How to teach comparing and ordering numbers
Kindergarten to Grade 4
Comparing numbers means deciding which is greater, which is less, or whether they are equal, and writing it with the symbols >, < and =. It rests on place value: to compare multi-digit numbers you look at the biggest place first.
How to teach it
- Start with quantities, not digits: which pile of counters is more? Match them up to see.
- Teach the symbols with the 'crocodile eats the bigger number' image, but move quickly to reading them properly ('greater than', 'less than').
- For multi-digit numbers, compare place by place from the left: hundreds first, then tens, then ones.
- Line numbers up by place value so the columns match before comparing.
- Extend to ordering a set of numbers smallest to largest, and to a number line.
Common mistakes
- Thinking a longer number of digits always means bigger without checking (true for whole numbers, but the reasoning matters for decimals later).
- Comparing from the right-hand digit instead of the largest place.
- Mixing up which way the > and < symbols point.
Frequently asked questions
What does comparing numbers mean?
Comparing numbers means deciding which is greater, which is less, or whether they are equal, and writing it with the symbols greater than, less than or equals. It rests on place value: to compare multi-digit numbers you look at the biggest place first.
What age or grade is comparing numbers taught?
Comparing and ordering numbers runs from Kindergarten to Grade 4. Young children compare quantities of objects, then use the symbols, and older students compare larger multi-digit numbers by place value and order whole sets from smallest to largest.
How do you compare multi-digit numbers?
Compare place by place from the left. Look at the highest place first, the hundreds before the tens before the ones, and the first place where the digits differ decides it. Lining the numbers up by place value so the columns match makes this reliable.
Which way do the greater than and less than symbols point?
The symbol always opens towards the larger number and points to the smaller one. So 8 greater than 3 is written with the open side facing the 8. The 'crocodile eats the bigger number' image helps at first, but move quickly to reading them as 'greater than' and 'less than'.
Does a number with more digits always mean it is bigger?
For whole numbers, yes: 100 has more digits than 99 and is larger. But teach the reasoning, not just the shortcut, because it fails for decimals later, where 0.45 has more digits than 0.5 yet is smaller. Comparing by place value is the reliable method.
Why does my child compare from the wrong end?
A common error is comparing from the right-hand digit instead of the largest place, so the child judges 0 versus 9 in the ones and ignores the hundreds. Teaching them to start from the leftmost place, and lining the numbers up in columns, fixes this.
What comes after comparing numbers?
Comparing leads into ordering whole sets of numbers and placing them on a number line, and it feeds directly into rounding, where you decide which friendly number a value is closer to. Secure place-value comparison supports all of these.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.