2nd Grade · 2.NBT.B.9

Addition strategies in 2nd grade

Addition strategies are different ways to add, such as adding the tens and then the ones, or making a round number first. In 2nd grade, your child uses addition and subtraction strategies with two-digit numbers and explains why each one works.

What the standard says

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

2.NBT.B.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

What it means, in plain words

A strategy is a way to work out an answer. Children in 2nd grade learn several and choose one that fits the numbers. To add $47 + 25$ , one child adds the tens first: $40 + 20 = 60$ . Next come the ones, $7 + 5 = 12$ , and together that makes $60 + 12 = 72$ . Another child moves 3 from the 25 to the 47 to make 50, then adds $50 + 22 = 72$ .

What is new this year is the explanation. Your child says why a strategy works, often with blocks or a drawing. Adding tens and ones works because 47 really is 4 tens and 7 ones, and nothing is lost when the parts are added separately. Moving 3 from one number to the other works because the total stays the same.

Subtraction strategies use the same ideas. To find $83 - 29$ , a child can take away 30, which is easier. That takes away 1 too many, so the child adds 1 back: $83 - 30 = 53$ and $53 + 1 = 54$ . Another child counts up from 29 to 83 and adds the jumps.

Your child should be able to:

Add two-digit numbers by adding the tens, then the ones
Move part of one number to the other to make a ten or a round number
Subtract by counting up, or by taking away a round number and fixing the difference
Explain with blocks or a drawing why a strategy gives the right answer

Example

Use tens and ones to find $56 + 38$ . Why does it work?

Split each number into tens and ones: 56 is 50 and 6, and 38 is 30 and 8.
Add the tens: $50 + 30 = 80$ .
Add the ones: $6 + 8 = 14$ .
Put them together: $80 + 14 = 94$ .
It works because every part of both numbers is still there, just added in a different order. The sum is 94.

Example

Find $72 - 48$ by counting up from 48.

From 48 up to the next ten, 50, is 2.
From 50 to 70 is 2 tens, or 20.
From 70 to 72 is 2.
Add the jumps: $2 + 20 + 2 = 24$ .
It works because subtraction finds how far apart two numbers are, and counting up measures that same distance. So $72 - 48 = 24$ .

Where children usually get stuck

For $46 + 37$ , your child writes $40 + 30 = 70$ and $6 + 7 = 13$ , then answers 713.
The child puts the two parts side by side instead of adding them. 13 ones is 1 ten and 3 ones, so 7 tens become 8 tens and the answer is 83.
What helps. Ask your child to read each part as a number, seventy and thirteen. Then add them together on your fingers or with coins: 70, 80, 81, 82, 83.
For $91 - 39$ , your child takes away 40 to get 51, then takes away 1 more and answers 50.
The child remembers that the round number needs fixing but not which way. Taking away 40 removed 1 more than 39, so 1 has to be given back: the answer is 52.
What helps. Act it out with 9 dimes and 1 penny. Take away 4 dimes, which is 1 cent more than 39 cents. Then put 1 penny back and count what is there: 52 cents.
Your child gets the right answer but, asked why it works, says "that's how my teacher showed us."
The steps were learned as a recipe. A recipe without the place value behind it stops working as soon as the numbers look different.
What helps. Ask your child to show the problem with a quick drawing: a stick for each ten and a dot for each one. Talking through the drawing is the explanation the class is asking for.

