Day 5 of Fractions....and the students are hanging in there! We only have one basic function left to discuss about fractions...Subtraction! Subtracting fractions is as simple as eating a pizza! If you have three-fourths of a pizza left, and you then eat one-fourth of that three-fourths, three-fourths minus one-fourth is two-fourths...which is true, but we must REDUCE! The answer would be one-half.
Subtracting fractions can be easy; however, what happens when the denominators are not the same?! Luckily, we talked about this idea today, and found out...it is exactly like adding fractions, in that we must find a common denominator by finding the LEAST COMMON MULTIPLE! We must change one or both fractions (top and bottom) in order to have common denominators and then we just Subtract the second one from the first and leave the denominators alone. The least common denominator will be the denominator at the end unless we must reduce!
It has been an exciting week in the world of Mr. Joines as we worked through everyone's favorite concept...FRACTIONS! Next week we will begin looking at Metric conversions, but for now...this blog made me hungry, it must be pizza time! Here's a 20-second video of my likely situation in a few minutes!
http://www.youtube.com/watch?v=Csktxx1OrBU&feature=player_embedded
Wednesday, June 15, 2011
Fractions...Like, What's Common?
Fractions-Day 4! We continued examining our concept of adding fractions today, but the mean, old teacher threw a curve at the students...not all fractions that you add will have the same denominator! After briefly experiencing panic with the room, I quickly explained that we would learn how to solve the problem of unlike denominators TOGETHER! Joy and song broke out throughout the room in anticipation for the task at hand...(dreaming once again)!
When an addition problem has two fractions with unlike denominators, we must compare the denominators and find the LEAST COMMON MULTIPLE! The least common multiple will be our new denominator, but you must adjust each of the fractions individually. Lets say the first fraction had a 3 in the denominator, and the least common multiple we will use is 12. Well to get from 3 to 12, you multiply by 4, so on the top of the fraction you must multiply that number by 4 also, since we already did on the bottom to get that least common multiple. Easy phrase: "WHAT YOU DO TO THE TOP, YOU MUST DO TO THE BOTTOM." You will do something similar for the second fraction to come up with an equivalent fraction to what was there before, except now it must have the common denominator. With practice you might just feel like this cartoon, and I know everyone can get there!
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When an addition problem has two fractions with unlike denominators, we must compare the denominators and find the LEAST COMMON MULTIPLE! The least common multiple will be our new denominator, but you must adjust each of the fractions individually. Lets say the first fraction had a 3 in the denominator, and the least common multiple we will use is 12. Well to get from 3 to 12, you multiply by 4, so on the top of the fraction you must multiply that number by 4 also, since we already did on the bottom to get that least common multiple. Easy phrase: "WHAT YOU DO TO THE TOP, YOU MUST DO TO THE BOTTOM." You will do something similar for the second fraction to come up with an equivalent fraction to what was there before, except now it must have the common denominator. With practice you might just feel like this cartoon, and I know everyone can get there!
Fractions...Common Addition
Day 3 of our exciting exploration of fractions! Today's new idea, adding fractions! Addition is entirely different than multiplying and dividing fractions, and requires a much slower pace for students to understand. When you add fractions you must have a common denominator, which for convenience purposes and because we want to start with the basics, every single problem already had today!
If the fractions you are adding together have a common denominator already, then you add the numerators (the top numbers) and leave the common denominator (the bottom number) as whatever number it was. Do not add the denominators together! One concept does still apply today from the other two days....at the end of the problem we must still make sure it is REDUCED! Also, I am so very thankful that no one in my class has experienced this feeling...because everyone is still exciting over FRACTIONS!
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If the fractions you are adding together have a common denominator already, then you add the numerators (the top numbers) and leave the common denominator (the bottom number) as whatever number it was. Do not add the denominators together! One concept does still apply today from the other two days....at the end of the problem we must still make sure it is REDUCED! Also, I am so very thankful that no one in my class has experienced this feeling...because everyone is still exciting over FRACTIONS!
Fractions...Divide to get Bigger?!
Welcome to a review of Day 2 with fractions! This time we experienced dividing a fraction by a fraction. We took the information we gained from yesterday's class and now we have added in the dividing aspects and left everything else the same! When you divide a fraction by a fraction they simply need to remember to "flip the second one and multiply!" Nothing too crazy, because everything else remains the same as yesterday after that! I have provided two examples for you as a visual reminder in case your child is struggling and might need some extra help. The first is multiplying straight across and the second is using the cross-cancel method. If you click on the picture it will appear in a separate screen.
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At the end of the problem what should we always check...............that the fraction is REDUCED fully!
When we divide fractions the answer will sometimes get bigger! Just like the second example...why? Because when you have a set amount of something and then divide that amount into several pieces that are a smaller than the original, you now have more pieces than you started with!
When we divide fractions the answer will sometimes get bigger! Just like the second example...why? Because when you have a set amount of something and then divide that amount into several pieces that are a smaller than the original, you now have more pieces than you started with!
Fractions...Multiplying the Ease
Today we began discussing fractions in class! Fractions are always a topic that students can't wait to experience, because they bring so much joy to people everywhere! Well alright, maybe that is the hopeful math teacher in me that wants it to be fun for every student, but I have the right to dream!
Today we started simple, with multiplying them. The lesson today was quite possibly the greatest that the world has ever experienced on multiplying fractions...in fact to prove my point, why don't you ask your child this question, "What are the two ways to multiply fractions?" They should be able to answer that question with "straight across or cross-cancel!" Hopefully, they say it with the enthusiasm, because that is the basic idea they need to know! Please remind your child that they must REDUCE the fraction at the end, unless they cross-cancel fully. Either way, they should check to ensure they entirely finished the problem. Well this was day one of fractions and the excitement is probably going to prevent them from getting any quality sleep tonight, as they are anxious for tomorrow's class!
Today we started simple, with multiplying them. The lesson today was quite possibly the greatest that the world has ever experienced on multiplying fractions...in fact to prove my point, why don't you ask your child this question, "What are the two ways to multiply fractions?" They should be able to answer that question with "straight across or cross-cancel!" Hopefully, they say it with the enthusiasm, because that is the basic idea they need to know! Please remind your child that they must REDUCE the fraction at the end, unless they cross-cancel fully. Either way, they should check to ensure they entirely finished the problem. Well this was day one of fractions and the excitement is probably going to prevent them from getting any quality sleep tonight, as they are anxious for tomorrow's class!
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