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

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Counting
Counting grouping symbols to create each of the counting numbers from 0 to 10.

  • Did humans always do math as we do it today?

  • Did they always use the symbols we use?


Numbers vs numerals
Numbers vs Numerals grouping symbols to create each of the counting numbers from 0 to 10.


Early numerals
Early Numerals grouping symbols to create each of the counting numbers from 0 to 10.


Early numerals1
Early numerals grouping symbols to create each of the counting numbers from 0 to 10.

  • 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.


Numeration systems
Numeration Systems grouping symbols to create each of the counting numbers from 0 to 10.

  • Tally systems: ||||

  • 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


Egyptian numerals
Egyptian Numerals grouping symbols to create each of the counting numbers from 0 to 10.

Used at about the same time as Babylonian numerals--many similarities

1 10 100 1000 10,000

More symbols for 100,000 and 1,000,000


Egyptian numeration
Egyptian Numeration grouping symbols to create each of the counting numbers from 0 to 10.

  • 300 + 10 = 310 (Notice no ones)

  • 20,000 + 30 + 4 = 20,034


Roman numerals
Roman Numerals grouping symbols to create each of the counting numbers from 0 to 10.

Symbols: I V X L C D M 1 5 10 50 100 500 1000

If the Roman Numerals are in order from greatest to least, then add:VII = 5 + 1 + 1 = 7

XVI = 10 + 5 + 1 = 16


Roman numerals1
Roman Numerals grouping symbols to create each of the counting numbers from 0 to 10.

If the Roman numerals are NOT in order from greatest to least, then subtract where the order is wrong.IV = 5 - 1 = 4

IX = 10 – 1 = 9

XCII = 100 - 10 + 1 + 1 = 92


Babylonian numerals
Babylonian Numerals grouping symbols to create each of the counting numbers from 0 to 10.

  • Initially, no zero. Later developed:

  • Two symbols only: = 1; = 10

  • Additive when written from greatest to least:    = 10+10+1+1+1

  • Uses 60 as a base--there is a break after 60.    means 60+60+60+10+1


Babylonian numeration
Babylonian Numeration grouping symbols to create each of the counting numbers from 0 to 10.

   =

1 • ____ + 11 • 60 + 21 =

1 • 60 • 60 + 11 • 60 + 21 =

3600 + 660 + 21 = 4281


   = grouping symbols to create each of the counting numbers from 0 to 10.

1 • ____ + 11 • 60 + 21 =

1 • 60 • 60 + 11 • 60 + 21 =

3600 + 660 + 21 = 4281


Exploration 2 8
Exploration 2.8 grouping symbols to create each of the counting numbers from 0 to 10.

This exploration takes you out of your comfort zone and encourages you to think about what is involved in developing a numeration system.


Alphabitia
Alphabitia grouping symbols to create each of the counting numbers from 0 to 10.

  • Read the introduction.

  • Use the “artifacts”. Unit Long

    Flat


Your job
Your job: grouping symbols to create each of the counting numbers from 0 to 10.

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.

Write your group’s numeration system in the table.


Mayan numerals
Mayan Numerals grouping symbols to create each of the counting numbers from 0 to 10.

  • Used the concept of zero, but only for place holders

  • Used three symbols: • --- 1 5 0

  • Wrote their numbers vertically:••• is 3 + 5 = 8, --- is 5 + 5 = 10


Mayan numeration
Mayan Numeration grouping symbols to create each of the counting numbers from 0 to 10.

Uses base 20

New place value… left a vertical gap.

• is one 20, and 0 ones = 20.

•• • is two ____ + 5 + 1 = _____


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