Greater than less than: how to teach the symbols to kids

Greater than, less than and equal to are the three ways two numbers can compare. The greater than sign (>) and the less than sign (<) show which number is bigger. Teach comparing with objects first: line up two groups and see which has more. Then bring in numerals and a number line, and the symbols last.

What do greater than, less than and equal to mean?

Greater than means “more than.” Less than means “fewer than” for things you can count and “smaller than” for amounts. Two groups can also be equal, which means the same. Every comparison of two numbers has exactly one of three answers: greater, less or equal.

Children compare long before they see a symbol. A child who says “she got more grapes than me” is already doing it, and the signs are shorthand for that.

The US kindergarten standards list two kinds of comparing. Children identify whether one group of objects is “greater than, less than, or equal to” another, “by using matching and counting strategies,” with groups of up to 10. They also compare two written numerals between 1 and 10. The symbols >, = and < first appear in the Grade 1 standards.

The IES practice guide on teaching math to young children recommends teaching number “using a developmental progression.” Its steps for comparing start with collections of objects and words such as “more” and “fewer,” and only then move to numerals. It also recommends linking symbols to what children already know. Its example for < and > is two cans of pennies and the question “Which can has more?” So start with the words your child already uses, like “more” and “bigger,” and connect them to “greater than” and “less than,” which are the words the standards use.

How do I compare with objects first?

Use two small sets of household items, such as spoons, socks or blocks. Keep tiny items like beads and coins away from children under 3.

1. Put 4 blocks in one row and 7 blocks in another.
2. Ask “Which row has more?” Let your child guess first.
3. Match them up one to one. Put each block from the short row opposite a block in the long row. The blocks left over show the difference.
4. Count each row and say the result in a full sentence: “Seven is more than four. Four is less than seven.”
5. Swap the rows and say it again. The groups have not changed, and the sentence flips.

Try a pair that looks tricky, too. Spread 5 blocks wide apart and keep 8 blocks close together, so the row with fewer blocks looks longer. If your child picks the longer row, count both rows together, then match them one to one so the leftover blocks show which has more.

Make some pairs equal. Ask “Is there a row with more?” and let your child find that there is not. Equal is a real answer, and the IES guide suggests showing two groups with the same number so children learn the word for it.

How do numerals and a number line help?

Once your child can compare groups, move to the numbers alone. Write 3 on one card and 7 on another. Ask which is more, and let your child check with blocks if needed.

A row of numerals in order shows the idea well. Numbers further right are greater, and numbers further left are less. The IES guide calls this a number list: a number line that starts at 1, with no 0, which it describes as easier for young children to use. You can place numbers on our free number line to see which is further right.

Do this with a real line, too. Stick a strip of painter’s tape on the floor, mark it from 1 to 9 and let your child hop to a number. Ask “Is the number I picked to the left or the right of yours?” The line depends on knowing the counting order, which our guide on how to teach a child to count covers.

How do I teach the greater than and less than symbols?

Wait until your child can compare numerals under 10 with confidence. Then:

1. Write two numbers with a gap between them, such as 3 and 7. Say which is greater.
2. Draw the sign between them. The wide side faces the greater number and the narrow point faces the smaller. For 7 and 3 that gives 7 > 3 and 3 < 7.
3. Read it from left to right as a sentence: “Seven is greater than three.” Reading aloud is a useful habit here, because it ties the symbol to words your child already knows.
4. Write the same pair both ways, 7 > 3 and 3 < 7, and say each aloud. Both are true. They say the same thing from opposite ends.
5. Use the equal sign for matching pairs: 5 = 5.
6. Cover one number with your hand and ask your child to draw the sign that makes the sentence true.

Short sessions are enough. Five minutes at the table and a few pairs a day is plenty.

What about the alligator trick?

Some teachers and parents use a hungry mouth: the sign is an alligator that opens toward the bigger number because it wants the bigger meal. The idea is to help a child write the sign the right way around from the start. We found no research comparing it with other ways of teaching the signs, so the points below are our own reasoning.

It has limits. The picture tells your child which way to point the sign, but it does not say what the sign means. A child who relies on it alone may be able to write the symbol and still be unsure which number is greater. The trick also asks the child to find the bigger number first, so it only works for someone who can already compare.

A few ways to use it well:

• Start with objects, as above, and bring the alligator in only when your child is ready for the symbol.
• Say the full sentence every time: “Seven is greater than three.”
• Fade it out. After a few weeks, ask your child to draw the sign without the teeth and eyes.
• If the trick confuses your child, drop it. Another memory aid is that the narrow point always touches the smaller number. Pick one aid and stay with it.

How do I compare two-digit numbers?

The US Grade 1 standards ask children to compare two two-digit numbers “based on meanings of the tens and ones digits” and to record the result with >, = or <. Grade 2 extends this to three-digit numbers.

Take 38 and 83. Both use the digits 3 and 8, which can fool a child. Build each with sticks of ten and single ones: 38 is 3 tens and 8 ones, and 83 is 8 tens and 3 ones. Compare the tens first. 8 tens is more than 3 tens, so 83 > 38. If the tens match, as in 46 and 49, compare the ones.

Our guide to place value goes into tens and ones in more detail.

What mix-ups should I expect?

Watch for these mix-ups, and try the fix next to each one.

• Mixing up the two signs. Go back to reading the sentence aloud.
• Choosing the number that looks bigger. A child may say 9 is greater than 12 because 9 is a “big” digit. Use objects: build 9 and 12 and match them one to one.
• Choosing the number written first. Switch the order and ask again.
• Choosing the longer row of objects. Counting and matching fix this.
• Treating “equal” as “no answer.” Practice with matching pairs.

If your child is still stuck after weeks of calm practice with objects, talk to their teacher.

Which games help?

Two free games on this site build the skills behind comparing:

• Number Path: step on numbered stones in counting order. A number that comes later in the count is greater, so knowing the order helps with comparing.
• Count and Tap: tap each bug once to count a group, which is the counting step before comparing two groups.

Sit beside your child and ask comparing questions as you play, such as “Which is more, 6 or 9?” The Kindergarten curriculum page shows where comparing sits among the other topics, and the Grade 1 page covers comparing two-digit numbers. For a wider picture of what a child of five is working on, see what math a 5-year-old should know.