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The Coolest Number System?

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Different Number Systems

Throughout history and throughout the world, there have been different systems devised for recording numbers.

Some of these you are probably familiar with…

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Tally Marks

Australia South America China

North America France Japan

Most of Europe Spain Korea

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Roman Numerals

1

I

2

II

3

III

4

IV

5

V

6

VI

7

VII

8

VIII

9

IX

10

X

11

XI

12

XII

13

XIII

14

XIV

15

XV

16

XVI

17

XVII

18

XVIII

19

XIX

20

XX

50

L

100

C

500

D

1000

M

2024

MMXXIV

There was no symbol for zero in Roman numerals.

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There are II types of people:

those who understand Roman

numerals, and those who

don’t!

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Binary Numbers

1

1

2

10

3

11

4

100

5

101

6

110

7

111

8

1000

9

1001

10

1010

11

1011

12

1100

13

1101

14

1110

15

1111

16

10000

17

10001

18

10010

19

10011

20

10100

2024

11111101000

Binary numbers are used extensively in coding.

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There are 10 types of people:

those who understand binary

numbers, and those who

don’t!

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Kaktovik IΓ±upiaq Numerals

Kaktovik is a city in northern Alaska.

In the 1990s, students in Kaktovik realised that there were problems matching the Hindu-Arabic numerals to the pattern of their IΓ±upiaq language. As part of their math enrichment class, they set out to create new numerals that fit their language.

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The IΓ±upiaq language of Alaska uses a Base-20 for its numerals with subdivisions for groups of 5. There are some rule breakers (looking at you, 6) and numbers before a multiple of 5 have a subtractive element '-utaiαΈ·aq' included so 14 is a bit like saying 15 – 1.

The students devised a brilliant numeral system that matched their language.

​

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Crack the Code

​

+

​

=

​

Γ—

​

=

​

+

​

=

​

+

​

=

​

+

​

=

​

Γ—

​

=

​

Γ—

​

=

​

–

​

=

​

Γ—

​

=

Find all the Kaktovik numerals for 0 to 19.

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Kaktovik IΓ±upiaq numerals.

What is:

​

? Twentys Ones

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Try These

Mild Medium Spicy

​

+ + Γ—

+ + +

– + +

​

+ + Γ—

​

+ + Γ—

​

+ – Γ·

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The students were pleased with this new number system. It was easy to remember, iconic, easy to write, distinct from Arabic numerals, and aesthetically pleasing.

It also honoured their culture.

With the encouragement of their teacher William Bartley, taught it to younger students. They built abacuses to help them work with this new system.

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In Summary

  • There are pros and cons to any number system
  • Don’t assume that what you are familiar with is always the best way
  • Anyone can create math that will have a positive impact on their community

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Open-Middle Problem

… Γ— … =

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Using to Calculate

Calulating with Kaktovik IΓ±upiaq Numerals