Subtraction Across Ten — How to Teach Crossing the Tens (13 − 5)

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.

Before you cross: show it with real objects

Before your child counts across the ten "in their head," it helps to see it with objects — the concrete → pictorial → abstract path³. The best tool is a ten-frame: a simple grid of ten spaces (two rows of five). Lay out 13 — a full ten, plus three in a second frame — and show how, to subtract 5, you first take off the three "loose" ones to leave a clean ten, then two more from the full frame. The child sees exactly what they'll write in symbols a moment later.

Ordinary blocks or a bead string work the same way: set out 13 as ten in one colour and three in another — it's obvious where to "take from" and when you break into the full ten. This stage looks slower, but it's what builds understanding; skip it too fast and the child falls back on guessing. Only after a few of these demonstrations move to a drawing (a jump left on a number line), and finally to the bare notation. Show the same route on a second example: for 15 − 8, set out 15 (a full ten and five), take the five "loose" ones down to a clean ten first, then three more from the full frame — leaving 7. After two or three demonstrations like this, a child starts to "see" the ten even without the frame.

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.

The most common slip in this method is taking away too much or too little in the first step. That's why the first question is always the same: "how far from the number to a full ten?" — not "how much do we subtract," but "how much to the ten." Once the child answers that, the rest is easy.

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).

This route is often handier when you're subtracting a lot (like 12 − 9): instead of stepping down in small hops, you take the 9 straight from the ten. There's no "correct" method to force — show both and ask your child which feels clearer. Choosing their own strategy is itself a small win: it teaches that maths is something to understand, not just perform.

Notation that helps

A young child easily loses the in-between result, so it's worth writing the two steps down rather than holding everything in memory. The simplest way is to draw a little "branch" under the number being subtracted: under the 5, write 3 and 2 (how much reaches the ten, and how much is left). Now the whole route is visible: 13 − 3 = 10, then 10 − 2 = 8.

This isn't "cheating" — it's a support for memory that the child will drop on their own in time. Early on, say and write in parallel: "down to the ten… two left… take two." With the steps visible on paper, the child doesn't have to hold it all in their head and can focus on understanding rather than juggling numbers. It's the same principle behind starting with blocks — offload memory so there's room to think.

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.

There are three simple signs a child is ready for crossing ten: they name pairs that make 10 quickly (6 and 4, 7 and 3), they split any number to 10 into parts without counting one by one, and they subtract confidently within 10. If one of these is missing, that's exactly where the work is — before moving to numbers above ten.

Why ten is the stopping point

"Getting to ten" can look like just a neat trick. In fact it's the first step toward understanding the base-ten system that all later maths sits on. We group numbers in tens: 13 is "one ten and three," and the round tens (10, 20, 30) act like knots where a number rounds up to a full bundle.

When a child breaks 13 − 5 through the ten, they're using that structure: first back to a full ten, then working in the familiar range to 10. That's why the same skill pays off later with numbers to 100 (34 − 8 is again "first to 30") and with column subtraction. Teaching crossing ten, then, isn't drilling one example — it's laying the foundation for work with bigger numbers.

Common mistakes and how to respond

A few slips show up with almost every child — each has a simple response:

• 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.
• Going the wrong way from the ten. The child reaches 10 and… adds the remainder instead of subtracting it (10 + 2 rather than 10 − 2). A number line and saying "I'm going down" out loud both help.
• Mixing it up with bridging in addition. Since "bridging through ten" works both ways, a child sometimes adds when they should subtract. Name the direction: in subtraction we "go down," in addition we "go up."

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).

Once those feel easy, add a couple closer to twenty and check each with addition: 13 − 7 (13 − 3 = 10, 4 left, 10 − 4 = 6; check: 6 + 7 = 13) and 18 − 9 (18 − 8 = 10, 1 left, 10 − 1 = 9; check: 9 + 9 = 18). Checking with addition isn't extra work — it's how a child convinces themselves the answer is right, and it reinforces that addition and subtraction are one "number family."

When frustration shows up

Crossing ten is often the first time maths feels "hard" — and the first time a child might say "I can't." Your reaction then matters more than the next example. A few things that help:

• Drop a level, don't push. If you see tears or guessing, go back to number bonds to 10 with blocks. That's not going backward — it's patching the real gap.
• Praise the route, not just the answer. "Clever — you got to ten first" teaches that the thinking is what counts.
• Short and often. Five calm minutes a day beats a half-hour battle at the table.
• Don't compare. "Jack can already do it" doesn't motivate — it intimidates. Every child has their own pace, and that's fine.

A parent's calm is contagious: when you don't make crossing ten a drama, your child stops fearing it too.

Crossing ten in everyday problems

Crossing ten doesn't have to live only in a workbook. Everyday moments are full of it: "we had 13 stickers, you gave away 5 — how many are left?", "there are 12 stairs and we've climbed 7 — how many to go?", "the box had 15 crayons and 8 went missing — how many now?" Each time it's the same two-step method, just on real things.

Working out change is especially rich. When you pay with a round coin and the bill has odd pennies, a child naturally "gets to the ten." Examples counted in passing like these stick better than a row on a worksheet — because the child sees that crossing ten is for something.

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.

Can my child use fingers for crossing ten? Yes — early on it's natural, since fingers are a concrete model of ten (two hands make 10). As number bonds become a habit, the child will start working in their head on their own. Don't ban fingers; instead add other images, like a ten-frame.

How many examples a day are enough? Little and often wins — two or three well-understood examples a day beat twenty against the clock. The point is that the child understands the two steps each time, rather than reciting an answer.

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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 — the bridging-through-ten strategy and why number bonds underpin it.
2. Subtraction Strategies Progression, Maine Department of Education: maine.gov — subtraction as the difference between numbers, reached by counting back or counting on.
3. The importance of the CPA approach in the early years, Maths — No Problem: mathsnoproblem.com — concrete-to-abstract teaching and the ten-frame as a bridging tool.