What is place value and why does my child's teacher keep talking about it?

Place value is the rule that a digit's worth depends on where it sits in a number. In 347 the 3 sits in the hundreds place, so it is worth 300, and the number written in expanded form is 300 + 40 + 7. Each place is ten times the place to its right, which is why carrying, borrowing and decimals all work.

What is place value in simple terms?

Place value is the rule that a digit's worth depends on the column it sits in. In 347 the 3 sits in the hundreds column and is worth 300, the 4 is worth 40, and the 7 is worth 7. Move that same 3 one column to the right and it is worth 30 instead. The digits never change; the columns decide what they mean.

What grade do kids learn place value?

Children meet place value in grade 1 under the US Common Core standards, where two-digit numbers are read as tens and ones. Grade 2 adds hundreds and numbers to 1000, grade 3 uses place value to round and to add within 1000, grade 4 states that each place is worth ten times the place to its right, and grade 5 extends the same system to decimals.

What is expanded form?

Expanded form writes a number as the sum of what each digit is worth, so 347 becomes 300 + 40 + 7. It shows the place value of every digit at once, which is why teachers ask for it before column addition. Grade 5 uses the same form for decimals, writing 347.392 as 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

What is a place value chart?

A place value chart is a grid with one labeled column for each place, usually ones, tens, hundreds and thousands. Writing one digit per column shows which place each digit occupies and keeps the columns lined up during addition and subtraction. Teachers extend the same chart to the right of the decimal point in grade 5.

Why does my child read 307 as thirty-seven?

A child reads 307 as thirty-seven when the zero is treated as nothing rather than as a placeholder for an empty tens column. Cover the 0 and the number does read as 37, so the zero is what keeps the 3 in the hundreds column. Building 307 with base-ten blocks, leaving the tens row empty on purpose, fixes this faster than correcting the answer.

Place Value Explained: A Parent's Guide

Your second grader comes home with a worksheet that asks what the 3 in 347 is worth, then asks for the same number in expanded form, and the phrase place value is printed across the top. You know the answer is 300. Explaining why it is 300, in words a seven-year-old accepts, is the harder part.

What is place value in a number?

Place value is the rule that a digit's worth depends on the column it sits in. The number 347 uses the digits 3, 4 and 7, and each one carries a different amount: the 3 is worth 300, the 4 is worth 40, and the 7 is worth 7. Written out, that is the expanded form of the number, 300 + 40 + 7.

Every place is ten times the place to its right and one tenth of the place to its left. Ten ones make a ten, ten tens make a hundred, and ten hundreds make a thousand. In US numbers the columns run ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions.

Three words get mixed up constantly:

The digit is the symbol on the page: 3.
The place is the column it sits in: hundreds.
The value is what it is worth there: 300.

The National Research Council's 2001 report Adding It Up chose to concentrate on the mathematics of numbers and their operations, because that is the ground school arithmetic stands on.

Zero is a placeholder, not an empty space

Zero does a job inside a number even though it counts nothing. In 706 the 0 announces that there are no tens, and it holds the 7 in the hundreds column so the number cannot collapse into 76.

The grade 2 standard uses that exact example: 706 equals 7 hundreds, 0 tens and 6 ones (2.NBT.A.1). Children who skip the zero have not yet accepted that an empty column still counts.

A place value chart with three hundred-squares, four ten-rods and seven cubes above the digits 3, 4 and 7.

Why place value carries everything that comes later

Place value is the foundation the rest of elementary arithmetic sits on, so a gap here surfaces years later as a mystery. Column addition, borrowing, rounding, long multiplication and decimals are all rules about columns. A child who cannot read the columns memorizes each procedure as a separate trick.

The What Works Clearinghouse practice guide Assisting Students Struggling with Mathematics recommends that intervention materials give in-depth treatment to whole numbers from kindergarten through grade 5. Depth in whole numbers means place value, because that is what whole numbers are made of.

