Four-digit numbers

What it is

A four-digit number works by the same rule as place value to 1,000, with one more column on the left. In 3406 the 3 is three thousands, the 4 is four hundreds, there are no tens, and the 6 is six ones, so 3406 = 3000 + 400 + 6. Each column is still worth ten of the column to its right, which is what makes the thousands column ten hundreds.

The four-digit numbers that catch children out are the ones with a zero inside them. 3406, 3046 and 3460 are built from the same four digits, and what tells them apart is which column the zero is holding open. Read aloud, three thousand and forty-six names thousands, tens and ones and says nothing about hundreds, so a child writing from the sound of the words rather than column by column has nothing to put in the hundreds column and closes the gap up.

Year 4 also counts in 1,000s and compares numbers beyond 1,000. One thousand more than 3406 is 4406: only the thousands digit changes, and the other three stay where they are. Comparing works from the biggest column down, moving right only when two numbers tie, so 3460 is bigger than 3406 on the tens, after the thousands and the hundreds have matched.

When children learn it

Four-digit place value is a Year 4 requirement. The programme of study asks pupils to recognise the place value of each digit in a four-digit number, count in multiples of 1,000, find 1,000 more or less than a given number, and order and compare numbers beyond 1,000. Year 3 asks the same things of three-digit numbers, Year 5 goes to at least 1,000,000 and Year 6 to 10,000,000, so each year adds columns rather than a new idea.

A class that meets four-digit numbers late in Year 4 is not behind.

What it looks like when it goes wrong

These patterns come up again and again in children's answers on this skill. Each one points at a specific missing idea, not carelessness.

• The comparison stops at the first digit. Asked which is biggest of 3406, 3064 and 3460, they answer 3406. All three start with the same thousands digit, so the comparison has to carry on into the hundreds and then the tens; a child who compares the first column and stops is left picking between numbers that look the same to them. It shows up most on sets built from the same digits, which is how the app asks it.
• One thousand more changes the wrong column. Asked what one thousand more than 3406 is, they answer 3506. One column has been stepped, but the hundreds rather than the thousands. The idea that adding 1,000 changes one digit is there; which digit the thousands are is not, and writing the number into a place-value chart before stepping it usually settles that.
• The zero left out when writing the number. Asked to write three thousand and forty, they write 340. The words name thousands and tens and say nothing about hundreds, so the hundreds column is skipped rather than filled with a zero to hold it open. A child doing this on four-digit numbers is usually doing it on three-digit numbers too, which the place value guide covers.
• The number rounded down whatever it is nearer. 3670 rounded to the nearest 1,000 answered as 3000. Rounding to the nearest 1,000 is a separate Year 4 skill that comes after four-digit place value, so a child who reads every digit correctly and still rounds down has not made a place-value mistake. The rule is the one described in rounding to the nearest 10 and 100, applied one column further left.

How to help at home

• Ask what a digit is worth rather than what it is, using the new column: in 3406, what is the 3 worth? Three thousand is the answer to listen for.
• Dictate numbers with a zero inside them and ask for the numerals: 3040, 5007, 4600. A number whose middle column is empty is where the gap shows.
• Count on and back in 1,000s from a number that is not a multiple of 1,000: 3406, 4406, 5406, and then back down again. Only the thousands digit changes each time.
• Ask which of 3460 and 3406 is bigger, and how they can tell. Listen for an answer that names the column the two numbers differ in.

Other guides

• Place valueWhat each digit in a number is worth, what partitioning is, and the wrong answers that show the idea is missing.
• Rounding to the nearest 10 and 100Which digit decides which way a number goes, what happens at halfway, and the wrong answers that show the rule is landing on the wrong column.
• Column additionThe written method from Year 3: carrying, lining up digits, and the errors to watch for.
• Roman numeralsThe seven symbols, the four pairs that are read by taking away, and what Year 4 is actually asked to do with them.