My weekend math

Hi math fans! I'm just going to briefly talk about my experience with math over the weekend. I didn't get a chance to do any paper and pencil math, but I did watch a few basketball games and revisited one of my favorite awful-yet-amazing TV shows Xena: Warrior Princess.


I don't get a chance to watch a lot of professional basketball, but one of my roommates is a die-hard Spurs fan. So we watched the Spurs play the Suns on Friday night and again on Sunday night. Some players are much better mathematicians than others. Steve Nash is a genius at basketball math and while Tim Duncan is a good defender and guard, his math for making free throws needs work. Just listening to the sportscasters was interesting, they talked about basketball statistics a lot, how many shots they've taken and how many they've made. The percentages for whole team, how many points the bench has, etc. Lots of math, but no one went to the AT&T stadium to hear or think about math. It's sad that the Spurs lost, but I got to see lots of math in action.

I also found that Netflix has Xena online for members, and I took advantage of that by watching a few episodes of season 1. Keep in mind, Xena the Warrior Princess is a very old-school action show with low budget graphics, exotificiation of cultures, campy humor, and plotholes galore. But I grew up watching the show with my family on Saturday nights, and I'm obsessed with Lucy Lawless (who is more talented than most people give her credit for).


No matter how improbable or completely outrageous the show is, Xena is an excellent mathematician. One of her main weapons is the chakram, or a metal disc with sharp edges that she either 1) chucks at the bad guys or 2) uses to cause avalances. She takes her geometry and trigonometry into consideration before she throws her chakram and always hits her target. She uses angles to ricochet her chakram all over the place. It's some pretty accurate math if you ask me. Sure, the laws of physics make it difficult to tell if she can actually do such chakram acrobatics, but it makes for a good show.

A video of her chakram

And that's what a math nerd thinks about over the weekend. More soon!


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MAM Day 8: Time Part II

Today is Boston Partners in Education's big Gala, so this is the downtime I've got to blog before the storm.

I was planning on discussing time zones, the passing of time beyond 24 hours, and how it still relates to math today. This was before I found this website that has lots of information and pretty pictures and animations. I'll include links from various websites because they explain things much better than I do.

I just found another website that documents the history of calendars. It's the first slideshow with information on calendar systems, just click on the pictures to continue through the rest of the history. Documenting time and the rotation of Earth around the sun has been around in many different civilizations. Mathematicians, early scientists and astronomers were able to figure out the best approximation of the Earth's rotation around the sun which is why our current calendars are based around the solar cycle. There are also calendars that are based around the lunar cycle. The Earth's rotation around the sun also causes seasonal differences.

Time zones are necessary because the entire world can't have the same time. If it is 10:30 AM here in Boston, it shouldn't be 10:30 AM in Europe also. The sun's position in relation to a geographic location is how time zones were formed. This website explains time zones pretty well, and this website has large cities and their respective time. You can use this link to convert time. From my blog's statistics, there has been one visitor from Mozambique. With a few clicks I found out that Mozambique is 6 hours ahead of Boston's time, which means that as of right now, it's almost 4:45 pm in Mozambique. I hope they check in again!


One of the things I wanted to discover through today's post was how fast we are traveling around the sun. This website helped answer my question - our rotation on Earth alone is approximately 1000 miles per hour at the equator, and our rotation on Earth around the Sun is approximately 67,000 miles per hour.

The website says we can calculate a more precise estimation of how fast we are moving around earth's axis by multiplying the cosine of Boston's latitude by the speed of rotation at the equator (1000 mph) to get our speed. Why do we have to do this? A person standing on the equator is traveling a different path around the Sun because of the tilt of the Earth.


Don't worry! I did all the math and came up with ~738.95 miles per hour. So in 24 hours, everyone in Boston has traveled ~17734.8 miles around space at over 700 miles per hour! And you didn't even have to go anywhere!

I'm not an astrophysicist so I'm sure my calculations are off. I didn't take into account that because we're rotating around Earth's axis and also around the Sun, the distance we're actually traveling is probably more, but that doesn't matter because I did some math today and I'm fairly satisfied with what I came up with :D Finally, as if my math nerdiness has no bounds, I really appreciated this online calculator.

Some cool space links. I'm always amazed at how cool space is.
Space missions diagram
Rotation of the planets in audio form
NASA's archive of awesome pictures

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Also one of my Fellows at Science Club for Girls sent me this link on the positive effects of mentoring on the mentors! Mentoring leads to "measurable benefits for the volunteers, who showed improved physical activity and health compared with adults of similar age and demographics."

I've found that mentoring makes me happier, I look forward to certain days and the knowledge I will get to see my students. I laugh a lot during tutoring sessions, I get to play games and act like a student again. To top it off, after I started volunteering in the Boston area, I found a job - this job! Volunteering may not pay much (haha), but the benefits are the best!


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MAM Day 4: Math & language

I've thought about the connections between math and language a few times throughout my time at Boston Partners. Working with students, I find this connection quite often when we're doing word problems. I also notice that students don't read the instructions very often. Sure, we're doing math, but they skip the instructions (which always tell you how to approach the problem, what the problem is asking for, and sometimes hints to the solution) and then say "I don't know how to do this."

