What's more fun than a barrel of monkeys? Solving equations using order of operations!

     Please Excuse My Dear Aunt Sally! Actually, there is no "Aunt Sally" but you'll wish there was so you could thank her for making your math troubles vanish into thin air. This is a mnemonic device which will help you solve all your tricky order of operations math conundrums. So how does it help? Glad you asked.
P lease- Parentheses
E xcuse- Exponents
M y- Multiplication
D ear- Division
A unt- Addition
S ally- Subtraction
     These are the steps you will use in this particular order to solve a problem when there are multiple operations to be used within a problem. If you do not use "PEMDAS" you will without doubt come to the wrong solution to your problem. Using PEMDAS, you will solve 3+2x3=? with the correct answer of 6. If you solve left to right as when reading, you will get the wrong answer of 15.
     And with that, prepare to dazzle and amaze your friends at parties and special events.
Let's say we have to solve this mysterious problem:
(3+4)-(7-3x2)=?
Well, we solve parentheses first.
(3+4)=7
But what about (7-3x2)
Ok, we solve the multiplication part before the subtraction part like so:
3x2=6
Now we have
7-6=1
That leaves us with the simplified problem of
7-1=6
Ta da! Thank you, you've been a great audience. I'll be here all week.

What?!? You're ready to try? Alright, have at it!

ROCKIN' MATH GAME ---> Math Frog Order of Operations game
KILLER ORDER OF OPERATIONS VIDEO  ----->

Embarassed old lady photo: Corbis Photos Add to Lightbox RF Royalty Free

Fractions are Fun!

Photo: http://www.imaginativeteacher.com/Fractions_ebook.html

Fractions are everywhere, from cooking, to time telling. But sometimes understanding fractions can be a difficult concept to grasp, especially when it's listed so abstractly such as with numbers. I found a cute game on PBS kids, Melvin's Make-a-Match, which asks kids to pick two bottles off the shelf that match; one having the fraction listed numerically, the other depicted with a pie style diagram. What I like so much about this game, is that kids get to see the fraction listed both numerically and as a picture, hence the fraction is no longer abstract, but pulled into focus and visually tangible.
FUN GAME ----> Melvin's Make-a Match

So what is a fraction anyway? It represents a portion of a whole. Let's say I have 3 quarters out of a dollar. We can write this a few ways but they all mean the same thing.
                                     75             3        
                                     ----    =     ----
                                     100           4         

They are both equal. Why? A quarter equals .25 and a dollar equals 1.00. We have 3 .25 quarters. .25x3=.75 so we have .75 out of 1.00. Also, there are 4 quarters in a dollar, and we already have 3 of the 4. Therefore, 75/100=3/4!

Can't get enough? Want more? Here's a nice little source for all your fraction needs: Fraction Lessons

One valuable lesson I'll take away with me from my Math for Elementary Teachers class is to not underestimate the importance of visual aides. My classroom will most likely be loaded with them as you never know which visual or musical aid may reach which student. While the school district may assign the curriculum and tell me what and which methods they'd like me to teach primarily, how can I help but offer alternatives? Could this not put a new spin on the lesson or perhaps reinforce what has been taught and learned? I look forward to Fall 2013 when I will be able to have my own classroom with 20 pairs of wide little eyes looking at me with the whole world in front of them. I look forward to learning right along with them.

Funny Math Song

     I thought this was a pretty cute song to spark children's interest and awareness of math in daily life and points out places where they can witness math in action, such as bouncing a ball off a wall, folding a sheet, or using measurements in cookbooks. I know when I was younger, I struggled to find the daily relevance of math and why exactly it applied to me.
     I think its so important to use any media available to engage kids in learning and a catchy little math tune might be the trick to reach those kids that math just isn't clicking for. By pointing out the fact we are surrounded by math, perhaps they'll start seeing things a little differently and that little light bulb may turn on when they least expect it.
FUNNY MATH SONG!-----> "Math Song" http://www.youtube.com/watch?v=ZPMRA4yFeeM

Math's Uniting Powers

"A yupana (Quechua for "counting tool") is a calculator that was used by the Incas. Researchers believe that calculations were based on Fibonacci numbers to minimize the number of necessary grains per field.^[1]"


The Fibonacci Sequence is really an elegant pattern building upon itself by adding a given number to it's preceding number in the sequence. The sequence can begin with any number but generally beginning with 0, 1, 1. 0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8 and so on and so forth creating the pattern 1, 1, 2, 3, 5, 8, 13, 21...

