1. Warm Up Activity Four 4s
Use four 4s and the arithmetic operations (+, -, x, /) plus grouping symbols to create each of the counting numbers from 0 to 10.
Use exactly four 4s for each number.

2. Counting Did humans always do math as we do it today?
Did they always use the symbols we use?

3. Numbers vs Numerals

4. Early numbers Numbers did not start out as 1, 2, 3, …
The first numeration systems were often 1, 2, many. More complex number systems arose out of need.

5. Numeration Systems Tally systems: |||| at a time.
Egyptian--probably earliest known
Babylonian--only two symbols
Roman--most widespread, all over Europe from the Roman Empire
Mayan--only three symbols
Hindu-Arabic--what we use today

6. Egyptian Numerals
Used at about the same time as Babylonian Numbers--many similarities
More symbols:
,000
More symbols for 100,000 and 1,000,000

7. Egyptian Numeration 300 + 10 = 310 (Notice no ones)
20, = 20304

8. Babylonian Numerals Initially, no zero. Later developed:
Two symbols only:  = 1; = 10.
Additive when written from greatest to least:    =
Use 60 as a base--there is a break after 60.     means

9. Babylonian Numeration
   =
1 • ____ + 11 • =
1 • 60 • • =
= 4281

10. Mayan Numerals Used the concept of zero, but only for place holders
Used three symbols: •
Wrote their numbers vertically: ••• is = 8, --- is = 10

11. Mayan Numeration New place value… left a vertical gap.
• is one 20, and 0 ones = 20.
•• • is two ___ + 6

12. Roman Numerals
No zero.
Symbols: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000
If the Roman Numerals are in order from greatest to least, then add: VII = = 7; XVI = = 16

13. Roman Numerals
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000.
If the Roman numerals are NOT in order from greatest to least, then subtract where the order is wrong. IV = = 4; IX = ; XCII = = 92

14. Exploration 2.8
Exploration 2.8--We will not do this entire thing--it is too long! But we will do parts. Today, we will begin with manipulatives.

15. Alphabitia
Read the introduction.
Use the “artifacts”. Unit Long
Flat

16. Your job:
Create a numeration system for your tribe using the artifacts left by the member who died. Think about what features are desirable in a numeration system. Make notes, and be ready to explain it to others who are not part of this tribe. It should be logical, and be able to be continued past Z.
Be ready to present your group’s numeration system for the Alphabitians on Tuesday.

17. Alphabitia Numeration System Proposals
What did you come up with in your group?
What are the pros and cons of your group’s system and the other groups’ systems?