When it comes to prime numbers I ask myself, who comes up with these numbers? At first look, they are just numbers, but what really makes them prime numbers? By definition, a prime number is one that can only be divided by one, and itself, everything else is a composite number. How did mathematicians figure this out? Is there a pattern?
Come to find out, there is a pattern! A Greek man named Eratasthenes, studied mathematics over 2000 years ago came up with a model that is called the Sieve of Eratosthenes. Essentially, it takes the first prime number, 2, and then crossed off every 2nd number from there on out. The next prime number is 3 so, he crossed out every 3rd number and continued that pattern with each prime number. All the numbers he was crossing out were composite numbers. He was making a sieve that drains out composite numbers and leaves prime numbers behind. Is this not crazy? I'm just amazed on how this works.
The question you always hear from a student in class is, why are prime numbers important? Is there any use for them outside of math? You bet there is a use for them and I bet you didn't even know it. Large prime numbers are used in RSA cryptographs for sending secret information like your credit card over the internet. The first step is to take 2 large prime numbers, multiply them together and their product is what is what makes factoring out the prime number difficult. Watch the video and try and follow along, it's pretty complicated after the first step I just explained but well worth the view.
July 21, 2011
July 19, 2011
1510 Divisible Numbers
Who says you can't teach an old dog new tricks? With the amount of math classes I've taken over the years, I've never been taught some of the shortcuts that are out there for testing number divisibility. I was blown away by how easy this process is. Any textbook out there will refer to them as rules of divisibility, but I still like to call them shortcuts because of how easy it just made my life...too bad it took 30+ years.
The "rules" state, a number is divisible when you can divide one number by another and the result is a whole number. Now, for every number 1-12, there is a special rule that follows it and I encourage you to take a look at these tricks. It's almost freaky how this works out and it makes you wonder how someone figured this out. Knowing these tricks, rules, or shortcuts can really make reducing numbers or fractions a breeze. I can't tell you how long I would spend punching each number into the calculator to see if it was divisible or not. Now, I've made a little cheat sheet with all the rules on it that I keep with my math work and just refer to it when I need it.
Students will be able to memorize 2, 5, and 10 with no problems because they are easily recognizable, but what about 3 or 9? Here is a video that might help them out.
I aspire to be this teacher in a couple of years. If I can rap, I can get my students to learn the divisibility rules, or shortcuts!
The "rules" state, a number is divisible when you can divide one number by another and the result is a whole number. Now, for every number 1-12, there is a special rule that follows it and I encourage you to take a look at these tricks. It's almost freaky how this works out and it makes you wonder how someone figured this out. Knowing these tricks, rules, or shortcuts can really make reducing numbers or fractions a breeze. I can't tell you how long I would spend punching each number into the calculator to see if it was divisible or not. Now, I've made a little cheat sheet with all the rules on it that I keep with my math work and just refer to it when I need it.
Students will be able to memorize 2, 5, and 10 with no problems because they are easily recognizable, but what about 3 or 9? Here is a video that might help them out.
I aspire to be this teacher in a couple of years. If I can rap, I can get my students to learn the divisibility rules, or shortcuts!
July 18, 2011
1512 -Looney Toons
For students, math may become boring and stagnant so, how do we, as teachers, make math more fun? How about having students make a cartoon about their favorite math problem? Inspiring students to be creative and artistic in math class is not a common practice, but with this exercise you can combine art, language arts, and math all into one.
The idea in creating a cartoon for math is to help the student understand the different concepts better. Any time you do a project, there is a better comprehension of the material because the student has researched all the finite details about it. When you combine that with your math concepts, students will walk away learning more about what the teacher intended.
Creating a cartoon is a relatively simple task. Toon Doo and Go Animate are two websites in which you can create and publish your work on the internet for free. They are simple and easy to use while still allowing creative minds to prosper.
The idea in creating a cartoon for math is to help the student understand the different concepts better. Any time you do a project, there is a better comprehension of the material because the student has researched all the finite details about it. When you combine that with your math concepts, students will walk away learning more about what the teacher intended.
Creating a cartoon is a relatively simple task. Toon Doo and Go Animate are two websites in which you can create and publish your work on the internet for free. They are simple and easy to use while still allowing creative minds to prosper.