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
Sam is finding $31 - 18$ . The blocks show the top number after Sam regrouped.
Complete the sentence to explain why we regrouped.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
There are not enough
in the top number. So we trade 1 ten for
.
ones
10 ones
tens
1 ten
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
The first blank is 'ones' (there are not enough ones to subtract). The second blank is '10 ones' (which is what 1 ten equals).
1. 1Look at the subtraction problem $31 - 18$ . The blocks show the top number after Sam regrouped.
2. 2We try to subtract $8$ ones from $1$ one. There are not enough ones! So Sam traded $1$ ten for $10$ ones.
3. 3Now $31$ is shown as $2$ tens and $11$ ones. The first blank is 'ones' and the second blank is '10 ones'.
Common mistake. A common mistake is choosing '1 ten' for the second blank. But we are not getting another ten — we are breaking $1$ ten apart into $10$ smaller pieces: $10$ ones.
The idea underneath. When you can't subtract a smaller unit, you trade ONE of the next-larger unit for TEN of the smaller unit. The total amount stays the same — only how it is grouped changes.
2On level
The blocks below show $523 + 234$ . Drag a tile into each empty box to complete the equation.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
523 + 234 = (500 + 200) + (20 +
) + (3 +
)
30
4
2
3
234
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
The first empty box is $30$ (the tens of $234$ ), and the second empty box is $4$ (the ones of $234$ ). Pairing like place values together: $523 + 234 = (500 + 200) + (20 + 30) + (3 + 4) = 700 + 50 + 7 = 757$ .
1. 1The blocks show $523$ in cyan and $234$ in pink. To add them, look at each place value separately.
2. 2Break $234$ into hundreds, tens, and ones.
3. 3Now group hundreds with hundreds, tens with tens, and ones with ones. The hundreds pair $500 + 200$ is already filled. The tens pair adds $20$ from $523$ and $30$ from $234$ . The ones pair adds $3$ from $523$ and $4$ from $234$ .
4. 4So the first empty box is $30$ and the second empty box is $4$ .
Common mistake. A common mistake is using the tile $3$ for the first empty box because $234$ has the digit $3$ in it. The $3$ in $234$ is in the tens place, so it stands for $3$ tens, which is $30$ — not just $3$ .
The idea underneath. When adding numbers, you can pair up like place values — hundreds with hundreds, tens with tens, ones with ones — because each place stands for a different unit ( $100$ , $10$ , or $1$ ).
3On level
Look at the blocks below. Which digit will change in the answer?
A
the ones digit
B
the tens digit
C
the hundreds digit
Show the answer and how to solve it
The hundreds digit changes from 2 to 3. The tens digit and the ones digit do not change because only 1 hundred was added.
1. 1Look at the blocks. The first group shows the number 234 (2 hundreds, 3 tens, and 4 ones). The second group shows 1 hundred flat being added.
2. 2Adding 1 hundred grows the hundreds place by 1. So 2 hundreds plus 1 hundred makes 3 hundreds. The tens and ones do not change because no tens or ones were added.
3. 3Compare the digits in 234 and 334:
4. 4The hundreds digit changed from 2 to 3. The tens digit (3) and the ones digit (4) stayed the same. So the hundreds digit is the digit that changes.
Common mistake. A common mistake is picking the ones digit because students often think any addition changes the ones place first. The unit you add tells you which place changes: 1 hundred flat changes the hundreds digit, not the ones digit.
The idea underneath. The unit being added tells you which place-value digit changes. A hundred flat changes the hundreds digit. A ten rod changes the tens digit. Match the unit to the place name.
4Stretch
Look at the blocks. They show $35 + 18$ . Choose the sentence that explains why 10 ones become 1 ten when we add.
A
Because we always make a new ten when we add.
B
Tens come before ones in place value.
C
10 ones have the same value as 1 ten.
D
1 ten is more than 10 ones.
Show the answer and how to solve it
The correct sentence is "10 ones have the same value as 1 ten." The trade works because 10 ones and 1 ten name the same amount — only the way we show it changes. So when 5 ones and 8 ones make 13 ones, we can swap 10 of those ones for 1 ten and end up with 53.
1. 1The first group is 35 (3 tens and 5 ones, in cyan). The second group is 18 (1 ten and 8 ones, in pink).
2. 25 ones + 8 ones = 13 ones. That is 10 or more, so we can trade.
3. 3Why is the trade fair? Because 10 ones have the same value as 1 ten. We can swap 10 of the ones for 1 ten without changing how much we have. The blocks change shape, but the total stays the same.
4. 4After the trade, we have 5 tens and 3 ones, which is 53. The reason the trade works is that 10 ones have the same value as 1 ten.
Common mistake. A common mistake is thinking that 1 ten is MORE than 10 ones because 1 ten looks like fewer blocks. But 1 ten and 10 ones name the same amount — a ten rod is exactly the same value as 10 ones cubes lined up.
The idea underneath. Regrouping is a fair trade. 10 ones and 1 ten name the same amount — only the way they look changes.