Xmanian Number system

Once upon a time, in a far away land, the people had a number problem.

ABC

Xmanians use letters to name quantities:

So counting is done….

ABCDEE objects

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

Many

Many

Many

Many

Many

Many

Many

Many

Many

Many

This worked fine for a while, but eventually …. what do you think happened?

This worked fine for a while, but eventually too many collections were described as "many". Furthermore, the description of "many" often didn't provide the citizens of Xmania with enough information about the quantity of items in the "many" collections.

The mathematicians on Xmania decided that they needed to solve this "many" problem, and set out to invent other number systems. After some time, there was a conference called so that the mathema-ticians could get together to share their ideas.

Several proposals for new number systems were on the program, but the one that generated the most excitement was a system which only used the symbols "0", "A", "B", "C", and "D".

Several proposals for new number systems were on the program, but the one that generated the most excitement was a system which only used the symbols "0", "A", "B", "C", and "D". It was rumored that this system solved the "many" problem: you could count as high as you wanted and you could identify exactly how many items there were in a set.

Several proposals for new number systems were on the program, but the one that generated the most excitement was a system which only used the symbols "0", "A", "B", "C", and "D". It was rumored that this system solved the "many" problem: you could count as high as you wanted and you could identify exactly how many items there were in a set. To everyone's amazement, it was further rumored that the mathematician had developed algorithms for adding, subtracting, multiplying and dividing within the new system.

Unfortunate News…..On the eve before the new system was to be revealed, she disappeared mysteriously, leaving behind several artifacts.

Clues found ….• System uses the symbols "0", "A", "B", "C", and "D".

• It looks like the mathematician was counting in her system: A, B, C, D, A0, AA, AB….

• There is one more clue to her work. We have a set of blocks that she created to model her system.

We need to work together to reconstruct the system that our dear colleague had planned to share with us.

Process

• Step 1: Take 5 minutes in silence and each think about a possible number system using only the 5 symbols given and that relates somehow to the artifacts. Jot down your ideas.

Process

• Step 2: As a group, decide on your number system. Write down the rules of your number system. Explain how to write small and large numbers in your system. Also decide how to do basic arithmetic such as adding, subtracting, multiplying, etc. Remember, you can only use the symbols that the mathematician has introduced (0, A, B, C, and D).

Process

• Step 3: After you have written down your ideas for step 2, create a poster for the class to see your number system. This poster should include the information listed in step 2, with pictures using the “artifacts” found on Xmania. Be prepared to answer questions from the class on how to use your number system.

Process

• After your poster is done:– Think of some limitations or perks of your number

system.– Can you imagine a more efficient number system

based on the artifacts? (Quicker to write the numbers / shorter numbers / easier to perform operations)