2nd Grade · Number & Operations in Base Ten
2.NBT.B.9: Explain why addition and subtraction strategies work
2.NBT.B.9 is a 2nd grade Common Core math standard in Number & Operations in Base Ten. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The standard
Explain why addition and subtraction strategies work, using place value and the properties of operations.
In plain words
Explain why addition and subtraction strategies work.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
Question 1 of 6
Why can you add the ones digits and the tens digits separately when solving 23 + 45?
- Because the numbers are small.
- Because you are adding groups of ones and groups of tens.
- Because you always start adding from the right.
Where students can get stuck
Explain why addition strategies work.
- Describing the steps but not the reason, saying "I carried the one" without knowing that the one stands for a ten.
- Using a drawing that doesn't match the numbers, such as drawing 36 as 6 tens and 3 ones.
- Working out 9 + 27 all over again after finding 27 + 9, rather than explaining that order doesn't change a sum.
Explain why subtraction strategies work.
- Saying "you can't take 7 from 2" for 52 - 17, instead of explaining that a ten becomes ten ones to make 12.
- Taking 20 from 45 to find 45 - 19, then taking 1 more away instead of adding it back, and getting 24, not 26.
- Believing that order doesn't matter in subtraction, as it doesn't in adding, so 8 - 15 seems the same as 15 - 8.
Effective teaching strategies
- Have students draw base-ten blocks for 47 + 15 and describe each trade in place-value words, such as 10 ones becoming 1 ten, instead of saying they carried the one.
- Ask students to solve 53 - 29 by taking away 30 and then putting 1 back, and to explain why 1 is added back: they took away 1 too many.
- Show why 34 + 28 equals 30 + 32 by moving 4 from one addend to the other, so students explain a strategy with the properties of operations.
Units that teach this standard
Find where 2.NBT.B.9 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
Bridges in Mathematics
enVision Mathematics
Eureka Math
Eureka Math²
Go Math!
i-Ready Classroom Mathematics
Illustrative Mathematics
Into Math
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Each skill has its own guide for families, with a plain-language look at the skill, three questions to try together, and ideas for helping at home.
Help every student practice place value at home
In Bobby's Math Club, students practice at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free for every family.
See how it works for teachers
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.