1512 Measurement labels
How important is it to label you work? Labels come all different forms, how many times have you forgot to put your name on homework? Your name is a label, but we usually use labels as a way to measure figures precisely. When we look at any figure we want to measure, we need to know what we are looking at and what the the numbers represent. Are they cm, inches, feet, meters, or miles? This is extremely important for two reasons. One, anytime a figure is represented, it has to be legible to someone else so, they can interpret it just as the author did and two, the labels provide a framework for conversions.
Converting can become difficult if labels are missed or forgotten. Most times this leads to either a miss label or a mistake in your calculations. Think about when you try and kill all those pesky dandelions in your yard. How do you figure out how much product to put in your hand sprayer? Most homeowners will go and buy a premixed product because they don't know how to figure it out. The product label may say, spray at 2.5oz/1000ft2. What does that mean? That is the rate at which you mix your product with water, So, first you need to figure out how much your hand sprayer sprays out. That will give you your square footage and then you figure how much product is equivalent to the rate at which your sprayer puts out. Rather simple, but what if your were spraying a golf course? Your hand sprayer would take long time so you would use a much bigger sprayer and your conversions would be in gallons and ounces. When the process of converting gets longer that two steps, that is where most mistakes are made because of mislabeling.
Converting can become difficult if labels are missed or forgotten. Most times this leads to either a miss label or a mistake in your calculations. Think about when you try and kill all those pesky dandelions in your yard. How do you figure out how much product to put in your hand sprayer? Most homeowners will go and buy a premixed product because they don't know how to figure it out. The product label may say, spray at 2.5oz/1000ft2. What does that mean? That is the rate at which you mix your product with water, So, first you need to figure out how much your hand sprayer sprays out. That will give you your square footage and then you figure how much product is equivalent to the rate at which your sprayer puts out. Rather simple, but what if your were spraying a golf course? Your hand sprayer would take long time so you would use a much bigger sprayer and your conversions would be in gallons and ounces. When the process of converting gets longer that two steps, that is where most mistakes are made because of mislabeling.
1512 Geometry and Tessellations
I've always enjoyed doing geometry and I'm amazed by how geometry surrounds us everywhere. I really enjoy the process of figuring out an answer rather than just plugging in numbers into something. One thing that has sparked my interest, that I wasn't really aware of before, are tessellations. I've never really put much thought into them, but I think they are really neat on how they work out.
Think of the last puzzle you put together, that is a tessellation. A tessellation is when you put together geometric shapes, so that when you are finished there are no gaps in between each shape. Now, that is a very basic definition and not too mathematical so, we must have some rules for a regular mathematical tessellations to exist.
1. Tessellations must be a geometric figure that fits together without gaps or overlaps and covers an infinite plane.
2. The geometric figures must be regular polygons and the same.
3. The vertex must look the same.
Equilateral triangles, squares, and hexagons are all great examples of regular tessellations, but you can combine different regular tessellation shapes to make a semi-regular tessellation.
Wait a second, I've seen this before. This looks like when you tile a floor or a shower. Who knew this was a tessellation? Now that I'm aware of them, I started noticing them more and more in everyday life, like on this McDonald's commercial. Again, geometry surrounds us in so many ways. I found a great educational website that allows students to create their own semi-tessellations.
Think of the last puzzle you put together, that is a tessellation. A tessellation is when you put together geometric shapes, so that when you are finished there are no gaps in between each shape. Now, that is a very basic definition and not too mathematical so, we must have some rules for a regular mathematical tessellations to exist.
1. Tessellations must be a geometric figure that fits together without gaps or overlaps and covers an infinite plane.
Wait a second, I've seen this before. This looks like when you tile a floor or a shower. Who knew this was a tessellation? Now that I'm aware of them, I started noticing them more and more in everyday life, like on this McDonald's commercial. Again, geometry surrounds us in so many ways. I found a great educational website that allows students to create their own semi-tessellations.
July 11, 2011
1510 - Working with Manipulatives
With so many different manipulatives available on the internet, how do you choose which ones are the best? You Tube is always my first stop shop for help as they provide countless video options for all ages to to explore. This is where I start, and it's pretty reliable. Yes, there is some non-factual videos on there, but for the most part, you can find what you need. Here is one on using math manipulatives for teaching addition, subtraction, multiplication and division. As you can see, it's done very professionally and looks legit. So, are there better options on the internet that are more reliable? You betcha.
