What Are Roman Numerals?

Hey there kids – it’s number 2!

number2Have I got an interesting topic for you!

You’ve met numbers 1 through 9
Let’s learn about different ones this time!

Roman numerals are good to know
They were used to express value a long time ago

Instead of writing 1,2, 3
Try the Roman way with I, II, III – see?

Roman numerals are used today
On some clocks, in books and plays

But what’s so cool about when you use ‘em
Is how hard it is to really confuse ‘em

Let’s take a Roman numeral tour
And learn to write 1, 2, 3, and 4

I, II, III are easy to see
But, 4 is IV– how can that be?

Because 4 is one less than 5, we show
IV which is “I” less than 5 or “V,” Oh!

Roman numerals use “I” after or before
To show one less or even one more

VI is 6 and VII is 7, then
VIII is8, IX is 9 -one less than “X” (or 10!)

Roman numerals are a great way to learn
A new way of viewing numbers – now it’s your turn!

Talk to your teacher or mom or dad,
About using Roman numerals to subtract or add.


Can You Count the Continents?

Hi there kids, number 7 here!
I’ve traveled back from far to near

Around the world through land and seaseven
Each country, an interesting place to be

And because I know you love to count
I’ll ask if you know the continent amount

A continent’s a piece of land
From outer space, each one looks grand

They cover the earth and fill each big gap
I’m sure you’ve seen them on a map

Do you know how many there might be?
If you’re not sure, count them all with me!

Africa, Asia, Australia, North America,
Antarctica, Europe, South America

That makes seven – can you see why
People call me the Continent Guy?


Continent Discontent

Here’s a question you probably think you know the answer to:

How many continents are there on the planet earth?

For generations of Americans, the answer is simple: seven. The list of continents includes Asia, Africa, North America, South America, Europe, Australia and Antarctica.

But, before you assume this blog post is done, consider this: Some geographers disagree with that number, and instead choose to count Europe and Asia as one mass of land labeled Eurasia.  And, in other parts of the world, children are taught there are only five continents: Eurasia, Australia, Africa, Antarctica and the Americas.

To confuse you even further, researchers recently made the argument that a large mass of land completely submerged under water – and part of New Zealand – qualifies as a continent and should be recognized as such.

All this continent discontent might make you want to throw your geography book out the window, but it certainly shines a spotlight on the question, “what counts as a continent?”

Exactly What IS a Continent?

Good question.

Although one accepted characterization of a continent maintains it is a large, continuous mass of land, bigger than an island and separated on all sides by water, that classification is somewhat arbitrary, which is why Greenland is considered an island, but Australia – only a couple more million km in size – is considered a continent.

In fact, by that definition, many purists believe there are only four continents – since Europe and Asia are part of one land mass, Asia and Africa are joined by an isthmus, as are the two Americas – which would just leave Australia and Antarctica.

The reason much of the world can’t agree is that there is no one definition of what makes up a continent. Some accepted factors beyond the physical attributes include distinctive flora and fauna, cultural uniqueness – and even local agreement on continental status, which I suppose means that if you believe it, it’s so!

Too Much on Your Plate

As a math-minded person, I find it difficult to define physical structures by cultural differences, so as a last resort –what about how continents relate to the tectonic plates beneath them? Surely, there must be an alignment there.

Tectonic plates are the earth’s rocky outer crust and they continue to drift, ever so slowly, across the surface of the globe. This accepted theory of continental drift explains Pangea – one super continent that began breaking up 175 million years ago into the modern configuration of continents we know today.

But, if we look at the location of the continents over these plates, we’ll realize that while Europe and Asia mostly share one plate, the Americas are separated and the country of India shares a plate with Australia. Greenland and the Philippines each have their own plates – although neither is defined as a continent today.

The only concept that becomes clear here is that depending where you are, who you are and WHEN you were – you may have a very different opinion on the total of continents.  And, here we thought numbers was a definitive subject!

Math Comprehension Wasn’t Built in a Day: Roman Numerals Can Help

As I was about to turn off my television set the other night at the close of this year’s Super Bowl, I was struck by the irony of the blazing ancient Roman numerals across the screen that proclaimed the annual number of times this decidedly modern American game had been played:

Super Bowl LI

Other than counting professional football games or adorning a fancy watch or two, the practice of using Roman numerals within the mainstream or teaching them in elementary school has gone the way of penmanship, cursive and the dodo.

Perhaps, some of you might remark, that’s as it should be. Like learning Latin, using an abacus or powdering one’s wig, striving to understand Roman numerals seems to foster a history lesson rather than a necessary skill for young people today.

But, from a math perspective, nothing could be further from the truth. Roman numerals help bridge a gap in mathematical comprehension for elementary school-aged children. Here are three reasons why:

Roman Numerals Show Amounts in a Visual Way

When you first learned to draw a “2” and were told it represented two of something, you had to memorize it. The symbol for “2,” or any other number from 0-9 for that matter, is not inherently demonstrative of the value it represents.

