Lesson: Subtractive Notation
Intermediate lesson on IV, IX, XL, XC, CD, and CM.
Difficulty: Intermediate · Classroom support material (not claimed as aligned to a specific state standard)
Objective
Students will correctly use the six standard subtractive pairs and reject invalid forms such as IL and IC.
What students need to know
- Symbols I–M
- Basic conversion for 1–100
Explanation
Modern canonical Roman numerals allow only six subtractive pairs: IV, IX, XL, XC, CD, CM. A smaller symbol before a larger one subtracts. Forms such as IL (for 49) or IC (for 99) are invalid because I cannot subtract from L or C.
Examples
- 4 = IV
- 9 = IX
- 40 = XL
- 49 = XLIX
- 90 = XC
- 99 = XCIX
- 400 = CD
- 900 = CM
Short guided practice
- Build a wall chart of the six pairs.
- Compare IIII vs IV and discuss clock-face IIII as a special convention.
- Check student spellings with the online checker.