The three symbols
The greater than symbol (>) means the number on the left is bigger: 7 > 3 reads seven is greater than three. The less than symbol (<) means the number on the left is smaller: 3 < 7 reads three is less than seven. The equal sign (=) means both sides are the same amount.
The shape helps: the wide, open end faces the bigger number and the narrow point faces the smaller one. That is what the alligator trick is really saying. The trick is fine as a memory aid; the problem is stopping there.
Read the sentence aloud, every time
Children should say the whole statement out loud from left to right: eight is greater than five, two is less than nine. Reading it as a sentence fixes the direction of the symbol, links it to the words that appear in word problems and tests, and stops children from writing the correct symbol for the wrong reason. If a child can only say the alligator eats the eight, they have not yet learned the symbol.
A teaching sequence
- Compare quantities: two piles of counters. Which has more? Which has fewer? Say it in a sentence.
- Compare single digits with the number line: the number further right is greater.
- Introduce the symbols as shorthand for the sentences children are already saying.
- Two-digit numbers: compare tens first, then ones. 47 and 52: 5 tens beats 4 tens, so 52 is greater, whatever the ones digits.
- Three-digit numbers: hundreds, then tens, then ones. 347 and 374: same hundreds, 7 tens beats 4 tens, so 374 is greater.
- Ordering: put three or more numbers in order using the same comparisons.
- Later: compare fractions and decimals with the same symbols and the same left-to-right reading.
Comparing by place value
The rule that makes comparing any whole numbers easy: if the numbers have different numbers of digits, the one with more digits is greater (1,000 beats 999). If they have the same number of digits, compare the leftmost digit first, and only move right if the digits are equal. Children who line the numbers up in a place-value chart see this at once.
Worked example: 5,806 and 5,860. Same thousands (5), same hundreds (8), then 6 tens against 0 tens. 5,860 is greater. Write 5,806 < 5,860 and read it: five thousand eight hundred and six is less than five thousand eight hundred and sixty.
Common mistakes
- Reversing the symbol because the child worked out which number was bigger but forgot which way the symbol points. Reading the sentence aloud catches it.
- Comparing by the first digit only without checking the number of digits: thinking 98 is greater than 102 because 9 is bigger than 1.
- Comparing the ones digits first. Always start from the left.
- Treating the symbols as arrows. The narrow end is not pointing anywhere; it is the small end.