On one hand, math is universal. Pi is still approximately 3.14159 regardless of what country you are in. Numbers are the same in any language and math algorithms are just that, standard processes for getting certain answers. Multiplying 84 by 2 comes out with the same answer 168 no matter where you are.

However, understanding math word problems depends on knowing the language of math and the common terms that are used in conversation and language. Volume, area, and perimeter mean very specific things, but if students have learned them, they should be able to apply the correct formulas to get the right answer.


I just made up a word problem:
Alex bought a bag of oranges because she needed a dozen oranges to make orange juice. When she opened the bag, she had 5 more oranges than she needed. How many oranges were in the bag Alex bought?

In the problem, there are certain terms that help you figure out what the question is asking, and also some terms that may or may not be common knowledge. "A dozen" is a math term that we often know equals 12. If students don't know what a dozen means, they will probably not know how to figure out this question. "Five more oranges than" signifies she has extra oranges and that you should add 5 to 12 to get the total number of oranges.

This is why when I'm working with students I always emphasize that they read the instructions, either out loud or to themselves before asking me "how do I do this?" questions. If the questions are tricky or involve "intrinsic" terms (like a dozen), I tend to go over the vocabulary that will help the students. I point out or ask "what does 'more than' mean?" to help my students figure out the process for themselves.
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On a different note:

My co-worker Karen and I had a conversation about the Chinese numbering system and how their number and math vocabulary is much easier in Chinese. One of her acquaintances told her they mentally compute in Chinese because it's much more efficient.

Math terms and language are also hidden in everyday conversations. These are just food for thought:

• For example, "he and I" is simple addition! "A, B, C, and D went out last night" is also addition.
  
• I use the phrase "more or less" quite often. "From time to time" is also another math phrase. I would also argue that "often" signifies frequency and is therefore math related.
  
• Greater than / more than / less than
  
• Questions of "How many times?" or "How much?" or "When" are all math related
  
• Pairs of shoes or pants are math related
  
• I've started phrases with "odds are..."
  
• What does it mean to be an "average person?"
  

There are far more examples of the connections between math and language, but I'm done for today. More math tomorrow!


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MAM Day 3: Estimation

Yesterday we talked about counting, which is getting an accurate number. Today I'll briefly talk about estimation, how, when, and where we use it.

My first thought was estimating how many jellybeans are in the jar. Thanks to Wendy, who is the Math Rules! Manager at Boston Partners in Education, we have Easter candy to munch on. Chocolate isn't my favorite, but the jars full of jelly beans are awesome. We've all done it at some point in school or seen it at a fair - guess how much is in the jar. While I don't have any advice for getting the right answer, winning the prize depends on how well you can estimate.

Estimation is using a logical reasoning process to guess at an answer - how many jelly beans, or how much time it will take, or how many people are in the auditorium, or approximately how much food we'll need for an event.

I've used estimation for large scale shopping. My sisters and I used to go thrift shopping on big 50% off sale days and we would have to estimate approximately how much money we spent. I also use estimation when I go grocery shopping. My siblings and I used to play a game where we would 'The Price is Right style' guess the closest total cost without going over. It's a fun estimation game that my family of nerds liked to play. I would suggest you try it out sometime with your friends, family, roommates, and anyone else.

Estimation can also be used in grade school math. Working with elementary students, we haven't gotten to a point where my students use estimation to help them check their answers. We're still very focused on getting the one right answer to the question. I would argue that students need to learn and really understand estimation before we move on to multiplication or division accuracy.

How else are students going to know if they made a mistake on a multi-digit multiplication problem? To multiply 83 x 6, a student could estimate 80 x 6 = 480 and know that their answer should be a little more than 480. It gets harder with more digits. 314 x 57 can be rounded off and estimated at 300 x 60 = 18000. It would help if a student forgot a place value zero, or multiplied wrong to check their answer. If they got an answer in the low thousands, they could realize and start over.


Estimation only works if you're using logic to make an educated guess. Sure, I can estimate there's one million jelly beans in the jar, but it doesn't make sense and I wouldn't have won the prize. Estimation works well within valid reasoning of your guess. I could guess there are three jellybeans in the jar, but that's also a bad estimation.

So I took this jar and asked some of my co-workers how many they thought were in the jar. My supervisor Erin was the closest. Post any guesses or strategies for these types of games! If you feel compelled to share an example of estimation, I will give you a handful of jellybeans as a prize!


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Math Awareness Month is coming!

Did you know that Math Awareness Month has been held in April for the last 24 years? I sure didn't!

Math Awareness Month was started in April 1986 by President Ronald Regean who emphasized that a good math education is crucial for highly skilled professions in the sciences such as "medicine, computer sciences, space exploration, the skilled trades, business, defense, and government." We may forget about how much math we do on a daily basis, but I'm making it my duty to remind you all about how and when we're doing math daily. Suggestions and any ideas are helpful and very appreciated!

This year's Math Awareness Month's theme is Math and Sports! I learned today that a soccer ball is a spherical truncated icosahedron, which has 20 hexagonal sides, and 12 pentagonal sides. Well if a soccer ball is spherical, it doesn't have "sides" but you get what I mean.


Although I don't play sports, I can appreciate the amount of math that goes into sports games. I'll attempt to use my knowledge of math to show you how much math is involved in tennis, basketball, or ice skating. More to come!


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