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Ordinal Numbers
This lesson introduces ordinal numbers, the words and abbreviations (1st, 2nd, 3rd, 4th...) used to describe order or position rather than amount. Students learn the difference between cardinal and ordinal numbers, the spelling pattern behind ordinal words, and how to use them when reading number grids and sequences.
Cardinal Numbers vs Ordinal Numbers
It helps to compare ordinal numbers to the numbers we already know well, called cardinal numbers. Cardinal numbers answer the question "how many?" Ordinal numbers answer the question "which position?"
- Cardinal number: There are 5 apples on the table.
- Ordinal number: The red apple is the 3rd apple from the left.
Notice that ordinal numbers are usually written with a short abbreviation, like 1st, 2nd, 3rd, and 4th, or spelled out fully as first, second, third, and fourth.
List of Ordinal Numbers
Here is a list of ordinal numbers from 1st through 20th. Notice that most ordinal words are simply the cardinal number word with an ending added, but a few of the smallest ones look completely different.
| Cardinal | Ordinal | Cardinal | Ordinal |
|---|---|---|---|
| 1 | 1st (first) | 11 | 11th (eleventh) |
| 2 | 2nd (second) | 12 | 12th (twelfth) |
| 3 | 3rd (third) | 13 | 13th (thirteenth) |
| 4 | 4th (fourth) | 14 | 14th (fourteenth) |
| 5 | 5th (fifth) | 15 | 15th (fifteenth) |
| 6 | 6th (sixth) | 16 | 16th (sixteenth) |
| 7 | 7th (seventh) | 17 | 17th (seventeenth) |
| 8 | 8th (eighth) | 18 | 18th (eighteenth) |
| 9 | 9th (ninth) | 19 | 19th (nineteenth) |
| 10 | 10th (tenth) | 20 | 20th (twentieth) |
The Spelling Pattern Behind Ordinal Numbers
Once you know the first four ordinal words, first, second, third, and fourth, most of the rest follow a simple pattern: add the letters "th" to the cardinal number word.
- five becomes fifth
- six becomes sixth
- seven becomes seventh
- eight becomes eighth
- nine becomes ninth
- ten becomes tenth
The abbreviations follow their own short pattern too. Most numbers end in "th" (4th, 5th, 6th...), but numbers ending in 1 use "st" (1st, 21st), numbers ending in 2 use "nd" (2nd, 22nd), and numbers ending in 3 use "rd" (3rd, 23rd). The only exceptions are 11th, 12th, and 13th, which always use "th."
Using Ordinal Numbers with Sequences and Number Grids
Ordinal numbers show up whenever we talk about order, not just in races. If you are counting values in a number grid up to 100, you might be asked to find the number in the 3rd row and 4th column. If you are studying number sequences with 1, 2, 3, 5, 10, you can describe each term in the pattern by its ordinal position, such as the 1st term, the 2nd term, and the 3rd term.
Ordinal thinking is also useful when checking a number grid with missing values: knowing that a missing number sits in the 5th position of a row helps you figure out exactly which counting number belongs there.
Worked Examples
Example 1: Eight kids are standing in a line to buy tickets. Maria is 5th in line. How many kids are standing in front of her?
Since Maria is 5th, there are 4 people ahead of her, in positions 1st, 2nd, 3rd, and 4th.
Example 2: Write the ordinal word for the number 9, then write its short abbreviation.
The number 9 becomes "ninth" as a word. Since 9 does not end in 1, 2, or 3, the abbreviation uses "th," giving us 9th.
Example 3: A calendar shows the date "23." How is this date written using an ordinal number?
Because 23 ends in 3, but 13 is an exception, we use the "rd" ending: the 23rd.
Practice Tips
When practicing ordinal numbers, try lining up toys, drawing pictures, or pointing to objects in a row and naming each position out loud: 1st, 2nd, 3rd, and so on. Comparing ordinal numbers to the related idea of identifying a number as even or odd can also be a helpful reminder that numbers describe more than just quantity, they can describe patterns and positions too.