Unlike languages, where it is common to hear and translate from one language to another, the world has pretty much converged on one number system — the Hindu-Arabic decimal system with its 10 digits – 0,1, 2, 3, 4, 5, 6, 7, 8, 9. But there was a time when there were many number systems.

#### A Brief History of Number Systems

A Native American tribe used an 8-digit system because they counted with the spaces between their fingers. The Babylonians used a 60-digit system, because it is easier to split things up when counting up to a number that has many factors. Roman Numerals have survived the test of time for their simple aesthetic beauty and easy-to-recognize symbols. The electronics around us are hushedly whirring in a binary number system while the engineers are thinking in hexadecimal and octal.

#### The Number System of Cartoons

Today our third grade math club visited cartoon land to see a different number system — you may not have noticed this before, but cartoon characters have four fingers on a hand, its a world where counting is done on eight fingers instead of ten.

Wearing cartoon gloves, with some math friends in full Minnie and Pluto costume, we entered cartoon land and counted our age. Our 8 year-olds learned that they would be 10 years of age in cartoon land, which they very much enjoyed.

#### The Roman Numeral System

Our fourth graders became Romans to see how their number system works. They each wore shirts with big roman numerals and we each learned the value that our own shirt had on it (I=1, V=5, X=10, L=50, C=100, D=500, M=1000) and the roman numeral rules (add each value, unless if the value to the right is bigger, than we subtract).

The children then went on to collaborate on translating decimal numbers into Roman Numerals, arranging themselves in a line to form a bunch of challenging numbers based on the Roman Numeral on their tee. We started with easier numbers such as 7, 15, 20, and then worked our way up to 9, 19 and 4. And then we split into two groups and competed to see which group could build big Roman Numerals first — 49, 99, 504, and 999.

#### The Binary Number System

Our fifth and sixth graders watched a video on binary numbers (see below).

They were so inspired by this work that they came up with a new project for math club — to transform the entire school floor into binary. The math friends collaborated, building a range of devices and transformations — and with approval from the principal — about four weeks of work, the transformation was made. The children built a binary clock, revised the phone to binary, number 2 pencils became number 10s, all room numbers and locker numbers were tagged with their binary equivalent. A device was built and installed in the middle of the floor that would enable all students to convert a decimal number into binary. They were very excited to share with their friends the next day how we convert numbers into binary.

#### Why Study Other Number Systems?

Why is this important? Looking at other number systems helps us better understand the building blocks of our decimal number system because now we have something to contrast it with. We get to see a number system with no symbol for zero and no place value, or a number system with only zeros and ones that does use place value — but surfaces that we truly didn’t have a deep understanding of the mechanics behind how all of that works.

And for our mathletes, math contests frequently include base-8 and Roman Numeral questions, and there are often problems that are actually easier to solve when we convert the numbers to binary.

But the most important reason to study other number systems is — because we are curious about how things work!

#### More on Number Systems

For our parents and caregivers interested in learning more about binary and other number systems, there is a wonderful video on this history of number systems by Why U (see below.)

## Thank You!

We at NJ Loves Math so much appreciate your taking the time to read this article. Please feel comfortable to provide any feedback as to its usefulness.