BEAUTIFUL FIBONACCI VIDEO -----> The Fibonacci Sequence

 It is amazing to me how math is the undisputed universal language, tying together different cultures, periods in history that are hundreds, even thousands of years apart, varying levels of technological sophistication and advancements, as well as the enduring quest of humankind for understanding of the order of things. To think that the Fibonacci sequence is found naturally occurring in places such as the makeup of nautilus shells and  petal organization of flowers, and was recognized and mastered by humans is, to me, a testament to the importance of mathematics and it's influence of the world both around us and in us.

Photo and quote found on Wikipedia from http://www.quipus.it/english/Andean%20Calculators.pdf Holder of the copyright grants permission for use by anyone as it is released into public domain.

Video found on YouTube

Photo on file from Wikipedia Commons.

Early Counting Systems

While going over my notes regarding early counting systems, I was really amazed how many symbols it took to notate numbers in some societies. I was wondering how in the world people managed to put up with it as long as they probably did, being that so many symbols were needed to be used. As I got a little further in my notes, I came to the section regarding the reading and writing of numbers. For example, to write out in long hand 32,157, one would have to write Thirty-two thousand, one-hundred fifty-seven. That's 41 characters, including hyphens and commas. I was a little hard on the Egyptians for having notated it such as they had(I use symbol substitution) ###$$%^^^^^&&&&&&&. That's only 18 characters. Now, luckily we have our universal numeric system in place to save us the time of writing numbers out long hand, but it just struck me that if we didn't have that luxury, perhaps the Egyptian system would look mighty quick and convenient.
COOL COUNTING VIDEO -----> Egyptian couting simmilar to modern computer's computation?

                                                                             


While on the subject of ancient counting systems, I looked up Mayan counting systems. I have always been facinated by the Mayan society and have taken a lot of Cultural Anthropology classes which delt with the numeric system, but this video really gets in depth dealing with the organizing into the different placecolumns relating to the base 60 table used. It's pretty fast paced, but it's a good visual as to how Mayans counted using a physical representation of the items counted using beans and a grooved clay tablet.
MORE COOL COUNTING---->Mayan Abacus

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Sesame Street Introduction to Venn Diagram Concept

     So you are bored and have a few hours to kill. What to do, what to do? Practice your organizational and classification skills and make some sweet Venn Diagrams! But say you want to organize more than your A's and B's. Perhaps you need to sort your sticker collection into red stickers and star stickers. Your stickers that are red will go one one side, your stickers that are stars will go on the others. But wait, you have a red star sticker, what side should it go on? The middle section of course because it shares BOTH characteristics. Uh oh, where do you put your green heart sticker? Because it is neither red nor a star, it can't go inside the diagram, so it must go outside. And presto, there you have a pristinely organized sticker collection highlighting both your red stickers and star stickers!

     Here is a game my son really enjoyed a lot. While it doesn't have the overlapping section of a true Venn Diagram, I think it's a good introduction to the concept. Sesame Street character Zoe asks children to sort animals based on color, size, and tail and ear length.
     The game encourages children to focus on one specific characteristic at a time while ignoring others. It's a simple game, but a great start to sorting and organizing in a fun, entertaining way which really engages children to continue to further levels.
GAME! -----> Zoe's Pet Shelter, Introducing Venn Diagrams

Photo attributions: Weisstein, Eric W. "Venn Diagram." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/VennDiagram.html
Image Source Page: http://www.kindergartenkindergarten.com/math-problem-solving/

A Math Blog?

     I was really unsure of what to expect from my new math class; it's been about twelve years since my last math class, which had been right here in Bodie Hall back in 1998. Would I be able to follow along? Could I hold my attention on math for almost three hours? I have classmates in my university class who have been in a Math for Elementary Teachers class and I've heard mixed reviews; it's fun, it's hard, it's easy. So, I had no choice but to walk in with an open mind. So what did I think? Turns out, elementary kids are smart! This is kind of tricky! But, wow, I'm surprised how much of the math knowledge I had collecting dust and completely unused in the back of my brain for all those years was returning to me and FINALLY clicking! As I sit in class, it's really hitting home the importance of mastering different ways to solve and teach a problem to my future students. My teachers throughout the years would answer, "because that is how we do it" when I would ask, "but why?"

     Because of my loathing of math as a young student, I owe it to my future students to not impose the same feelings upon them by lacking a well-rounded knowledge of math and how to effectively teach it to them. As a result of this pact I have with them, I have taken more notes than my previous twelve years of math class notes combined. Who knows, maybe through the benefit of my aging and maturing as a student, this will be the time I not only learn math but understand the how and why of math. Anything is possible I guess; after all I never would have guessed I'd have a math blog.

Image Source Page: http://www.moremarin.com/.a/6a00e55001eaef88340120a6a8d498970c-popup