001. Historical Number Systems

Learning Intentions

• To understand that there are different number systems that have been used historically in different cultures
• write numbers in the Egyptian number system
• write numbers in the Babylonian number system
• write numbers in the Roman number system

Pre-requisite Summary

• Place value understanding (ones, tens, hundreds)
• Reading and writing whole numbers
• Understanding additive number representations
• Familiarity with symbols representing quantities
• Understanding base-10 counting
• Basic multiplication by 10
• Comparing numbers
• Decomposing numbers into parts

Worked Examples

Worked Example 1

Explain how number systems can differ.
a) Compare base-10 with a system that uses symbols for each power of ten
b) Identify whether each is positional or non-positional: Egyptian, Roman, Babylonian

Worked Example 2

Write 2,346 in the Egyptian number system.

Worked Example 3

Write 5,709 in the Egyptian number system.

Worked Example 4

Write 73 in the Babylonian number system.

Worked Example 5

Write 125 in the Babylonian number system.

Worked Example 6

Write 48 in Roman numerals.

Worked Example 7

Write 394 in Roman numerals.

Problems

Problem 1

a) Describe one difference between positional and non-positional number systems
b) Classify Roman and Babylonian systems

Problem 2

Write 1,432 in the Egyptian number system.

Problem 3

Write 6,215 in the Egyptian number system.

Problem 4

Write 52 in the Babylonian number system.

Problem 5

Write 184 in the Babylonian number system.

Problem 6

Write 63 in Roman numerals.

Problem 7

Write 749 in Roman numerals.

Exercises

Understanding and Fluency

1. Write 324 in the Egyptian number system
2. Write 2,018 in the Egyptian number system
3. Write 6,430 in the Egyptian number system
4. Write 41 in the Babylonian number system
5. Write 96 in the Babylonian number system
6. Write 132 in the Babylonian number system
7. Write 27 in Roman numerals
8. Write 89 in Roman numerals
9. Write 246 in Roman numerals
10. Write 1,399 in Roman numerals

Reasoning

11. Explain why the Egyptian number system is not efficient for very large numbers.
12. A student writes IIII instead of IV. Explain why this may or may not be acceptable.
13. Compare Babylonian and Roman systems. Which one uses place value? Explain.
14. Explain why zero is important in positional number systems.

Problem-solving

15. Write 2,759 in Egyptian numerals and then convert it to Roman numerals.
16. A Babylonian number shows two symbols in the 60s column and three in the ones column. What number is it?
17. Create a number that would require at least four different Roman numeral symbols and write it.
18. Write your birth year in Roman numerals.

Potential Misunderstandings

• Students may think all number systems use place value.
• Students may assume Egyptian symbols combine like digits rather than being repeated.
• Students may forget Babylonian numbers are base-60.
• Students may assume Babylonian numbers always include a zero symbol.
• Students may apply Roman numeral subtraction rules incorrectly.
• Students may repeat symbols more than three times in Roman numerals.
• Students may confuse additive and positional systems.

Next: 002. Place Value and Comparing Numbers