Roman Numerals + No Zero

Yesterday, when I read that Roman Numerals had no zero, I wondered why?  It doesn't seem right that a culture who did so much for the world would not have that one concept. 

There are a couple of reasons including the fact that Roman Numerals were not used for arithmetic so they didn't need a zero.  Instead they used an abacus or counting frame to carry out addition or subtraction.  An empty space played the part of zero.

In addition, it is said the Romans developed their numerals as an easy way of pricing goods and services but not for adding or subtracting as noted before.  One reason they use IV instead of IIII for four is that Romans do not like seeing four of the same numerals appearing in a row so they created the concept of subtraction since IV means one less than five.  If the numeral appears after as in VI it indicates addition or five plus one more is six.  But note, this addition and subtraction concept only applied to creating numbers, not to doing arithmetic.

It is said that Roman Numerals composed of combinations of the seven letters of I, V, X, L, C, D, and M sometime between 900 and 800 BC.  Each of these letters refers to hands and counting such as the I represents one finger, the V is the shape between the thumb and forefinger and represents 5.  The X is two V's and represents two hands and so on. 

Although the Greeks understood the concept of zero meaning nothing they didn't think of it as a number.  It wasn't until about 1500 years ago in India that the number zero made its appearance as a dot but over time, it expanded to the 0 that we know today.  The Arabs stumbled across it in the 8th century and were responsible for spreading it around Europe.

Zero itself was not well received because it was considered suspect because it came from Arabs.  In 1259, a law was passed which prohibited bankers from using zero or any other numerals introduced by the Arabs but eventually these new numbers joined the others to create the numerical system we know today which includes zero.

Let me know what you think.  I'd love to hear. 

12 Interesting Mathematical Facts.

  Today for something different, I'm going to share a few interesting mathematical facts just for the fun of it.  Ones that could make life a bit more interesting for students.

1.  If there are 23 people in the room, there is a 50 percent chance that at least two people will share the same birthday.

2.  If you shuffle a new deck of cards seven times, you have created maximum "randomness" of the deck.

3. The decimal equivalences of fractions with seven as the denominator produce the same six repeating digits in a slightly different order.  They do not use 3, 6, or 9 in any of the decimal equivalents.
1/7 = .142857142857
2/7 = .285714285714
3/7 = .428571428571
4/7 = .571428571428
5/7 = .714285714257
6/7 = .857142857142

4. 26 is the only number between a perfect cube (3^3) and a perfect square (5^2)

5. Although you can fold paper more than 7 times, it usually requires either toilet paper or special heavy equipment that will press it flat, in general its hard to fold more than 6 times without extra help.  If you could fold the paper as 104 times, the thickness would be 93 billion light years.

6. Hundred is said to come from the Norse word Hundrath which  means 120 not the 100 we use it for.

7. if you multiply 111,111,111 by 111,111, 111 you get 12,345,678,987,654,321.

8. William Shakespeare used the word Mathematics in his wonderful play "The Taming of the Shrew".

9. Zero does not exist in Roman Numerals. 

10. The addition (+) and subtraction (-) signs were used as early as 1489 AD.

11. A jiffy is actually 1/100th of a second.

12. 10! seconds is equal to exactly 6 weeks.

I was feeling a bit silly today so decided to look for some interesting mathematical facts to share with everyone.  Have a good day and let me know what you think. 

The Math of Olympic Figure Skating

  Growing up in Hawaii, I never got the hang of how they score figure skating.  I learned to ooohhh when the announcers said to and I groaned when they did but I never actually learned much about it.  I actually did my first ice skating in Tucson Arizona at the combination bowling alley and skating rink.  I managed to stay up but my mother fell, dislocating her shoulder. 

So how do they score the ice skaters who perform at the Olympics.  Its more complex than I ever anticipated especially as they changed the system after a scandal in 2002.  Prior to this they used a scoring system based on a 6.0 being perfect but now, its way different. Are you ready for it?  I am.

The first step in scoring ice skaters is when the judges look for six moves, the Axle, flip, loop, Lutz, Salchow, and the toe loop that must be in every performance.  These jumps are looked at for technical and for overall performance and skaters receive two scores, one for each.

The technical award is done by two groups of people.  One is a nine judge panel who look at the quality of execution while the other is a five judge panel who looks specifically at the technical aspects of each jump.   Every move has a predetermined score such as the triple axle is worth 8.5 points for its base.

 If you perform a move with a higher difficulty rating, you get more points.  Sometimes just attempting a more difficult move, even if you don't make it, will give a higher score than performing a simpler one.  Furthermore, it is possible to get extra points by performing certain moves during the second half of the program when an athlete is more tired.

