1. How many different ways can you represent the quantity “7”

2. Symbols as abstract concepts
Number Systems
Symbols as abstract concepts

3. 2 1 3 5 4

4. What do we know about numbers?

5. Is this a number? 4 7 H 

6. Numbers are natural law
Symbols are abstractions
Helps us with the concept
Numbers can be represented many ways
Arabic
Roman
Tally marks
Symbols
 = 10 people

7. Number systems - base
Number systems may be represented in different ‘bases’ Our 10 digit number system (Decimal) – Deca meaning 10 [decade] The Base has n-1 unique symbols (all have zero): Base 10 has symbols 0 – 9 Base 16 has symbols 0 – 15 Base 2 has symbols 0 – 1 et cetera

8. Could we create our own number system?
Could we create symbols [abstractions] to represent numbers?
As long as the symbols are agreed upon as meaning – we could use
Important: Numbers systems have rules

9. Circle Square Triangle
Because we have determined that the symbols are somewhat arbitrary, let’s use other symbols.
We will use a Circle, Triangle and Square
Base 3

10. You and a group will create a number system
Groups of 3 symbols (base 3)
Create as many unique patterns as you can using only circles, triangles, and squares
ORDER MATTERS
Record your findings:
Number each order as 1, 2, 3… (to keep track)
Could there be a pattern to finding all the orders (permutations)?