Less Than Sign: Why Children Mix It Up With Greater Than, and How to Fix It

Children mix up < and > because the two symbols are mirror images and neither one looks like what it means. The usual fix is the hungry alligator: the open end is its mouth, and the alligator always eats the bigger number. So 4 < 7 is the alligator turning to face 7.

That trick gets most children through the week. It does not get them through the year, because it explains nothing about why the symbol works, and a child who forgets which animal is hungry has nothing left. This page covers the alligator, what to say when it stops working, and what the US standards actually expect and when.

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What is the less than sign?

The less than sign, <, says the number on its left is smaller than the number on its right. So 4 < 7 reads "four is less than seven". The pointed end always faces the smaller number and the open end always faces the larger one.

It is one of four comparison symbols a child meets in primary school. The greater than sign is its mirror image, and the two with a line underneath add "or equal to".

Why do children mix up the greater than and less than signs?

Because the two symbols carry no clue about their meaning. They are the same shape rotated, so until the orientation is fixed in memory there is nothing to fall back on but a guess.

Three things make it harder than it looks:

• Reading direction does not help. In every other part of school a child reads left to right and the meaning comes from the words. Here the meaning comes from which way a shape points, which is closer to reading a road sign than reading a sentence.
• The same statement is true both ways round. 4 < 7 and 7 > 4 say the same thing. That is obvious to an adult and genuinely confusing to a six year old who has just learned that changing the order changes the answer in subtraction.
• It arrives alongside place value. Comparing 48 and 52 means looking at the tens first, not the ones. A child can know the symbol perfectly and still get the comparison wrong, which looks like a symbol problem and is not.

How do I explain the less than sign to a 6 or 7 year old?

Use the hungry alligator, but teach it properly rather than as a slogan. The whole trick is one rule: the alligator is greedy, so its mouth always opens toward the bigger number.

Say it out loud with your child while pointing at the numbers:

1. Read both numbers first. "Four and seven. Which is bigger?" Get the answer before the symbol appears at all.
2. Point the mouth. "The alligator wants the bigger one, so the mouth opens toward the seven."
3. Read the whole line back. "Four is less than seven." Reading it aloud, left to right, is what fixes the direction.

A second version some children prefer: the symbol is an arrow. The point is small, the opening is wide, so the small end goes with the small number. Use whichever one your child repeats back without prompting, and then use only that one. Two tricks at once is worse than one.

Where the alligator stops working, and what to say instead

The alligator is a memory aid, not an explanation. It runs out in three places:

• Negative numbers. A child who thinks "bigger" means "the number that looks bigger" will write -1 < -4. Here you need the number line: whichever number sits further left is the smaller one, and -4 sits left of -1.
• Fractions and decimals. 0.5 and 0.25 look the wrong way round if a child is counting digits. Same fix, put them on a line.
• Variables. x < 7 does not have two numbers to compare, so there is nothing for the alligator to eat. Read it as a sentence instead: "x is any number smaller than seven."

When the alligator fails, draw a number line. It is the one explanation that works for whole numbers, negatives, fractions and decimals without changing.

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What grade do children learn the less than sign?

Grade 1 and Grade 2, and the US standards are specific about the difference.

Common Core 1.NBT.B.3 asks Grade 1 children to compare two two-digit numbers using the meanings of the tens and ones digits, and to record the result with >, = and <.

Common Core 2.NBT.A.4 extends it in Grade 2 to two three-digit numbers, using hundreds, tens and ones.

Both standards ask for the same thing underneath: compare by place value, then write the symbol. That is worth knowing, because it tells you where a mistake actually sits. If your child writes 48 > 52, the symbol is not the problem. They compared the ones digits, saw 8 against 2, and answered a different question.

Common misconceptions about the less than sign

Four errors come up again and again.

• Confusing < with >. The symbols look nearly identical. The open side faces the larger number, every time.
• Reading right to left. 5 < 3 gets read as "3 is less than 5", which is true but is not what was written. Read the line left to right as it stands, then decide whether it is correct.
• Getting word problems backwards. "John has fewer than 8 apples" becomes J < 8, not J > 8. The trick is to put the thing you are describing on the left, then ask bigger or smaller.
• Thinking it only works with whole numbers. The less than sign works with fractions, decimals and negatives too: -4 < -1, and 0.25 < 0.5.

Where is the less than sign used?

Beyond comparing two numbers on a worksheet, it turns up wherever a limit or a range needs writing down.

• Inequalities in algebra. x < 7 describes every number below seven, not a single answer. This is the form it takes from around Grade 6 onward.
• Ordering numbers. Putting a list in order is a string of comparisons: 2 < 5 < 9.
• Everyday limits. Height restrictions, age ratings, speed limits and price comparisons are all the same idea written in words instead of symbols.

Our guide to inequality symbols goes further into the algebra side. For practice at home there are free Math worksheets to print.

How do we practice this at home?

Five minutes is enough, and the aim is for your child to say the whole sentence out loud rather than point at a shape.

1. Two numbers, one question. Write any two numbers. Ask which is bigger, then ask your child to put the symbol in and read the line back.
2. Use numbers from the room. Two door numbers, two prices, two ages. Comparing things that exist beats comparing digits on a page.
3. Draw the number line when they hesitate. Do not give the answer. Mark both numbers and let the position settle it.
4. Mix in negatives and decimals early. Once whole numbers are secure, throwing in -3 and 0.5 stops the alligator hardening into the only thing they know.
5. Try it backwards. Write 7 > 4 and ask them to write the same fact the other way round. Getting 4 < 7 shows they have understood it rather than memorized a picture.

Once comparing is secure, the symbols stop being the lesson and become notation your child uses everywhere else, from ordering fractions to writing inequalities. Other rules follow the same pattern of looking arbitrary until the reason lands, such as the associative property of multiplication.

Questions parents ask

What is the less than sign?

The less than sign is the symbol <, used to show that the number on its left is smaller than the number on its right. For example, 4 < 7 means four is less than seven. The pointed end always faces the smaller number and the open end always faces the larger one.

Why does my child keep mixing up the greater than and less than signs?

Because the two symbols are mirror images of each other and neither one looks like what it means. Nothing about the shape tells a child which is which, so without a fixed memory aid it is a guess. The open side always faces the bigger number. Saying the whole line out loud, rather than pointing at the shape, is what gives a child something to check against.

What are the inequality symbols in Math?

There are four: < means less than, > means greater than, ≤ means less than or equal to, and ≥ means greater than or equal to. The first two compare two different values. The two with a line underneath also allow the values to be the same.

What grade do children learn greater than and less than?

Grade 1 and Grade 2. Common Core 1.NBT.B.3 asks Grade 1 children to compare two-digit numbers using these symbols, and 2.NBT.A.4 extends it to three-digit numbers in Grade 2. Both standards ask children to compare by place value first, then record the result with the symbol.

What is the hungry alligator trick?

You treat the symbol as an alligator's mouth. The alligator is greedy, so its mouth always opens toward the bigger number. In 4 < 7 the mouth faces the seven. It works well for whole numbers and stops working for negatives, fractions and variables, where a number line is the better explanation.

Does the less than sign work with negative numbers?

Yes, and this is where children most often slip. With negatives, the number further left on the number line is the smaller one, so -4 < -1 even though four looks like the bigger digit. Drawing the line rather than comparing the digits is the reliable way through it.

The signs themselves take a few minutes to explain. Making them automatic takes a few weeks of short, spoken practice, and it is worth the effort because every inequality your child meets from here uses them. If you would rather have a teacher working through it each week, that is what our Grade 1 to 8 Math classes are built for.

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