Explain why addition and subtraction strategies using drawings or objects


2.NBT.9  Explain why addition and subtraction strategies work, using place value and the properties of operations 1.


1 Explanations may be supported by drawings or objects.

Solve problems and explain why strategies work


The teacher strategy is to provide opportunity for students to problem solve and explain how their place value or properties of operations work?


This standard allows students to apply and demonstrate their understanding of addition and subtraction strategies and to explain how they work.  


Daily Discourse would allow for students to practice the articulation of their thinking.  Students will also be use MP 3 when understanding the reasoning of others and critiquing correct or incorrect reasoning. 


Example of MP 3


I have 134 books in my library.  I want to have a total of 260 books in my library.  How many books will I need?


Student example- explaining their reasoning with place value strategies and decomposing and composing 


I know I need at least 100 more books and that will bring me to 234 books.  I can then add 6 more books to make 240 books.  Now I can see that I need 20 more books to make 260.  Altogether I need 126 books.


Critique the reasoning – 


Sam said he can subtract 134 from 260 to find the total number.  His work is below, is he correct?

260 – 130 = 130    and 130 minus 4 is 124.  You will need 124 more books.


More explanation and examples form FLIPBOOKS


2.NBT.9 calls for students to explain using concrete objects, pictures and words (oral or written) why addition or subtraction strategies work.  The expectation is that students apply their knowledge of place value and the properties of operations in their explanation.  Students should have the opportunity to solve problems and then explain why their strategies work.


There are 36 birds in the park.  25 more birds arrive.  How many birds are there?  Solve the problem and show your work.


Student 1

I broke 36 and 25 into tens and ones and then added them.  30 + 6 + 20 + 5.

I can change the order of my numbers, so I added 30 + 20 and got 50.  Then I added on 6 to get 56.  Then I added 5 to get 61.  This strategy works because I broke all the numbers up by their place value.


Student 2

I used place value blocks and made a pile of 36.  Then I added 25.  I had 5 tens and 11 ones.

I had to trade 10 ones for a 10.  Then I had 6 tens and 1 one.  That makes 61.

This strategy works because I added up the tens and then added up the ones and traded if I had more than 10 ones.


Students could also have experiences examining strategies and explaining why they work.  Also include incorrect examples for students to examine.  Operations embedded within meaningful context promote development of reasoning and justification.



One of your classmates solved the problem 56 - 34 = ___ by writing - I know that I need to add 2 to the number 4 to get 6.  I also know that I need to add 20 to 30 to get 20 to get to 50.  So, the answer is 22.  Is the strategy correct? Explain why or why not?



One of your classmates solved the problem 25 + 35 by adding 20 + 30 + 5 + 5.  Is their strategy correct?  Explain why or why not?

Kansas Association of Teachers of Mathematics (KATM) Flipbooks.  Questions or to send feedback:

Retrieved from Math Flipbooks.

Coherence and Connections: Need to Know

Grade Below




Grade Level




Grade Above

In the previous Numbers and Operations in Base Ten domain standards, students learn the strategies and skills at a concrete and conceptual level.  This standard is asking students to explain why the strategies work, specifically, using place value and the properties of operations.  Students need the opportunity to solve problems and explain why their strategies work.  


Grade 2 students use their understanding of place value to add and subtract within 1,000 (e.g., 237 + 616 or 822 – 237). They can explain what they are doing as they add and subtract. They become fluent in addition and subtraction within 100. 


* For word problems, students extend their ability by solving two-step problems using addition, subtraction or both operations. They also master more advanced one-step addition and subtraction problems in this grade (such as take from with start unknown)


PARCC Draft Model Content Frameworks: Mathematics Grades K-2

Also check out Student Achievement Partners Coherence Map.

Classroom Resources

2.NBT.9 Daily Discourse


The power point would be a great way to implement this standard in your class.  Student could also work in pairs, in order to engage all students and then be prepared to explain their reasoning (how they thought about their problem) and how they solved it. Teachers will want to honor all the strategies students use in order to Add and Subtract.  Examples of these strategies are: making ten, decomposing and composing numbers, using concrete models like open number lines, ten-frames, Rekenreks, and place value strategies.

HOT Questions

1.  Sam has a total of 2 dozen cookies.  10 of the cookies were homemade.  The other cookies were store bought.  How many     cookies were store bought? Explain how you solved the problem.

10 homemade

? store bought cookies

24 cookies

10 + ? = 24

2.  Kurt added 54 + 28, he claims there will be 4 ones in the final sum.  Is he correct?  Explain how know.


     Example: Kurt needs to add 8 ones plus 4 more ones.  There will only be 2 ones left over, because when you combine 8                and 4 more ones 2 of the ones make the 8 a ten and then you have 2 ones left over. 




3.  If I take 55 from 62, I will have three ones left.  Do you agree or disagree?  Explain why. 


    Example, I disagree, you will have 7 ones, because I can count up from 55, 7 ones to make 62. 



PARCC K-2 Content Model Frameworks - 1st grade Formative Assessment Example


This example does a good job of outlining the questioning strategies required by the teacher.  Feel free to adapt for 2nd grade. 

Remember students have not learned how to regroup or borrow 




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