Why place value comes before addition, not after
A child can add single-digit numbers correctly by counting on fingers without ever understanding that '23' means two groups of ten and three ones. That gap doesn't show up until carrying appears. Then it shows up as a wall, not a wobble.
Watch what happens when a child who hasn't grasped this hits 7+5. Some kids write '412': they add 7 and 5, get 12, and just tack the digits onto the page in whatever order feels right, because to them a number is a string of digits, not a structure with a ones place and a tens place. The '1' and the '2' aren't standing for anything. They're just what came out of the calculation.
If your child can solve 23+5 but freezes on 27+5, that's usually not a carrying problem — it's a place value gap. They don't yet see the '2' and the '3' as separate, differently sized quantities. One is worth ten times the other, and until that clicks, carrying will always feel like an arbitrary rule handed down from above rather than something that makes sense.
The mistake that gives it away
There's a specific error worth watching for, because parents often mistake it for carelessness when it's actually a diagnosis. Ask a child to add 8+6. If they write '14,' good. If they write '14' but moments later can't tell you which digit is the 'ten' and which is the 'four,' they've memorized an answer without understanding what it's made of.
A short list of what to watch for: digits written in reverse order (writing '51' for fifteen), a carried digit added into the wrong column, or a child who can recite 'carry the one' but can't explain what's actually being carried. None of these are signs of a distracted kid. All three are the same gap wearing a different disguise.
If you see this, don't drill more addition problems. More practice on a broken foundation just makes the mistakes more automatic. Go back to objects.
Teach it with objects before symbols
Bundle ten craft sticks with a rubber band and call it 'one ten.' Loose sticks are 'ones.' Building the number 23 becomes two ten-bundles and three loose sticks — a physical fact your child can see and touch, not an abstract rule to memorize.
A phrase that works well here: 'Show me 23 with your hands.' Not 'what is 23,' which invites a memorized answer, but 'show me,' which forces the child to actually build the quantity. If they reach for two bundles and three loose sticks without hesitating, they understand it. If they start counting out 23 individual sticks one at a time, they don't yet. That's useful information, not a failure.
Only after your child can build several numbers this way with objects should you move to place value charts or written column headings. The written version should describe something they already understand, not introduce something brand new.
A second technique: the trading game
Base-ten blocks work well for this, but so do dried beans and small paper cups if that's what you have around. Give your child a pile of loose beans (ones) and empty cups that each hold exactly ten. Roll a die, add that many beans to the pile, and every time ten beans collect, trade them for one filled cup.
This is the same idea as the stick bundles, but the trading mechanic matters: it turns 'regrouping' into a game move your child initiates themselves, rather than something a teacher marks on their worksheet. Kids who play this a few times a week for two or three weeks tend to stop needing the sticks altogether — the cups-for-beans trade becomes their mental model for what a ten actually is.
Connecting place value to carrying, concretely
When ten loose sticks pile up during a problem, physically bundle them into a new ten and move it to the tens column. That's it. 'Carrying the 1' stops being a mysterious rule and becomes something your child just did with their own hands, and only after eight or ten repetitions spread across a week or two should you write a small '1' above the tens column instead.
Signs your child has actually understood it
Ask your child to break apart a two-digit number in more than one way — 23 as 2 tens and 3 ones, but also as 1 ten and 13 ones. A child who's memorized a procedure struggles here; a child who understands place value finds it easy.
Another good check: ask which digit matters more for the size of a number, the tens or the ones, and why. A confident, reasoned answer, not just a guess, is the real signal to move forward. If your child is guessing rather than reasoning, that's a place value gap, not a carelessness problem, and it's worth naming that difference out loud so you're not chasing the wrong fix.
One more test, and it's the one that catches kids who look fine on paper: give them 47 and ask them to build it with the sticks, then ask them to build 74 right next to it. A child who truly understands place value notices immediately that the bundles and loose sticks swap roles. A child who's been pattern-matching digit positions on worksheets sometimes can't tell you why the two numbers, built from the same digits, aren't the same size.
Moving on to three digits and beyond
Once two-digit place value feels solid, hundreds are just 'ten groups of ten' — the same bundling idea repeated one more level up, not a new concept.
Resist the urge to rush this stage because two-digit problems 'look easy.' A shaky place value foundation is one of the most common reasons kids hit a wall in third or fourth grade math, long after addition worksheets stopped seeming like the hard part. Most kids who are genuinely ready for this jump can already tell you, without hesitating, how many tens are in 90. If they have to count up by tens to answer that, give it a few more weeks before moving on.