Comparing Numbers: How to Teach Greater Than and Less Than

Q: What is place value in simple terms?

Place value means a digit is worth a different amount depending on where it sits. In 52, the 5 is worth 50 (5 tens) and the 2 is worth 2 (2 ones).

Q: How do I help my child with estimating?

Ask “about how many?” before counting and use 10 as a yardstick: more or less than 10? Then count to check; a sensible guess is the goal, not an exact one.

At what age do children learn to compare numbers?

Comparing starts long before school: “Who has more grapes?” is already a comparison. England's Year 1 is for ages 5–6, a year younger than US 1st grade, so the table compares by age.

Comparing numbers by age: US Common Core and England's national curriculum
Age	US (Common Core)	England (national curriculum)
5–6	Kindergarten: compare groups of up to 10 objects (more, fewer or the same) by matching or counting; compare numbers from 1 to 10	Year 1: use words such as equal to, more than, less than (fewer), most and least; find 1 more and 1 less
6–7	1st grade: tens and ones; compare two-digit numbers using >, = and <	Year 2: tens and ones; compare and order numbers up to 100 using <, > and =
7–8	2nd grade: compare three-digit numbers using hundreds, tens and ones	Year 3: compare and order numbers up to 1,000
8–10	3rd grade: round to the nearest 10 or 100; 4th grade: compare and round multi-digit numbers	Year 4: round any number to the nearest 10, 100 or 1,000

England's DfE guidance already uses <, > and = with numbers to 20 in Year 1. Whatever the grade, words come before symbols. For other skills by age, see math skills by age.

How comparing develops: from “more” to symbols

The US What Works Clearinghouse describes a typical progression for young children. Each step builds on the one before:

Seeing small amounts at a glance. Children recognize 1, 2 or 3 objects without counting; this is called subitizing.
Counting to compare. With 9 bears and 6 bears, they count both groups and know 9 is more.
Knowing what comes next. They can say the number after 5 without starting from 1.
Comparing in their head. They can answer “Which is more, 7 or 8?” without objects.
Seeing the pattern. Each number is exactly one more than the number before.

Place value and the written symbols come after that.

Tip Spread out doesn't mean more

Lay 6 coins in a long row and 8 coins bunched together. Young children often say the long row has more. Instead of correcting them, pair the coins up, one from each row: the 2 coins without a partner show that 8 is more. US kindergarten standards describe exactly this matching.

Tens and ones: the key to comparing bigger numbers

Place value means a digit's value depends on its place: in 47, the 4 means 4 tens (40) and the 7 means 7 ones. A child who understands this can compare two-digit numbers in seconds. Build numbers first, with Lego towers of 10 and single bricks or bundles of 10 straws.

Example Compare the tens first

47 is 4 tens and 7 ones; 39 is 3 tens and 9 ones
4 tens > 3 tens, so 47 > 39
Same tens? Compare the ones: 62 < 68
Three digits: 305 > 298 because 3 hundreds > 2 hundreds

Watch the teen numbers in English. “Fourteen” says the 4 first, so some children write 41; saying “ten and four” while showing 1 tower and 4 bricks helps. In the same way, “seventy-two” can turn into 702 when a child writes what they hear: 70, then 2.

Tip One more, one less, ten more, ten less

Ask “What's one more than 39?” and “What's ten more than 47?”, then add a brick or a tower and watch the number change. US standards expect 1st graders to find 10 more or 10 less in their head.

Greater than, less than: the crocodile trick and its pitfalls

The symbols are simple once you know them: > means “is greater than”, < means “is less than” and = means “is equal to”. The open side always faces the bigger number; the point faces the smaller one.

Many children learn the hungry crocodile (or alligator): it always wants to eat the bigger number, so its open mouth faces it. It's a handy memory hook, but it has pitfalls:

The words get lost. A child may write 9 > 4 correctly but read it as “the crocodile eats the 9”. At school they need “nine is greater than four”.
Reading backwards. 3 < 8 is read from the left: “three is less than eight”. Children who lean on the crocodile may say “eight is bigger”, which is true but reads the sentence backwards and causes trouble with longer number sentences later.
Mixing up the direction. Some children remember the crocodile but not which way it faces. Decide which number is bigger first, then open the sign toward it.
Equal numbers. With 6 and 6 the crocodile has nothing to eat; children need to know = is an option too.
It skips the thinking. The trick only works once the child knows which number is bigger, which is the real skill.

Example Read it aloud, left to right

9 > 4: “nine is greater than four”
3 < 8: “three is less than eight”
6 = 6: “six is equal to six”
4 + 4 > 7: “four plus four is greater than seven”

Tip Say it before you write it

Get the answer in words first (“Which is bigger?”), then choose the sign. Some children like “the small point points at the small number”.