In fact, compared to ancient numbering systems, our modern number structure is confusing – especially to young children learning it for the first time.

Thousands of years ago, the human need for keeping track of belongings, animals or anything else gave birth to the counting or tallying systems. Historic people used sticks or pebbles to represent each of whatever they were trying to count.

Tally sticks were also used to mark amounts. Notches were cut into a stick to signify a number of items or perhaps sheep in a flock. The problem with using a unary system, one in which each line represents each item, is that you wind up with a lot of lines. Too many lines for the human eye to be able to decipher quickly and easily how many you actually have.

That’s why many tally systems evolved. When you got to five, you crossed through the previous four lines – to create an easier visual for that number.


It’s hypothesized that Roman numerals evolved from these tallying systems, with each fifth notch eventually being written as a diagonal or “V” and each tenth notch as an “X.” And, so on.

The Roman numeral system creates visual shortcuts for quickly counting and totaling amounts necessary for simple records or contracts.

Roman Numerals Differentiate Numeric Value

Unlike the base ten system we use globally today, Roman numerals are non-positional (do not involve place value). That means each number has a unique meaning. The letter for ten (X) is completely different than the letter for one hundred (C) – whereas in our systems, they are represented by the same numbers in a unique pattern: 10 versus 100. Place value is a critical but difficult concept for very young children to learn. Understanding that the “5” is “1,265” has a different value than the “5” in “542” can be confusing.

Roman numerals do a better job demonstrating the difference in value because the system uses unique characters. “5” is “V” and “500” is “D,” which are totally different – because five and five hundred really ARE totally different.

Roman Numerals Teach Addition and Subtraction

For preschoolers and kindergartners, addition and subtraction usually comes with visual representations of the equation. Apples, toy trucks, lima beans – anything to help associate how values can be combined or taken away from each other.

With Roman numerals, the addition and subtraction is built in! Depending on left or right placement, an “I” represents “less than” or “more than” consecutive numbers. Consider the number line from one to ten:

I One
II Two
III Three
IV Four = One less than Five
V Five
VI Six = One more than Five
VII Seven = Two more than Five
VIII Eight = Three more than Five
IX Nine = One less than Ten
X = Ten

Roman numerals eventually gave way to more modern systems for several reasons, including the need to increasingly account for accounting and represent numbers larger than several thousand and allow for algebraic concepts. Zero was critical to this change which happened around 1300 AD when the Arabs—the world traders- took the concept from India to much of the world.

However, Roman Numerals are still woven through many facets of our culture – from marking the scenes in plays to organizing our thoughts in outlines to letting us know which Star Wars movie is coming out. Having a basic understanding of the Roman numeral system creates a foundation for number visualization and more complicated math concepts – and by the way, they are just plain fun to learn!

Learn more about the history of Roman numerals: http://scienceblogs.com/goodmath/2006/08/16/roman-numerals-and-arithmetic/

Learn more about teaching them to kids: https://owlcation.com/academia/How-to-Teach-Roman-Numerals

US Patent 9403084 Issued


After four years of working on my Number Linx® puzzle, I am excited to announce that I have been issued the US patent for Polygon Puzzle and Related Methods (Patent No. 9403084). It appears to be the first utility patent issued for a puzzle in 20 years!

Why isn’t the name of my puzzle in my patent? The answer lies in the fact that there are multiple kinds of patent. In the past, I have received a design patent (Patent No. D737905) on Number Linx and our number characters, 0-9. According to the US Patent Office, a design patent is for a specific product. Design patents are “Issued for a new, original, and ornamental design embodied in or applied to an article of manufacture, it permits its owner to exclude others from making, using, or selling the design.” On August 2nd, however, I received my first utility patent;  it protects my concept, no matter its configuration. A utility patent is “Issued for the invention of a new and useful process, machine, manufacture, or composition of matter, or a new and useful improvement thereof, it generally permits its owner to exclude others from making, using, or selling the invention for a period of up to twenty years from the date of patent application filing” (http://www.uspto.gov/web/offices/ac/ido/oeip/taf/patdesc.htm).

Patents are public information for anyone to see; they can be found online or at the US Patent Office in Washington, DC. They are long though, this one is 13 pages of legal language with lots of drawings to illustrate exactly what is being protected.

To obtain my patent, I had to prove to the US Patent Office that there had never been a puzzle like it, with a polygon for each number made up of a varying number of polygons with the same number of sides. I began that long process almost exactly two and a half years ago.

In 2012, Graham Campbell cut the first prototype of Number Linx and we presented it together at the Chicago Toy Fair. When I finally began the patent application process in 2014 I had to demonstrate each part of Number Linx and explain how the puzzle is innovative. Listening in to many calls with patent examiner Steven Wong, I guided my lawyer in how to best present my puzzle and its unique features. All that work came to fruition when my patent was issued on August 2nd, 2016. That means my idea is protected, and no one else can make or sell a puzzle or something similar to Number Linx/Puzzling Polygons or the cards.

What good news after so much hard work – NumbersAlive! celebrated with some yummy cake!

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