Explaining why addition strategies work
In 2nd grade, children learn to explain why an addition strategy works, to show it with tens and ones, and to say why changing the order of the numbers keeps the sum the same.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 2nd grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
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.
Why this matters
Being able to say why a method works gives your child the confidence to use it with new numbers and to notice if something has gone wrong. If your child only follows steps, they can get stuck if a problem looks a little different. Knowing the reason lets them adjust. This habit of reasoning carries into every later grade, from multiplying in 3rd grade to fractions in 4th and 5th.
Next comes explaining why subtraction strategies work, which asks for the same kind of reasons with taking away.
Where kids can get stuck
- 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.
How you can help
- Ask "How did you figure that out?" after your child adds something in everyday life, such as two game scores, and listen to the whole answer before saying whether it's right.
- Solve a problem two different ways together, such as 48 + 27, and talk about why both ways give the same answer of 75.
- Ask your child to be the teacher. Add 36 + 25 as 30 + 20 and 6 + 5, then have them explain to you, or a stuffed animal, why the pieces make 61.
The kid-friendly video below explains it in a few minutes, and Bobby's Math Club offers free practice that grows with your child.
Kid-friendly explanation
Questions parents ask
Why does my child have to explain math instead of giving the answer?
Explaining shows that your child understands why a strategy works, not only how to follow it. That understanding helps them solve new problems, choose sensible methods, and catch their own mistakes. If they can say why 36 + 25 is 61, they're ready to try 136 + 25 next. It also builds clear thinking and talking, which matter in every subject.
My child gets the right answer but can't explain it. Is that a problem?
It's common and not a cause for worry. Being able to explain often comes after being able to do. Help by asking specific questions, like "What did you add first?" or "What does that 1 stand for?" Showing the problem with coins or small objects can give your child words for what they already did in their head.
What should a good explanation of adding sound like in 2nd grade?
A good explanation ties each step to tens and ones, or to the order of adding. For 46 + 35: "46 is 4 tens and 6 ones, and 35 is 3 tens and 5 ones. That's 7 tens and 11 ones. Eleven ones make another ten, so it's 8 tens and 1 one: 81." It doesn't need fancy words, only reasons.
Make learning math fun
Bobby's Math Club turns 2nd grade math practice into something fun to do together.
- Unlimited free practice
- Practice that starts where your child is and grows with them
- You see their progress and what to work on next
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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 2.NBT.B.9: “Explain why addition and subtraction strategies work, using place value and the properties of operations.” Learn how Bobby's Math Club can help your students grow. (Common Core 2.NBT.9)