2.NBT.9: Explain Why a Strategy Works
Also written as 2.NBT.B.9 and CCSS.MATH.CONTENT.2.NBT.B.9 · Cluster: Use place value understanding and properties of operations to add and subtract.
The Official Wording
Explain why addition and subtraction strategies work, using place value and the properties of operations.
Common Core State Standards, Grade 2, Number & Operations in Base Ten · Read it at the source · Checked October 14, 2026
What 2.NBT.9 Means in Plain English
Second graders say why a shortcut works, not only that it does. When a classmate turns 48 + 27 into 50 + 25, the explanation is that 2 moved from one addend to the other, so the total did not change. Drawings and blocks count as explanations.
The reasons come from place value (tens with tens, ones with ones) and the properties of addition (any order, any grouping). This standard is what keeps 2.NBT.5 and 2.NBT.7 from becoming tricks. In 3rd grade the same habit explains why 4 × 6 equals 6 × 4 (3.OA.5).
2.NBT.9 I Can Statements
- I can explain why a strategy gives the right answer.
- I can use place value to show why tens can be added first.
- I can show with blocks or a drawing why a shortcut works.
2.NBT.9 Worked Example
A classmate’s shortcut, 48 + 27 as 50 + 25, taken apart until the reason it works is in plain view.
Mia solved 48 + 27 by changing it to 50 + 25 = 75. Explain why her answer is right.
- Name what she did: she added 2 to the 48 to make 50, a friendlier number.48 + 2 = 50
- Adding 2 would make the total 2 too big, so she took the same 2 away from the 27.27 − 2 = 25
- The 2 moved from one addend to the other. Nothing was added to the total and nothing was taken away.48 + 27 = (48 + 2) + (27 − 2) = 50 + 25
- Now the sum is easy, and it is the same sum.50 + 25 = 75
Check it: Add the long way: 40 + 20 = 60, 8 + 7 = 15, 60 + 15 = 75. Same answer by a different route, which is what a good explanation predicts.
Common Mistakes with 2.NBT.9
Explaining by restating the steps
“It works because you make 48 into 50 and then add.”
Try this: Ask “why can you change the 48?” and wait. Push for the word total: the total stays the same because 2 moved, not vanished.
Adjusting one addend and forgetting the other
48 + 27 becomes 50 + 27 = 77
Try this: Model it with two piles of counters: slide 2 counters from the 27 pile to the 48 pile and count the whole table. Nothing changed.
Using the addition rule for subtraction
63 − 29 becomes 64 − 28 “because I moved a 1”
Try this: Draw the two numbers on a number line with the difference as a gap. Slide both up by 1 and the gap stays 34.
Where 2.NBT.9 Fits
Practice 2.NBT.9
Quick Check
- Leo solved 36 + 49 by doing 36 + 50 and then taking 1 away. Why does that work?
- Why can you add the tens first in 23 + 45?
- Zara says 72 − 38 is the same as 74 − 40. Is she right? Explain.