Comparing numbers up to a million

Q: Why is my child comparing numbers place by place?

Because a digit’s value depends on its place, looking at places is the reliable way to compare. First, your child checks how many digits each number has; a five-digit number is always larger than a four-digit one. If the counts match, they look from the left. The first place where the digits differ decides it: for 63,419 and 63,491, that is the tens place, 1 against 9, so 63,419 < 63,491.

Q: My child mixes up the greater-than and less-than signs. Any tips?

This is very common. One idea is that the wide, open side of the sign always faces the larger number, and the point faces the smaller one. Another is to read the sentence from left to right in words: 52 < 60 reads "52 is less than 60." Saying the full sentence out loud each time usually helps more than a memory trick alone.

Q: What if my child reads big numbers well but mixes up which one is larger?

That happens a lot, and it’s no one’s fault. Reading moves along one number digit by digit, but comparing means holding two numbers side by side and checking the same place in each. Try writing one number under the other so the places line up, then have your child circle the first pair of digits that differ. That circle tells the whole story.

In 4th grade, children learn to compare two numbers up to a million, place by place from the left, and to record the result with >, =, or <.

By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club

Try these with your child

These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.

Question 1 of 3

A bee farm counted 12,650 bees in Hive A and 12,560 bees in Hive B. Which hive has fewer bees?

Both hives have the same number
Hive A
Hive B

Why this matters

Comparing big numbers gives your child a reliable way to answer "which is bigger?", a question that comes up everywhere. It helps with rounding this year, and in 5th grade, comparing decimals like 0.45 and 0.5 uses the same place-by-place check from the left. You’ll see it all around: in sports crowds, in prices, and in which of two drives is longer.

If a big number is hard to say aloud, your child can review reading and writing numbers up to a million before comparing.

Where kids can get stuck

Judging by the first digit alone, so 9,850 seems greater than 12,400 even though it has fewer digits.
Comparing from the right instead of the left, deciding 45,719 is greater than 46,108 because 9 is bigger than 8.
Calling two numbers equal because they use the same digits, such as 52,301 and 52,310.

How you can help

Compare two numbers you see in the news or on a scoreboard, like the crowds at two games. Ask your child which is larger and which place told them, then say the whole comparison with "greater than" or "less than."
Play a number-building game with playing cards, with aces as 1 and tens and face cards set aside. Each person draws five cards and makes the largest number they can, and together you decide whose is greater.
Order a few numbers at bedtime. Say three, such as 408,150, 480,105, and 408,510, and have your child put them from least to greatest, explaining which place settled each one.

If it’s helpful, you can sign up for free, adaptive practice in Bobby's Math Club.

Questions parents ask

Why is my child comparing numbers place by place?

Because a digit’s value depends on its place, looking at places is the reliable way to compare. First, your child checks how many digits each number has; a five-digit number is always larger than a four-digit one. If the counts match, they look from the left. The first place where the digits differ decides it: for 63,419 and 63,491, that is the tens place, 1 against 9, so 63,419 < 63,491.

My child mixes up the greater-than and less-than signs. Any tips?

This is very common. One idea is that the wide, open side of the sign always faces the larger number, and the point faces the smaller one. Another is to read the sentence from left to right in words: 52 < 60 reads "52 is less than 60." Saying the full sentence out loud each time usually helps more than a memory trick alone.

What if my child reads big numbers well but mixes up which one is larger?

That happens a lot, and it’s no one’s fault. Reading moves along one number digit by digit, but comparing means holding two numbers side by side and checking the same place in each. Try writing one number under the other so the places line up, then have your child circle the first pair of digits that differ. That circle tells the whole story.

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Written by Robert “Bobby” Barnett

Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.

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Note for teachers: This skill is covered by Common Core math standard 4.NBT.A.2: “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NBT.2)

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