The National Library of Virtual Manipulatives is another great place to start in your search. This site is grade specific and covers multiple topics. As a teacher, this is an absolute bookmark for future references. If you ever get stuck or have a student you need to help, but you are unsure of how to help them, this site can help.
If you're not convinced manipulatives can help you teach, read this article from Marylin Burns, who is a creator of manipulatives for over 30 years. She gives great perspective on their effective use and how to implement then into your classroom. My favorite is how she allows parents to get their hands on them too, as it's important for parents to understand why children are using the material.
When looking for the best place, do your research and check them out, talk to other teachers or parents to see if they have had a positive experience with one over another. Remember, if it looks too good to be true, it probably is.
The National Library of Virtual Manipulatives is another great place to start in your search. This site is grade specific and covers multiple topics. As a teacher, this is an absolute bookmark for future references. If you ever get stuck or have a student you need to help, but you are unsure of how to help them, this site can help.
If you're not convinced manipulatives can help you teach, read this article from Marylin Burns, who is a creator of manipulatives for over 30 years. She gives great perspective on their effective use and how to implement then into your classroom. My favorite is how she allows parents to get their hands on them too, as it's important for parents to understand why children are using the material.
When looking for the best place, do your research and check them out, talk to other teachers or parents to see if they have had a positive experience with one over another. Remember, if it looks too good to be true, it probably is.
July 4, 2011
1512 - Gee, I'm a Tree
What did the acorn say when he grew up? Geometry!
It gets me every time. How about this one,
What do you call a crushed angle? A rectangle.I have plenty more, check them out.
One way to help us remember important things is to somehow relate the information we want to know to something that matters to us. A joke, silly saying, or even music are perfect examples of how, we as teachers, can help our students remember important information for years to come. For example, when I think of a angles and the terms acute and obtuse, which one is which? Here is a simple joke that will help you keep them straight. What to you call an angle that is adorable? Acute. Now, when I picture an acute angle, I think of something that is adorable and adorable things are small and cute. Where as obtuse is big and fat like obese.
Music is another great tool for memorization. I still remember when I was in grade school and we were learning about all the states in the U. S.. We were told the first day we started this lesson that by the end of this month, we will have all the name of the states memorized. WHAT? I thought for sure there was no way for me to memorize all 50 states, but we teamed up with our music teacher and he made a song for us to sing that named all 50 states alphabetically. 25 years later, I can still sing that song.
The "Are You Smarter Than a 5th Grader?' T.V. show is a perfect example of how some of our most basic knowledge is lost over the years because we fail to utilize it on a daily basis. State standards are set in place for students to know certain information at a given time in their academic careers, but how do we get the students to retain this information year after year? Hopefully, through some crazy jokes and educational music, students will be able to always retrieve information when they need it.
June 30, 2011
1510 Funny Math
As silly as it sounds, math can be funny, literally and figuratively. This week's video assignments caused a chuckle on my part with an easy way to multiply large numbers. I was hooked, I'm always looking for a way to make short cuts or make life easier. Like the old saying goes, "work smarter, not harder." The first video here shows two rather large numbers that will be multiplied together in "an easy way." Take a look.
At first, I thought it was going to show me the lattice method of multiplication when they started drawing the boxes, but I soon realized there wasn't enough boxes for all the place values correlated to the numbers shown. When it started to look like a calculator I thought, O.K. Where are they going with this? Well, the fast and easy way to multiply two large numbers together is, use a calculator. Awe, you got me! I'll be sure to use a calculator on big numbers.
This was an example of how math can be funny literally, but how can it be funny figuratively? As we all have experienced the ups and downs of math, we know our mind can play funny tricks on us or we make mistakes with simple addition. The Abbott and Castello video proved how easy it is for us to interpret math in different ways. Each way should have the same outcome or answer, but sometimes we have to look at the process of how we arrived at the answer to really understand what we are doing wrong or correct. With 28 donuts and seven officers to feed, like in this video, the simple answer for all of us is, four donuts per officer. Not for the baker though, in his mind, there were 13 donuts for seven officers. When he went to prove it, he showed us three different ways in which he came up with the answer. The crazy thing was, they all made sense if you looked at how he arrived at the answer and didn't understand the basics of math.
