## The Language of Numbers: Inventing and Comparing Number Systems

Students explore a variety of number systems, both real and invented, as a way to better understand the characteristics of our number system, including place value and exponential notation. Students begin by creating their own number system on a “mystery device” as a way to explore properties of number systems. They then use their mystery device as well as a Chinese abacus to investigate place value. Students compare several additive systems to place value systems and learn how exponents and powers contribute to a base system.

### NCTM Standard: Number and Operations

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another
• Compute fluently and make reasonable estimates

### Primary Mathematical Goals

• Understand and using base and place value
• Write and calculate values of arithmetic expressions
• Write equivalent expressions
• Identify and compare number patterns
• Use exponents to write expressions