Interactive place value chart

What the chart shows

A place value chart has one column for each place: ones, tens, hundreds and so on, and tenths and hundredths after the decimal point. Each disk in a column is worth that column's value, so three disks in the hundreds column are worth 300. Moving one column to the left makes each disk worth ten times as much.

On this page you pick which columns to see: up to thousands, up to millions, or hundreds down to hundredths. Tap + or − to add or take away a disk. A column can hold up to 20 disks, so a child can make 14 tens and see what that means. Regroup trades 10 disks for 1 disk in the next column to the left, and Break 1 trades one disk for 10 in the column to the right. The readout gives the standard form, the expanded form and the word form.

Why disks help

Disks sit between base ten blocks and digits. A hundreds block looks a hundred times bigger than a ones cube, but a hundreds disk looks like a ones disk with a different label. That makes children think about where the disk is, which is exactly what a digit's place does. Regrouping on the chart is the same move as carrying in addition and borrowing in subtraction.

Common mix-ups

• Leaving out zeros. A child builds three thousands, four hundreds and five ones and writes 345. The empty tens column shows why 3,405 needs its 0.
• Thinking a column with more than 9 disks breaks the number. Twelve tens are 120, and Regroup shows it as 1 hundred and 2 tens.
• Believing that more digits after the point means a bigger decimal. Build 0.5 and 0.35 and compare the disks.
• Reading 2.35 as "two point thirty-five." The word form says two and thirty-five hundredths.

A 10-minute place value routine

• Say a number such as 2,061 and have the child build it, then read the expanded form together.
• Add disks to the ones column until there are 13. Ask for the number, then press Regroup and compare.
• Build 500 and ask how to take away 1. Press Break 1 in the hundreds and then in the tens until there are ones to take.
• Press Build a number. When the target is in words, the child writes it in digits on paper first.
• Switch to Decimals and build 1.4, then 1.04, and talk about the difference.

Where it fits by grade

• Grades 1 and 2: tens and ones, then hundreds (1.NBT.B.2, 2.NBT.A.1), and reading and writing numbers to 1,000 in expanded form (2.NBT.A.3). In England, Years 2 and 3.
• Grade 4: a digit is worth ten times what it is worth one place to the right (4.NBT.A.1), and multi-digit numbers in words and expanded form (4.NBT.A.2). In England, Year 4 works to 10,000 and Year 5 to at least 1,000,000.
• Grade 5: decimals in expanded form (5.NBT.A.3). In England, tenths and hundredths begin in Year 4.

Learning more

Place value is a skill on Eurekami's skill map, and Daily Practice brings it back when it starts to fade. Lessons draw place value diagrams live from the numbers in each question, and teachers can print worksheets with answer keys on the same skills.