Place value means that the same digit is worth a different amount depending on where it sits in a number. In 352, the 3 is worth 300, the 5 is worth 50, and the 2 is worth 2 — three different values, three identical-looking digits. Number sense is the broader skill built on top of that: a feel for roughly how big a number is, and whether an answer is reasonable before you even check it.
Why this matters more than it looks like it does
Borrowing and carrying in addition and subtraction are really just place value in action — you’re regrouping ten of one place into one of the next. Decimal points work the same way, just continuing the pattern past the ones place. A child who truly understands place value isn’t memorizing a borrowing procedure; they’re watching value move between columns in a way that makes sense.
Let me show you one
What is 352 in expanded form? Break each digit out by its place: 300 + 50 + 2. Now try 4,019: that middle zero matters — it’s 4,000 + 0 + 10 + 9, and skipping the zero’s place would quietly turn the number into something else entirely. Reading the zero as “nothing here, but the place still counts” is one of the most useful habits in all of elementary math.
Rounding is place value, not a separate trick
Rounding 4,019 to the nearest hundred asks one question: is it closer to 4,000 or 4,100? Since 19 is less than halfway to 100, it rounds down to 4,000. Rounding isn’t a rule to memorize about “5 or more rounds up” — it’s just asking which neighboring landmark a number is closer to.
The mistake I see most
Treating a zero as if it isn’t really there — writing 4,19 instead of 4,019, or misreading which place a digit belongs to once a zero is involved. The fix is reading numbers out loud by place (“four thousand, zero hundreds, one ten, nine ones”) until the habit of checking every place sticks, even the empty-looking ones.
Want to work through it together?
If your child can compute but seems to be following steps without quite knowing why, that’s almost always a place value gap hiding underneath — and it’s one of the fastest gaps to close with the right hands-on examples.
