How to Teach Addition with Carrying — Clearing the Hurdle with "Groups of 10"
"8 + 5." Your child counts on their fingers, runs out, and the pencil stops. This is the first real hurdle in first-grade math: addition with carrying.
I am not a specialist in teaching math. Until I started researching it in order to build the diglabo worksheets, I didn't know why so many children stall right here. When I looked into it, the cause turned out to be clear — and so did what you can do at home.
The root cause: composing and decomposing 10 isn't automatic yet
Addition with carrying is addition whose sum goes past 10. Japan's Ministry of Education explains it this way in its commentary on the national curriculum guidelines for elementary mathematics (2017): children look at the numbers as "10 and how many more", break a number apart to make 10, and so reuse arithmetic they already know (Grade 1, Numbers and Calculation).
In Japanese schools this is taught as the sakuranbo ("cherry") method. For 8 + 5, you split the 5 into 2 and 3, add the 2 to the 8 to make 10, then add the remaining 3 to get 13. For that to work, two things have to already be in place:
- Composing 10 — instantly answering "8 and what makes 10?" (8 and 2, 7 and 3, 6 and 4…)
- Decomposing numbers — instantly answering "5 is 2 and what?"
Children who stall on carrying usually aren't confused about the method. These two steps just aren't automatic yet. If every split takes thought, they lose track of what they were doing halfway through. The place they're stuck is not "carrying" — it's one step earlier.
There isn't only one way to split
This is worth knowing, and it takes some pressure off. I assumed at first that there was one correct way to split the cherry. There isn't.
The same commentary states that "various ways of calculating are possible" for addition, and gives 8 + 7 with two of them side by side:
- Split the number being added (the 7): 7 into 2 and 5, so 8 + 2 makes 10, then 10 and 5 is 15
- Split the first number (the 8): 8 into 3 and 5, so 3 + 7 makes 10, then 10 and 5 is 15
So if your child splits the numbers differently from the diagram they saw at school, but is still making a 10, they are not doing it wrong. Matching the school's notation can wait until they understand it.
How to teach it at home
Step 1: Check the feel for "10 and how many"
Ask "10 and 3 is how many?" If "13" comes back instantly, the sense of a group of 10 is there. If they hesitate, start with a game: count "a group of 10, and how many singles" using an egg carton or blocks.
Step 2: Turn "how many more to make 10?" into a spoken game
In the bath, in the car: "8?" "2!" — repeat until it's instant. Cards or dice work too. Automate this spoken practice before any written calculation. Adding more worksheets while this is still slow only adds more thinking time to every problem.
Step 3: Write the method out loud
"8 + 5. 8 needs 2 more to make 10. Split the 5 into 2 and 3. 10 and 3 is 13." Saying the steps aloud stops them getting lost partway. As it settles, the voice gets quieter, until finally it's all in their head.
What to avoid
- Forcing them to stop counting on their fingers. Counting on is a normal stage. Once composing 10 is automatic, they let go of it by themselves
- Handing over a big stack of worksheets. Working through volume without understanding leaves only one memory behind: that math is unpleasant. I started building diglabo because I watched my own daughter get worn down exactly like that
How to practise
diglabo's free worksheets are ordered so you can start from the step before the one your child is stuck on.
- Start with Addition up to 10 to check that addition without carrying is smooth
- Addition with Carrying has worksheets in order, beginning with the make-ten method. One sheet a day, with different number variations of the same content to repeat
- In grade 2, 2-Digit Addition uses carrying inside written column addition. If instant recall is in place from grade 1, column addition goes in smoothly
Mark the work with the answer sheet, then redo only the problems that were wrong. There's no need to redo the whole page.
Frequently asked questions
Q. Does the cherry method have to be used?
A. The goal is seeing numbers in groups of 10; the cherry diagram is just a guide line. As shown above, the commentary itself lists more than one method. If your child is calculating correctly in their head, the notation doesn't have to be forced. That said, if a school test specifies a way of writing it, follow that.
Q. It feels like they've just memorised it, and that worries me
A. Memorising "8 + 5 = 13" isn't a bad thing in itself — adults calculate from memory too. What's worth checking is whether they can explain, even once, why it's 13. Memorisation on top of an explanation is fluency.
There's no rush. This is a place where a great many children stop, and stopping here is not a problem in itself. Once "10 and how many" is automatic, one day it simply works.
This article is written by a parent who builds diglabo. I am not a teacher or an education specialist. The general guidance here is based on how the topic is taught in Japanese primary schools, checked against Japan's national curriculum guidelines.
diglabo's worksheets follow the Japanese curriculum. What that means if you are outside Japan