Ordering numbers on a number line

A number line shows size as distance: the further right, the bigger the number. The What Works Clearinghouse recommends number lines for teaching number size in kindergarten to 2nd grade. Tape one on the floor, 0 to 20 at equal steps, and let your child stand on it: “Stand on 12. Is 15 to your left or right? Which is bigger?”

Then try an empty line with only 0 and 20 marked: where does 10 go? England's DfE guidance notes that children tend to squash the bigger numbers at the end, and suggests marking the midpoint first. A sensible “about here” with a reason is the goal, not precision.

Example Where does it go on a 0–20 line?

10 is halfway between 0 and 20
5 is halfway between 0 and 10
16 is just over halfway between 10 and 20
19 is 1 less than 20, right next to the end

Straight-track race

Ages: 4–6
Time: 10 min
You need: Paper, a pen, a coin and a small toy for each player

Draw a straight track of 10 equal squares and number them 1 to 10.
Take turns tossing the coin: heads moves 1 square, tails moves 2. Say the numbers as you move: “five, six.”
After each turn, ask: “Who is further along? Whose number is bigger?”
When 10 squares feel easy, draw a 1 to 20 track.

Why a straight, numbered track? In a study in the journal Child Development, preschoolers from low-income families (average age 5.4) who played such a game for about an hour in total got better at comparing numbers and placing them on a number line, with gains lasting 9 weeks. Classmates who played with colored squares instead of numbers did not improve. The Education Endowment Foundation's early-years guidance cites similar evidence.

Card compare

Ages: 5–8
Time: 10 min
You need: A deck of cards with the picture cards and 10s removed (ace = 1)

Deal the cards face down between two players.
Both turn over a card at once. The bigger number wins both cards, after saying the sentence: “8 is greater than 5.”
Equal cards? Say “7 is equal to 7” and turn over another card each.
Place value version, from about age 7: turn over two cards each and make the biggest two-digit number; 7 and 3 make 73.

Estimating: “about how many?”

Estimating means making a sensible guess, then checking, and it gives children a feel for how big numbers are. England's curriculum has children estimate numbers on a number line in Year 2, and US standards add rounding in 3rd grade.

Jar guess: put some pasta in a clear jar. “More or less than 10? More or less than 20?” Then count it in groups of 10.
Use 10 as a yardstick: a full ten-frame or two hands is 10; compare other amounts to it.
Number line guesses: “Where would 50 go on a 0 to 100 line?” Then try 25 and 90.
Rounding, from about age 8: “Is 47 closer to 40 or to 50?”

Example Nearest ten

47 is between 40 and 50
47 is 3 away from 50 and 7 away from 40
So 47 rounds to 50

Common mistakes (and quick fixes)

Judging by length or spread. “This row is longer, so it has more.” Fix: pair the objects up one by one.
Comparing the ones first. “39 is bigger than 47 because 9 is bigger than 7.” Fix: build both with towers; the tens decide.
Ignoring the number of digits. “100 is less than 99 because 1 is less than 9.” Fix: 100 is 10 towers; 99 is only 9 towers and 9 bricks.
Treating = as “the answer”. In 5 + 2 = □ + 1, some children write 7 in the box. Fix: = means “the same as”; 5 + 2 makes 7 and so does 6 + 1, so the box is 6. See our guide to missing number problems.

A 5-minute routine, and when to talk to the teacher

Which is more (1 minute). Say two numbers: “17 or 71?” “45 or 54?”
Build a number (1 minute). Your child builds 36 with towers and bricks; you add 1 tower: “What number is it now?” (46)
Sign of the day (1 minute). Write 28 □ 82; your child fills in the sign and reads the sentence aloud.
Estimate and check (2 minutes). “About how many grapes are in the bowl?” Count in tens to check.

Talk to the teacher if, by the end of 1st grade, your child still can't tell which of two numbers up to 20 is bigger without counting objects, or if tens and ones still don't make sense in 2nd grade after plenty of work with objects. If you see a lot of worry, read our guide to math anxiety; rounding and estimating also feed mental math later.

Frequently asked questions

How do I explain greater than and less than to a child?

Start with objects: which of two piles has more? Then compare numbers on a number line, where the bigger number is further right. Teach the signs last and have your child read them aloud from left to right: 9 > 4 is “nine is greater than four”.

What is the alligator or crocodile method for comparing numbers?

It is a memory trick: the hungry crocodile's open mouth faces the bigger number because it wants to eat more. It helps children draw the sign the right way round, but they still need to read it in words, left to right.

Which digit do you compare first in two-digit numbers?

The tens. 47 is greater than 39 because 4 tens are more than 3 tens; you only compare the ones when the tens are the same, as in 62 and 68.

At what age do children learn greater than and less than?

In the US, children compare numbers from 1 to 10 in kindergarten and use >, < and = with two-digit numbers in 1st grade. In England, the curriculum lists the signs in Year 2 for numbers to 100, and DfE guidance starts them with numbers to 20 in Year 1.

What is place value in simple terms?