Place Value Question Generator

What this generator does

Place value is the topic every later arithmetic difficulty traces back to, and it is usually assumed rather than checked. Each question names a digit and asks what it is worth where it stands, which separates the child who reads a number as a string of symbols from the child who reads it as a quantity.

How to use this tool

1. Choose how many questions you want and a level, which sets how many digits the numbers have.
2. Press make questions, and work through the sheet.
3. Show the answers to mark it, or show the working to see the columns named.
4. Enter a seed word to rebuild the same sheet later.

Understanding the controls

How many questions

One to thirty. Ten is generally enough — this is a diagnostic rather than a drill, and a wrong answer here explains a lot of other wrong answers.

Level

Gentle uses three-digit numbers, standard five-digit and stretch six-digit. The reasoning is identical; what changes is how many columns have to be counted before the right one is reached.

Seed

A word rebuilds the same sheet while the generator is unchanged, so the same numbers can be set again later to see whether anything has changed.

Show the answers / show the working

The working lists the column names from the right and states the multiplication, so the answer can be reconstructed rather than taken on trust.

Worked examples

Standard level, seed round9

What is the value of the digit 2 in 82,789? → 2,000, because the 2 sits in the thousands column.

Common use cases

• Place-value practice at home or school
• Diagnosing why a column method keeps going wrong
• Quick maths warm-ups
• Self-testing before a maths quiz

How this generator works

The digits are drawn one at a time with a non-zero leading digit, and the digit asked about is chosen only from positions holding something other than zero — the value of a zero is a legitimate question but always has the same answer, so it makes a poor sheet. The digit asked about also appears only once in its number: the question names a digit rather than a column, and 'the 8 in 883' would have two right answers. The check reads the answer back, divides it by its place and requires the digit; it also reads the digit straight out of the number shown and counts it there, so the prompt and the answer are tied to each other rather than to a variable.

Randomness and fairness

Which column is asked about is drawn from the positions of that particular number that hold a non-zero digit appearing nowhere else in it, so the question and the number are not independent — 4,070 can only be asked about in two ways, and a number with no such digit, like 999, is drawn again.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• Only the value of a digit is asked. Writing numbers in words, comparing two numbers and ordering are not produced here.
• Decimal place value — tenths and hundredths — is not covered; these are whole numbers only.
• A seed reproduces the numbers exactly, which means the seeded path is deterministic, not cryptographic, and gives away the whole sheet to anyone who knows the word.

Common mistakes

Saying a digit's face value rather than its place value

In 4,381 the 3 has a value of 300, not 3. The question is what it is worth, not what it looks like.

Counting columns from the left

Place value counts outwards from the units column on the right. Counting from the left gives a different answer for every different length of number.

Privacy and your data

Everything is generated inside your browser. The seed, the level and the numbers produced are never uploaded, never stored and never sent to a server.