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
