Number systems
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[edit] Overview
Most generally, number systems are the language we use to count. Our number system is a base-10 system, meaning that it has ten symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) and uses place values to represent amounts.
[edit] Base systems
The Mayan Civilization used a base-20 system using a combination of dots and lines (a line being equivalent to five dots)
The Babylonians used a base-60 system
Computers use a base-2 (binary) system
[edit] Place value
Unlike Roman numerals where a symbol will always represent the same thing, a '9' can represent many different quantities in our base-10 system. It can represent 9, 90, 900, etc, depending on its place value.
The number 25,387 can be thought of as 
or 
[edit] Motivating questions and problems
Why do computers use binary? What is binary?
What is a winning strategy for a random Nim game?
Do other civilizations use different numbers?
How do people from other countries count? In French? Spanish? Chinese? (or whatever languages some student knows) What is the same, and what is different?
Where do our numbers come from?
Find 20 + 21 + 22 + 23 + ... + 210.
[edit] Lesson plans
Specific ways to teach this topic, including:
[edit] places and/or concepts that are stumbling blocks
[edit] grade level that a certain lesson or activity has been used for
[edit] examples of student output
[edit] Exercises
Convert the following base-2 numbers into base-10.
Convert the following base-5 numbers into base-10.
Convert the following base-10 numbers into base-2.
Convert the following base-10 numbers into base-5.
[edit] Problems
Find 20 + 21 + 22 + 23 + ... + 210.
What are the advantages and disadvantages of using a base-60 number system instead of a base-10 number system?
What are the advantages and disadvantages of using a base-10 number system instead of the Roman number system?
The number 53,298 is a multiple of 2 because the number ends in an even number. Find a similar divisibility rule for 2 in base-8. What about base-5?
[edit] Extensions
History of different number systems
Operations in other base number systems
Fractions in other base number systems
Building a four-bit adder
What would a Fibonacci-base system look like?
What would a base-
system look like?
[edit] Motivating topics
The game on Nim
A deeper understanding of why our operation algorithms work
