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) Identify 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
Exercise 1.
Write 324 in the Egyptian number system
Exercise 2.
Write 2,018 in the Egyptian number system
Exercise 3.
Write 6,430 in the Egyptian number system
Exercise 4.
Write 41 in the Babylonian number system
Exercise 5.
Write 96 in the Babylonian number system
Exercise 6.
Write 132 in the Babylonian number system
Exercise 7.
Write 27 in Roman numerals
Exercise 8.
Write 89 in Roman numerals
Exercise 9.
Write 246 in Roman numerals
Exercise 10.
Write 1,399 in Roman numerals
Reasoning
Exercise 11.
Explain why the Egyptian number system is not efficient for very large numbers.
Exercise 12.
A student writes IIII instead of IV. Explain why this may or may not be acceptable.
Exercise 13.
Compare Babylonian and Roman systems. Which one uses place value? Explain.
Exercise 14.
Explain why zero is important in positional number systems.
Problem-solving
Exercise 15.
Write 2,759 in Egyptian numerals and then convert it to Roman numerals.
Exercise 16.
A Babylonian number shows two symbols in the 60s column and three in the ones column. What number is it?
Exercise 17.
Create a number that would require at least four different Roman numeral symbols and write it.
Exercise 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.