Why kids struggle with place value, and how column alignment helps
Place value is behind most carrying, borrowing and decimal mistakes. Here is what it is, how to spot gaps, and simple ways to build it at home.
Skill guide · Grades K–5
Place value
What place value means, why column alignment matters for carrying and borrowing, a worked example, and simple place value activities for home.
What it is
Place value means a digit is worth a different amount depending on where it sits. In 405, the 4 is worth four hundred, the 0 holds the tens place open, and the 5 is worth five. Each place is worth ten times the place to its right.
It starts with tens and ones in kindergarten and first grade, grows to hundreds and thousands in second through fourth grade, and carries on past the decimal point into tenths and hundredths.
A worked example
405 + 38 = 443
1
4
0
5
+
3
8
4
4
3
Every step, the way the pad explains it
- Add the ones: 5 + 8 = 13. Write 3, carry 1.
- Add the tens (with the carry): 1 + 0 + 3 = 4. Write 4.
- Add the hundreds: only 4 here. Write 4.
- 1Line up 405 and 38 on the right: the 8 under the 5, the 3 under the 0.
- 2Ones: 5 + 8 = 13. Write 3, carry 1 ten.
- 3Tens: 1 + 0 + 3 = 4. The zero in 405 still counts as a column.
- 4Hundreds: 4 comes straight down.
- 5The answer is 405 + 38 = 443.
Common mistakes
Lining numbers up on the left.
Line up on the right for whole numbers, and on the decimal point for decimals.
Writing numbers in the order they are heard, like 51 for fifteen.
Say teen numbers as “ten and five” while writing them.
Ignoring zeros inside a number.
Read 405 as “four hundreds, zero tens, five ones.”
Carrying without knowing what the 1 is worth.
Ask what the carried 1 means: one ten, or one hundred?
Grade range and practice
Usually taught in grades K–5. Schools order topics a little differently, so your child’s class may meet it earlier or later.
- Count piles of small objects by bundling them into tens.
- Use dimes and pennies: how many of each make 47 cents?
- Make the biggest and smallest number from three digit cards.
Read more on the blog
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