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.
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