How to Teach Subtraction with Borrowing — Why It's Harder Than Addition
Your child has finally got past addition with carrying — and then stops again on subtraction. The hand stops moving at 13 − 5.
I assumed at first that if addition worked, subtraction would be about the same difficulty. It isn't. Subtraction with borrowing is structurally one step harder than addition with carrying. There's a reason so many children stall here.
Why it's harder than addition
Japan's Ministry of Education, in its commentary on the national curriculum guidelines for elementary mathematics (2017), gives 12 − 7 with two methods (Grade 1, Numbers and Calculation):
- Subtract-then-add: (10 − 7) + 2. Split 12 into 10 and 2, take 7 from the 10 to get 3, then add the remaining 2 to get 5
- Subtract-then-subtract: (12 − 2) − 5. Split the 7 into 2 and 5, take 2 from 12 to reach 10, then take 5 more to get 5
Either way, your child splits and recombines numbers twice. There is more to hold in working memory than in addition with carrying, which makes it easy to lose the thread — "wait, what was I subtracting?" And if "10 − 5" or "10 − 7" doesn't come instantly, the first method collapses partway.
In other words, most children stuck here don't "not understand borrowing". Either a part they need earlier is missing, or they can't hold the sequence.
How to teach it at home
Step 1: Automate "subtract from 10" first
Check whether "10 − 4?" and "10 − 7?" come back instantly. This is the flip side of composing 10 ("4 and what makes 10?"). If this is slow, the question of where they're stuck in the borrowing procedure doesn't arise yet — the parts aren't there. Get it instant with a spoken game.
Step 2: Show "breaking up the group of 10" with blocks
Lay out 13 as one bar of 10 and 3 singles, and say "give me 5". Three singles isn't enough, so the only option is to break up the 10. Experiencing that break-up with your hands connects directly to what "borrowing" later means in column subtraction.
The commentary makes the same point: the difference between the two methods, it says, comes down to "taking from the group of 10 versus taking from the singles" when children work with blocks. Moving things by hand is the school's route to understanding too.
Step 3: Fix one method, said out loud
Start with whichever method they're being taught at school. "13 − 5. 13 is 10 and 3. 10 take away 5 is 5. 5 and 3 is 8." Saying the same steps aloud every time prevents them getting lost. Teaching both methods at once causes confusion — introduce the second only once the first is stable.
What to avoid
- "Why can't you get this?" Borrowing is objectively harder than carrying. Just knowing that stalling is normal changes how you say things
- Mixing in addition too early. Mixing before the borrowing sequence is stable makes the two procedures interfere
How to practise
- Subtraction up to 10 covers subtraction without borrowing and "subtract from 10"
- Subtraction with Borrowing moves in steps, starting from decomposition practice. Rather than finishing a whole sheet, repeat just the type they got wrong using a different number variation
- In grade 2, 2-Digit Subtraction turns that "break up the 10" action into the written borrowing symbol. Experiencing the meaning first cuts down mechanical mistakes
Frequently asked questions
Q. Which method should I teach — subtract-then-add, or subtract-then-subtract?
A. As a rule, match the school. The commentary says that which one to make primary should follow the size of the numbers and be handled flexibly, and that teaching should suit the individual child. In other words, the national guidance doesn't pick one either. Children can choose for themselves once both are stable.
Q. They got past this, but now they're stuck on column subtraction
A. When borrowing fails in column subtraction, the mental calculation from grade 1 usually isn't automatic yet. Stopping the column practice and going back to the "13 − 5" type is faster in the end. Going back is not going backwards.
Borrowing is a place most children take months to get through. Not being able to do it today is, for this topic, completely ordinary.
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