Bigger or smaller?
To compare numbers means to decide which is bigger, which is smaller, or whether they are the same. To order numbers means to put a whole list in a line from least to greatest (smallest to biggest), or from greatest to least.
You do this all the time: Who scored more points? Which toy costs less? Who is the oldest in your family?
Comparing with a number line
On a number line, numbers to the right are bigger.
0 — 5 — 10 — 15 — 20 — 25
So 21 is bigger than 14, because it is further right.
Comparing with place value
For two-digit numbers, look at the tens digit first:
| Number | Tens | Ones |
|---|---|---|
| 14 | 1 | 4 |
| 21 | 2 | 1 |
21 has 2 tens; 14 has only 1 ten. So 21 is bigger, even though 4 is bigger than 1 in the ones digit.
Rule: compare the biggest place first. Only look at the ones if the tens are the same.
| Compare | Tens the same? | Decide by | Bigger |
|---|---|---|---|
| 36 and 52 | No | Tens: 5 > 3 | 52 |
| 47 and 43 | Yes (4) | Ones: 7 > 3 | 47 |
| 9 and 12 | 9 has no tens | Tens | 12 |
A one-digit number is always smaller than a two-digit number.
Ordering a list
- Find the least number and write it first.
- Find the next smallest and write it next.
- Keep going until you reach the greatest.
- Check: does every number get bigger as you read along?
Worked examples
Example 1: Order from least to greatest: 14, 9, 21.
9 has no tens, so it is least. 14 has 1 ten, 21 has 2 tens. Answer: 9, 14, 21.
Example 2: Order from greatest to least: 58, 85, 55.
Tens: 8 > 5, so 85 is greatest. 58 and 55 both have 5 tens; ones: 8 > 5. Answer: 85, 58, 55.
Example 3: Which is smaller, 70 or 69?
Tens: 6 < 7, so 69 is smaller.
Common mistakes
- Reading only the ones digit. 19 is not bigger than 31 just because 9 > 1.
- Mixing up the direction. "Least to greatest" starts small; "greatest to least" starts big.
- Forgetting a number when rewriting a list. Cross each one off as you use it.
Try it yourself
- Which is greater: 38 or 83?
- Order from least to greatest: 27, 72, 7.
- Order from greatest to least: 40, 44, 14.
- Which is the least: 61, 16, 66?
Answers: 1) 83 2) 7, 27, 72 3) 44, 40, 14 4) 16
Quick recap
- Compare the tens digit first, then the ones digit.
- Numbers further right on a number line are bigger.
- Order from least to greatest or the other way, then check.