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

Symbols as abstract concepts Number Systems Symbols as abstract concepts

2 1 3 5 4

What do we know about numbers?

Is this a number? 4 7 H 

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

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

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

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

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)?