Place value for kids is the idea that a digit's value depends on where it sits in a number. In 352, the 3 means 3 hundreds, the 5 means 5 tens and the 2 means 2 ones. Teach it by bundling real objects into tens, building numbers with base-ten blocks, then writing numbers in expanded form.
This guide walks through what children learn and when, a step-by-step teaching order, games, and the mix-ups to watch for.
Our number system uses just ten digits, 0 to 9. Place value is what lets those ten digits make any number. The same digit means different amounts in different places:
In 7, the 7 means 7 ones.
In 70, the 7 means 7 tens, or seventy.
In 700, the 7 means 7 hundreds.
The key rule is that 10 of one unit make 1 of the next. The Common Core State Standards put it simply: 10 can be thought of as a bundle of ten ones, called a "ten," and 100 can be thought of as a bundle of ten tens, called a "hundred."
Zero matters too. The standards use the example that 706 equals 7 hundreds, 0 tens and 6 ones. The 0 holds the tens place so the 7 stays in the hundreds place.
Kindergarten: break the numbers 11 to 19 into ten ones and some more ones, for example 18 = 10 + 8.
First grade: understand that two-digit numbers are made of tens and ones, compare two-digit numbers with the symbols >, = and <, and find 10 more or 10 less than a number without counting.
Second grade: work with hundreds, tens and ones, read and write numbers to 1000 in numerals, words and expanded form, compare three-digit numbers, and mentally add or subtract 10 or 100.
Use these as a rough guide. Children move at different speeds.
Fill a ten frame, or an egg carton cut down to 10 cups, with 10 buttons. Put 4 more beside it. "Ten and four is fourteen." Do this for each number from 11 to 19 and write the matching equation: 14 = 10 + 4.
Count out a pile of craft sticks or straws, say 34. Every time you reach 10, wrap them with a rubber band. You end up with 3 bundles and 4 loose sticks. "34 is 3 tens and 4 ones." Now and then, unbundle a ten so your child sees that a ten is still 10 ones inside.
Base-ten blocks use small cubes for ones, rods for tens and flat squares for hundreds. A What Works Clearinghouse practice guide on math intervention points out that these blocks are proportional: ten ones match one ten, and ten tens match one hundred. It notes that place value is harder to grasp when the model isn't proportional.
No blocks? Draw quick pictures: a dot for each one, a line for each ten and a square for each hundred.
Draw three columns labeled Hundreds, Tens and Ones. Your child puts blocks or drawings in each column, then writes the digit underneath. Start with numbers that have no zeros, then try 305 and 260 to practice the zero.
Expanded form shows what each digit is worth, written as a sum:
352 = 300 + 50 + 2
706 = 700 + 6
84 = 80 + 4
The second grade standards ask children to read and write numbers to 1000 using numerals, number names and expanded form. So practice saying the number too: "three hundred fifty-two."
To compare 347 and 374, look at the biggest place first. Both have 3 hundreds. Then look at the tens: 4 tens is less than 7 tens, so 347 < 374. Next, play "10 more, 10 less." Say a number and have your child say the number that is 10 more or 10 less without counting. Later, do the same with 100.
Build my number: say a number and your child builds it with bundles, blocks or drawings. Then swap roles.
Biggest number dice: roll three dice and arrange the digits to make the biggest number you can. Read it aloud. Then try for the smallest.
Mystery number: give clues like "I have 4 tens and 7 ones. What number am I?" Add hundreds as your child grows.
Place value war: take the 10s and picture cards out of a deck, with aces as 1. Each player flips two cards and makes the biggest two-digit number they can. The bigger number wins.
Trade up: roll a die and collect that many ones. Whenever you reach 10 ones, trade them for a ten. First to 100 wins.
Hundreds chart hops: on a hand-drawn 10 by 10 grid of the numbers 1 to 100, moving down a row adds 10 and moving up a row takes away 10.
Mixing up teen numbers. We say "fourteen" with the ones first but write 14 with the ten first. Build the number with a bundle and loose sticks while saying it.
Dropping or adding zeros. A child may write "seven hundred six" as 76 or 7006. Use the place value chart so the empty tens place is easy to see.
Adding the digits. Writing 352 as 3 + 5 + 2 misses what each digit is worth. Ask, "What is the 3 really worth here?"
Calling it borrowing and carrying. The same practice guide suggests the word "regrouping" instead. It describes what really happens: trading 10 ones for a ten, or a ten for 10 ones.
It is the value of a digit based on its position. In 45, the 4 is worth 40 because it's in the tens place, and the 5 is worth 5 because it's in the ones place.
Under the Common Core, it begins in kindergarten with the numbers 11 to 19 as ten and some ones. Tens and ones are a first grade focus, and hundreds come in second grade.
Expanded form writes a number as the sum of what each digit is worth. For example, 528 = 500 + 20 + 8.
Adding and subtracting bigger numbers depends on it. The first grade standards explain that in adding two-digit numbers, you add tens and tens, ones and ones, and sometimes make a new ten. Our guide on how to teach addition shows this step.
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Common Core State Standards: Kindergarten, Number and Operations in Base Ten
Common Core State Standards: Grade 1, Number and Operations in Base Ten
Common Core State Standards: Grade 2, Number and Operations in Base Ten