Carrying, borrowing and decimals all rest on it

Carrying and borrowing are place value moves with shorter names. When 8 + 5 makes 13 in the ones column, ten of those ones are bundled and moved one column left; when you borrow, one hundred is unbundled into ten tens.

Rounding runs on the same idea. To round 347 to the nearest hundred your child has to know which hundreds it sits between, and grade 3 asks for exactly that (3.NBT.A.1). A few rounds of rounding numbers and two-digit addition make column talk familiar before the algorithms arrive.

Decimals extend the same columns to the right of the point. Grade 5 states it plainly: a digit represents 10 times as much as it represents in the place to its right and one tenth of what it represents in the place to its left (5.NBT.A.1).

How to build place value at home, step by step

Place value is built with objects before it is written with digits, and five short sessions beat one long one. Anything you have ten of works: pasta, beads, straws, pennies.

Bundle ten of something. Count out 10 straws and put a rubber band around them. Say out loud that the bundle is one ten, and keep it whole for the session.
Name the columns. Draw two columns on paper and label them tens and ones. Bundles go in the left column, loose straws in the right.
Say the number out loud. Read 34 as "three tens and four ones", then as "thirty-four". Hearing both names together links the pile to the written number.
Write it in expanded form. Write 34 = 30 + 4 next to the pile so the writing and the objects agree. Move up to 347 = 300 + 40 + 7 once ten bundles have become a hundred.
Break a ten. Ask for 7 loose straws when only bundles are left. Cutting one rubber band is the whole of borrowing, done with hands.

Ten minutes is enough. Repeat the five steps with bigger numbers the next day.

Play free in your browserPlace ValueGrade 1–2

The step families skip: saying the number out loud

Saying the number out loud is the step families skip, and it catches more errors than any written exercise. A child who reads 347 as "three four seven" has not met the hundreds yet, and a child who reads it as "three hundred forty-seven" has.

Grade 2 asks children to read and write numbers to 1000 using base-ten numerals, number names and expanded form (2.NBT.A.3). The spoken name is part of the standard. A round of place value practice in the browser runs the same drill when the straws run out.

Four ways to show a number: blocks, chart, expanded form, word form

Four models turn up in US classrooms, and each shows a different slice of place value. Your child meets all four, often in the same week.

Model	What it shows	Best for	Limits	347 looks like
Base-ten blocks	How much bigger a hundred is than a ten	Grades 1–2, the first meaning of bundling	Slow past 1,000, and needs new pieces for decimals	3 flats, 4 rods, 7 cubes
Place value chart	Which column each digit sits in	Lining up columns, regrouping, decimals later	Hides the size difference between columns	H 3, T 4, O 7
Expanded form	What each digit is worth, as a number	Mental addition, checking a carry, decimals	Long to write for big numbers	300 + 40 + 7
Word form	How the number is said and heard	Reading, writing and catching teen errors	Shows no size and no columns	three hundred forty-seven

The What Works Clearinghouse guide on intervention in the elementary grades recommends a well-chosen set of concrete and semi-concrete representations, plus the number line.

The number 347 split into 300 plus 40 plus 7.

Which model to use when

The model to reach for depends on the question in front of you. Blocks answer "how much", a chart answers "which column", expanded form answers "what is this digit worth", and word form answers "how do I say it".

Written practice is where the columns stay lined up or drift. An addition worksheet for 2nd graders gives your child ruled space and an answer key.

Free printable worksheetAddition — 2nd GradersWorksheet · PDF

What each grade is expected to know

The US Common Core standards introduce place value one column at a time, from grade 1 to grade 5. Each grade adds a single idea, and the code is the one your child's teacher works from.

