Place Value (Beyond Base 10)

Objective

To help students understand place value, we venture beyond our typical decimal number system and explore a Base 9 system. Students will be exposed to ancient Babylon's Base 60 system and computers Binary and Hexadecimal before creating their own number system.

Steps

1. Students consider what a "numeral" is and just how many we actually use.
2. We discuss our ten numerals and how the base 10, or decimal, system works. Then we introduce base 9, pondering what 8 + 1 would equal in a system without a symbol for 9.
3. We dig further into Base 9, asking students to complete a worksheet transforming base 9 numbers into base 10.
4. After correcting the worksheet, we explore real world number systems: Babylonian, Binary, and Hexadecimal. Finally, students develop their own, non-base-10 system and create two-digit numbers using this worksheet.

Resources

• Worksheet 1 (PDF)
• Worksheet 1 (Google Slides)
• Worksheet 2 (PDF)
• Worksheet 2 (Google Slides)