That brings me to my main point, each student has their own perceived knowledge on math concepts. They may be right or need some work with it, but this is what makes math funny figuratively. The craziness of our minds and how we think rationally to arrive at answers are sometimes goofy. When we understand the math concepts though, now our rational thinking is the correct way of thinking and we arrive at the correct answer. In the end, teachers need to remember to make math simple for students to understand and it's O.K. to laugh at ourselves, litterally
At first, I thought it was going to show me the lattice method of multiplication when they started drawing the boxes, but I soon realized there wasn't enough boxes for all the place values correlated to the numbers shown. When it started to look like a calculator I thought, O.K. Where are they going with this? Well, the fast and easy way to multiply two large numbers together is, use a calculator. Awe, you got me! I'll be sure to use a calculator on big numbers.
This was an example of how math can be funny literally, but how can it be funny figuratively? As we all have experienced the ups and downs of math, we know our mind can play funny tricks on us or we make mistakes with simple addition. The Abbott and Castello video proved how easy it is for us to interpret math in different ways. Each way should have the same outcome or answer, but sometimes we have to look at the process of how we arrived at the answer to really understand what we are doing wrong or correct. With 28 donuts and seven officers to feed, like in this video, the simple answer for all of us is, four donuts per officer. Not for the baker though, in his mind, there were 13 donuts for seven officers. When he went to prove it, he showed us three different ways in which he came up with the answer. The crazy thing was, they all made sense if you looked at how he arrived at the answer and didn't understand the basics of math.
That brings me to my main point, each student has their own perceived knowledge on math concepts. They may be right or need some work with it, but this is what makes math funny figuratively. The craziness of our minds and how we think rationally to arrive at answers are sometimes goofy. When we understand the math concepts though, now our rational thinking is the correct way of thinking and we arrive at the correct answer. In the end, teachers need to remember to make math simple for students to understand and it's O.K. to laugh at ourselves, litterally
June 20, 2011
Statistical Excitement- 1512 post #1
This week, we jump right into analyzing numbers. Yippee! I have a love/hate relationship when it comes to doing statistics. I love getting the answer right, I love the process of doing a problem, I just hate punching in all the numbers into a calculator or rearranging them in ascending order. I don't have patience for tedious work. Which is kind of funny if you think about it, my goal is to become a teacher and that has plenty of tedious work associated with it. Doing tedious work, and doing it well will make me successful as a teacher, I just have to remember how important it is to do. My love/hate relationship has more of a positive correlation towards love compared to hate as I receive a lot of satisfaction out of putting all the pieces of a problem together.
I remember taking a course in college on statistics and having some fun with it. Though, I always had trouble keeping straight the definitions of the mean and median. These are the nuts and bolts of statistics and I would keep mixing the two of them up. It took me for awhile before I came up with this great reminder for myself, just think of the middle of the road. What do you see in the middle of the road? The median, so your middle value of a set, is the median. This is something I never forgot over the years and it came in handy for this weeks' homework.
What do all these answers mean though? That is where statistics becomes fun. With statistics, you can really make the numbers look more in your favor when the odds may be against you. I always enjoy the campaign season when the news will project who is leading in the polls. There is always a discrepancy between each news outlet and who they figure is leading in the polls. That is why it is always important to look closely at the legend of any graph to ensure you know what data you are receiving.
I remember taking a course in college on statistics and having some fun with it. Though, I always had trouble keeping straight the definitions of the mean and median. These are the nuts and bolts of statistics and I would keep mixing the two of them up. It took me for awhile before I came up with this great reminder for myself, just think of the middle of the road. What do you see in the middle of the road? The median, so your middle value of a set, is the median. This is something I never forgot over the years and it came in handy for this weeks' homework.
What do all these answers mean though? That is where statistics becomes fun. With statistics, you can really make the numbers look more in your favor when the odds may be against you. I always enjoy the campaign season when the news will project who is leading in the polls. There is always a discrepancy between each news outlet and who they figure is leading in the polls. That is why it is always important to look closely at the legend of any graph to ensure you know what data you are receiving.
