Subtraction Across Ten: How to Teach Crossing the Tens

The easiest way to subtract across ten (like 13 − 5) is in two steps through the nearest ten: first subtract just enough to land on 10, then subtract the rest. For 13 − 5: 13 − 3 = 10, with 2 left to go, so 10 − 2 = 8. The one prerequisite is secure number bonds to 10 — once a child knows the "partners of ten," this becomes almost automatic. Below: the method step by step, a second approach, common mistakes, and how to practise.

Why crossing ten is hard

Within 10, subtraction is still "visible on fingers." Above it — 12, 15, 18 — a child runs out of fingers, and the number being subtracted won't "fit" into the ones digit (in 13 − 5, you can't take 5 from the 3). This is where memorised tricks fall apart and understanding the structure of a number takes over. In most early-elementary curricula, crossing ten is a second-year skill, so if your six-year-old isn't there yet, that's completely normal.

Method 1: get to ten, then subtract the rest

This is the most widely recommended strategy — "bridging through ten"¹. We split the number being subtracted into two parts: the bit that reaches 10, and the remainder.

Example 13 − 5:

1. How far is 13 from a full ten? Three. Subtract 3 first: 13 − 3 = 10.
2. We've only taken away 3 of the 5 — so 2 are left.
3. Subtract 2 from 10: 10 − 2 = 8.

Written out: 13 − 5 = 13 − 3 − 2 = 10 − 2 = 8.

Example 15 − 8: 15 − 5 = 10, 3 left, 10 − 3 = 7. Notice the one question that drives it: "how far to the next ten?" That's why it pays to master pairs that make 10 (number bonds) before you tackle crossing ten.

Method 2: subtract from ten

Some children find it easier to split the larger number into 10 and the rest, then subtract from the ten. For 13 − 5: 13 is 10 and 3. Take 5 from 10 (since you can't take it from 3): 10 − 5 = 5, then add back the 3 you set aside: 5 + 3 = 8. Both methods give the same answer — show one, and if it doesn't click, try the other. Because subtraction is really about the difference², a child can also just count up: "from 5 to 13 is how much?" (5 → 10 is 5, 10 → 13 is 3, so 8).

First, the foundation: number bonds to 10

Crossing ten rests on a single skill — instantly knowing what a number is "made of." 8 is 5 and 3; 10 is 6 and 4. Practise it with real objects: split 10 blocks into two piles in different ways, use dice, use hands (two hands make 10). Without it, a child counts across the ten "the long way" and gives up fast. We cover this foundation in our guide on how to teach subtraction.

Common mistakes and how to respond

• Subtracting digits separately. A child does "3 − 5 doesn't work, so 5 − 3 = 2" and gets a wrong answer. Return to concrete objects and the two-step method — it shows numbers can't be pulled apart at random.
• Losing the remainder. The child reaches 10 and… forgets how much is still left to subtract. Saying it out loud and writing it down helps: "I took 3 of the 5, so 2 are left."
• Starting too early. If number bonds to 10 aren't secure, step back. That's not lost time — it's the prerequisite.

Practising crossing ten with EduBert

Short daily practice works best — and it's easier to keep up when it feels like play. In the City, children practise subtraction with pictures: number bonds and checking answers by adding, with difficulty rising gradually so they naturally reach crossing ten at higher levels. Level 1 is free, so you can create an account and see whether the format suits your child. If you're also working on addition, see the companion piece on addition to 20 across ten — the same "partners of ten" work both ways.

A few more worked examples

The more you practise together, the more it sticks. Split each into two steps through the ten:

• 14 − 6: 14 − 4 = 10, 2 left, 10 − 2 = 8.
• 16 − 9: 16 − 6 = 10, 3 left, 10 − 3 = 7.
• 11 − 4: 11 − 1 = 10, 3 left, 10 − 3 = 7.
• 17 − 8: 17 − 7 = 10, 1 left, 10 − 1 = 9.

Notice the repeating rhythm: "how far to ten?" then "how much is still left?" When your child starts asking those two questions unprompted, they're well on their way. Don't correct every step — let them finish, then catch any slip together by checking with addition (8 + 6 = 14).

A simple week plan

You don't need a lesson plan — a few minutes a day is enough:

• Days 1–2: just number bonds to 10 (pairs that make a ten) with blocks and fingers.
• Days 3–4: only "getting to the ten," no subtracting yet ("how far from 13 to 10?").
• Days 5–6: full subtraction across the ten on 2–3 examples, with real objects.
• Day 7: the same in your head, without objects, writing optional.

If a stage doesn't land, stay with it a day longer. Pace is individual, and that's completely normal.

It works both ways

The same "friendship with ten" helps in addition (8 + 5: get to 10 first, then the rest) and in subtraction. Once a child sees the ten as a shared "stopping point" for both operations, they stop treating addition and subtraction as two separate, hard things — a good reason to practise them side by side rather than apart.

When to move on to harder numbers

There's no single age. A good sign to go further is when a child solves several problems in a row without reaching for fingers and notices on their own when they've "taken away too much." Then gradually add numbers closer to 20 (like 18 − 9) and drop the writing here and there, moving to mental work. If frustration appears, step back. And when you'd like to practise through play, see the set of subtraction games at home.

Frequently asked questions

Where do we start with crossing ten? With secure number bonds to 10 (pairs that make a ten). Only then introduce the two-step, bridge-through-ten method.

How do I explain 12 − 7? How far is 12 from 10? Two. 12 − 2 = 10, 5 left, 10 − 5 = 5. So 12 − 7 = 5.

Which is better — getting to ten, or subtracting from ten? Both are correct. Show one; if it doesn't click, try the other or counting up. Different children prefer different routes.

When should a child manage this? Usually in second grade (age 7). Earlier difficulty is normal — order matters, not the calendar.

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Crossing ten stops being scary once a child sees the ten as a "stopping point." Practise briefly, with real objects, and keep returning to number bonds to 10. If you'd like your child to train this as a game matched to their level, try the City in EduBert.

Sources

1. Addition and subtraction: bridging 10, NCETM (National Centre for Excellence in the Teaching of Mathematics): ncetm.org.uk
2. Subtraction Strategies Progression, Maine Department of Education: maine.gov