. 2Find the correct sum:
3. 3Maya's final landing is 557. Compare: $557 - 557 = 0$ . Maya's answer equals the correct sum — there is no error.
4. 4Check each landing one jump at a time. After +200, Maya lands at 512 — correct $(312 + 200 = 512)$ . After +40, Maya lands at 552 — correct $(512 + 40 = 552)$ . After +5, Maya lands at 557 — correct $(552 + 5 = 557)$ . All three landings match.
5. 5The statement that best describes Maya's work is: "Maya's 557 is the correct sum."
Common mistake. A common mistake is to distrust Maya's final number and look for an error that is not there. Students should check each landing — 512, 552, and 557 are all correct.
The idea underneath. On an open number line, errors cascade — once a landing is wrong, every landing after it is also wrong. Always check each landing one jump at a time.
3On level
Carlos's work is shown below.
$\displaystyle \text{Carlos said } 432 - 115 = 323.$
Choose the best description of Carlos's work.
A
Carlos's 323 is not correct because he forgot to take 1 ten away after regrouping.
B
Carlos's 323 is not correct because he did not subtract the hundreds.
C
Carlos's 323 is not correct because he did not regroup when needed.
D
Carlos's 323 is correct.
Show the answer and how to solve it
Carlos's 323 is not correct because he did not regroup when needed. The correct difference, using the regrouped blocks, is 317.
1. 1Look at the blocks. They show 432 already regrouped — 4 hundreds, 2 tens, and 12 ones — minus 115.
2. 2Subtract column by column using the regrouped blocks:
3. 3The correct difference is 317. Carlos said 323, so his answer is not correct.
4. 4Look at how Carlos got 323. He subtracted the smaller digit from the larger digit in each column — 3 in the ones, 1 in the tens, 3 in the hundreds — instead of using the regrouping the blocks show. So the best description is the one that says he did not regroup when needed.
Common mistake. A common mistake is to assume Carlos's answer is close enough and pick 'is correct' without computing the actual difference. Always work out the subtraction yourself first, then compare.
The idea underneath. When the blocks show regrouping (4 hundreds, 2 tens, and 12 ones for 432), each error mechanism leaves a different signature. Subtracting smaller-from-larger in every column gives 323 (no regroup); adding 10 gives 327 (forgot decrement); adding 100 gives 417 (skipped hundreds). Matching Carlos's 323 to its signature names the mistake.
4Stretch
Use the base-ten blocks to find the difference.
$\displaystyle 631 - 257 = \underline{\phantom{0000}}$
A
374
B
384
C
426
D
574
Show the answer and how to solve it
The difference is $374$ . After $1$ hundred is regrouped as $10$ tens AND $1$ ten is regrouped as $10$ ones, the columns subtract as: $11$ - $7$ = $4$ ones, $12$ - $5$ = $7$ tens, and $5$ - $2$ = $3$ hundreds.
1. 1Look at the blocks. They show $631$ with $1$ hundred regrouped as $10$ tens AND $1$ ten regrouped as $10$ ones — that is $5$ hundreds, $12$ tens, and $11$ ones.
2. 2Subtract the ones column.
3. 3Subtract the tens column. Use the $12$ tens shown by the blocks.
4. 4Subtract the hundreds column. After regrouping, only $5$ hundreds remain. The difference is $374$ .
Common mistake. A common mistake is keeping all $3$ tens when $1$ has been regrouped as $10$ ones. After the ones regroup, only $2$ tens remain, so the tens column is ( $2$ + $10$ ) - $5$ = $7$ , not ( $3$ + $10$ ) - $5$ = $8$ .
The idea underneath. When subtracting with two regroups, both the tens column and the hundreds column must be updated. Regrouping $1$ ten as $10$ ones means the tens column has $1$ less ten. Regrouping $1$ hundred as $10$ tens means the hundreds column has $1$ less hundred. The total stays the same — only the column counts change.