In addition, the nine member panel, they give a grade of execution from -3 to + 3 for every move.  This number is added to a predetermined base score for the move, but the highest and lowest scores are dropped so the average of the remaining seven scores makes up the technical score.

Furthermore, judges can award 1/4th to 10 points based on the five different components of skating skills, transitions, performance, composition, and interpretation.  The judges scores are averaged and then multiplied by 1.6 for the long program or .8 for the short program.  Finally, there is a referee who monitors the whole process

That is how they come up with the scores for ice skating at the Olympics.

Warm-up

Warm-up

Brain Pop

  While at the Alaska State Technology in Education conference I attended two different sessions presented by Brainpop.  Most of us know them as the people who produce those movies with the quizzes you can show your kids.  The movies star a cartoon young man and his robot.  The idea for most teachers is that you show the movie before giving the quiz to your students.

There are three versions most people are concerned with.  BrainPOP,  BrainPOP jr (k-3) and BrainPOPELL but I am looking at only at BrainPOP for this entry because I'm a high school teacher.  The first session highlighted the huge number of games offered so you can increase the gamification of your classroom while the other session was designed to discuss BrainPOP certification.

Through each session, I learned more about the extensive material offered by this site.  In addition to movies and quizzes, students can use the movies to create a graphic organizer of the material. They are even allowed to insert portions of the movie into the organizer.  As we know, research indicates that it is good for students to create graphic organizers as a way of helping them understand and learn the material.

Students can also make their own movie where they can answer a preset letter or a letter of their own on the topic.  They have everything they need to create the answer, just like the movies provided by BrainPOP.  Now the fun part starts here in that there are usually games associated with the topic and most are now HTML5 which means they will work on iPads.

I played a game or two and enjoyed them.  One game required me to find the value of colored money while the other was a time line of the American Revolution.  Since I teach math, the timeline one required a lot more work.  As I got close to the end of one set of questions, it asked me what the next topic would be.  It was challenging.

Add to that the NewsElA articles integrated into lesson.  NewsELA has articles at different reading lexiles and includes a quick quiz at the end.  There are some FYI which talk about the material in detail and might have a comic, activities and for a few topics, BrainPOP includes a primary source on the topic.

I've never seen primary sources applied to mathematical topics.  This is cool because it teaches students to interpret the data and shows them that there are primary sources out there we can use in mathematics.

They have an educator section with everything you need to integrate this into your classroom including lesson plans.  The other day I wrote about issues we have at school with our internet.  My frustration came out of wanting to use BrainPOP in my classroom but running into bandwidth issues which make it less likely I can use it.  I'm going to try but I can only hope.

Let me know what you think.  I'd love to hear. I  didn't publish yesterday because I was stuck in Bethel with limited internet so couldn't access my blogging account.  Have a good day.

Personality Types and Classroom Management? Yes or No?

  I am at a Technology in Education conference.  I have been to several sessions but today I went to one on how knowing their personality type can help you with classroom management. 

The session began by having all attendees take a personality test by Tony Robbins.  When done, you'd get the results of your test and honestly the test for me was ridiculous because it had me put in order statements. 

The statements were short and half of the I did not relate to so I just did anything.  We were told we needed to take this personality test so we'd understand the explanations better.  Baloney.  I didn't need that since all that really happened was the presenter showed video clips from movies on each personality type.  This one used dominance, inducement, compliance, and submission.

I was waiting for him to discuss how to use this information to help with classroom management but when he never discussed it.  What it mostly came down to was as a teacher I should look at my personality type and see how it interacts with the kids personality.  Yuck.  I got nothing out of it.

As far as I can tell, there is no real research done on this topic. There appears to be no reputable connection between these personality types and classroom management.  I did find that these personality test is used more in business than education.  Any information, I found on this topic used a different set of labels but these tended to divide people into either  extrovert or introvert, sensing vs intuition, thinking vs feeling, or judgement vs perception. 

With the introverts vs extroverts, it is said the introverts prefer to work alone and they like to take time to think before answering questions while extroverts do better in groups and love to talk out loud.  Sensing focus on concrete details while intuition learners like to focus on the big picture.  Thinkers apply their knowledge as they want to without regard for the specific situation while feeling students like the rules especially if the rules take thier motivations into account.  Finally, perceiving students like to keep deadlines flexible while judging students like solid deadlines.

Each one of these is associated with a preferred cognitive style, studying style, and instructional style based on which one they are.  The bottom line is that the two don't seem to related for education.  I think that students have aspects of all the personality types.

All I can say is that the presentation did not meet my expectations and I found it was a waste of my time.  I'd love to hear your thoughts on this topic.  Let me know.