Grade 1 (1.NBT.B.2). Two-digit numbers are read as tens and ones: 10 is a bundle of ten ones, 11 to 19 are a ten and some ones, and 10 through 90 are so many tens and 0 ones.
Grade 2 (2.NBT.A.1). Three-digit numbers are read as hundreds, tens and ones, with 100 as a bundle of ten tens. Grade 2 also counts within 1000, skip-counts by 5s, 10s and 100s, and compares three-digit numbers with >, = and <.
Grade 3 (3.NBT.A.1). Place value becomes a tool: children round to the nearest 10 or 100 and add and subtract within 1000 using strategies based on place value.
Grade 4 (4.NBT.A.1). The ten-times rule is stated for the first time, so a digit is worth ten times what it is worth one place to the right. The standard gives 700 ÷ 70 = 10 as its example.
Grade 5 (5.NBT.A.1). Decimals join the system, each place worth ten times the place to its right and one tenth of the place to its left.

What math each grade should know covers the other strands, and Common Core math explained answers the question underneath most homework arguments: why the method looks nothing like yours.

Where decimals join, in grade 5

Decimals join the place value system in grade 5, and the columns keep behaving the way they always did. Grade 5 asks children to read, write and compare decimals to thousandths, and it writes 347.392 in expanded form as 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000) (5.NBT.A.3).

How to check your child has it

Five short questions tell you whether place value has landed, and none needs a worksheet.

Which digit is worth more? Ask which is worth more in 347, the 3 or the 7. The answer is the 3, because it is worth 300 while the 7 is worth 7.
What is the value of this digit? Point at the 4 in 347. "Four" is a digit answer, and "forty" is a place value answer.
Ten more, ten less. Ask for 10 more than 347 and 10 less. Grade 2 expects this mentally for any number from 100 to 900 (2.NBT.B.8).
Build it two ways. Ask for 40 using only tens, then using only ones. Four bundles and forty loose pieces are the same amount.
Compare two numbers. Ask which is bigger, 4,102 or 4,120, and why. A game of comparing numbers drills the same column-by-column habit.

The 347 test, and what a wrong answer means

A wrong answer to the 347 question points at one of two gaps. A child who answers "the 7" is reading digits as symbols with no column attached, and a child who answers "the 3, because it comes first" has the right answer for a reason that fails on decimals. Build 347 with blocks, build 743 beside it, and ask which pile is bigger.

Common place value mistakes, and your checklist

Five mistakes account for most of the place value trouble in grades 1 to 4.

Reading 307 as thirty-seven. The zero gets skipped because it looks like nothing. Cover the 0, agree that what is left reads as 37, then uncover it and ask what the 0 holds open.
Naming the digit instead of its value. A child asked about the 4 in 347 answers "four". Insist on the column every time: "four tens, which is 40".
Treating zero as nothing at all. Compare 4 and 40 with blocks side by side. The 0 turned four cubes into four rods.
Teen numbers. English says "thirteen", putting the three before the ten, while 13 puts the ten first. Say "one ten and three ones" alongside "thirteen" until both sound normal.
Regrouping twice in one problem. In 395 + 17 the ones make 12, so a ten is carried, and the tens then make 11, so a hundred is carried, giving 412. Do it once with bundles and the double carry stops being magic.

Your place value checklist

Six signs tell you the foundation is solid.

Says any number two ways. 347 is "three hundred forty-seven" and "3 hundreds, 4 tens, 7 ones".
Names the value, not the digit. Asked about the 4 in 347, your child answers 40.
Explains what a zero is doing. Asked about 307, your child says there are no tens.
Adds and subtracts 10 and 100 mentally. 347 plus 10 is 357, and 347 minus 100 is 247.
Writes expanded form unprompted. Any three-digit number becomes hundreds plus tens plus ones.
Compares column by column. 4,120 beats 4,102 because the tens differ, and your child can say so.

Short daily practice keeps the columns familiar between homework nights. The MathIt app has about 90 game types with adaptive difficulty, so the numbers grow as your child does, and its 2–5 player battles turn a column drill into a race.