June 17, 2011
1510 Week 2 post - Base 10
The bases are loaded and with this weeks reading about 3rd graders learning about pace value, we as teachers are striking out with our at-bat in teaching them this material. Place value, as simple as it sounds, is very confusing to students because they don't understand the value of numbers more than 0-9. I can see how this is confusing to a student, you are taught at a young age all about your 10 fingers and there isn't much emphasis put on what you do after that. The number 10 is held in high regards and is like this magic number that we never go above. So, with a number like l5, students don't recognize the place value and that there is a tens and ones position. A number as simple as 15 is looked at as a 1 and a 5, not as 10 and 5.
The one thing our Hindu-Arabic number system has going for itself is that is is very quick to use, especially when you want to write out a number. It's just not as easy to understand for new learners. Looking at the Mayan and Egyptian numbering systems, they use symbols to illustrate their numbers. This proves to be very easy for learners to assign symbols with the place value because they aren't all the same like with the Hindu-Arabic, 0-9 numbering system.
Pictures are always more fun to draw than numbers, but with the Egyptian and Mayan number system, you have to draw a lot of pictures or symbols to compose a number like 528. As great of an artist that I think I am, I would still try and short had some of the symbols when trying to solving a math problem in one of these systems. These systems look to be great for learning, but not practical in their use in everyday society.
The one thing our Hindu-Arabic number system has going for itself is that is is very quick to use, especially when you want to write out a number. It's just not as easy to understand for new learners. Looking at the Mayan and Egyptian numbering systems, they use symbols to illustrate their numbers. This proves to be very easy for learners to assign symbols with the place value because they aren't all the same like with the Hindu-Arabic, 0-9 numbering system.
Pictures are always more fun to draw than numbers, but with the Egyptian and Mayan number system, you have to draw a lot of pictures or symbols to compose a number like 528. As great of an artist that I think I am, I would still try and short had some of the symbols when trying to solving a math problem in one of these systems. These systems look to be great for learning, but not practical in their use in everyday society.
June 15, 2011
Hey, Ho, Let's Go! - General Information
Here we go, I'm diving head first into school again and there is no easing into it, I'm going pedal to the metal, full speed ahead. What have I got myself into? It's been 10 years since I last picked-up a book and now I'm looking at 10 credits. How will I do this, especially during the summer? I want to be on the boat soaking up the sun and swimming in the water. The end goal of becoming a teacher is pushing me to accomplish these classes so I can still enjoy my summers.
Last week, I attempted to do my math assignment and all of a sudden I realized I couldn't remember how to divide fractions. What was I doing wrong? I was bound to figure this out on my own because I knew how to do it, I just couldn't remember. I was too stubborn to look it up in the book, or ask someone for help, so I spent over 45 minutes on one problem. Are you kidding me? 45 minutes? This can't go on, I have to figure this out because my time is too valuable (and the sun was getting warmer). So, I broke down and consulted Mr. You Tube. He fixed my problem and within 2 minutes, I was on my way. Lesson learned I guess.
So, here we are. Week 2 and we're looking at doing a blog for math class. How do I keep this interesting enough for people to continually read it? We are talking about math here. This is what I need to figure out, not only for this assignment, but as a teacher too. How do I keep you engaged and wanting to come back for more? The good news is, some of you have to check-out my blog and for you, I will try and put a smile on your face. I'm excited to I accept this challenge.
Last week, I attempted to do my math assignment and all of a sudden I realized I couldn't remember how to divide fractions. What was I doing wrong? I was bound to figure this out on my own because I knew how to do it, I just couldn't remember. I was too stubborn to look it up in the book, or ask someone for help, so I spent over 45 minutes on one problem. Are you kidding me? 45 minutes? This can't go on, I have to figure this out because my time is too valuable (and the sun was getting warmer). So, I broke down and consulted Mr. You Tube. He fixed my problem and within 2 minutes, I was on my way. Lesson learned I guess.
So, here we are. Week 2 and we're looking at doing a blog for math class. How do I keep this interesting enough for people to continually read it? We are talking about math here. This is what I need to figure out, not only for this assignment, but as a teacher too. How do I keep you engaged and wanting to come back for more? The good news is, some of you have to check-out my blog and for you, I will try and put a smile on your face. I'm excited to I accept this challenge.
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