Fantastic Fractions!

This week I am learning about fractions, goodness me there is a lot to learn about fractions! Adding fractions, subtracting fractions, dividing fractions, and multiplying fractions. Are you lost yet? Well let me tell you my mind is circling just thinking about it all. If I am a 26 year old woman with a circling mind I just think about my students, especially those that really struggle with Math. I thought about how easy it can be to show students that adding, subtracting, multiplying, and dividing fractions can be fun and interesting. 

First, let's start with adding fractions, in order to add fractions you have to first find the common denominator and then you will have to change the numerator, by finding how many you multiplied the bottom by and then multiplying that number to the numerator. Once you have your new fractions you can add and then simplify. I know this sounds confusing so let's look at a problem. 

Once we have mastered adding fractions let's try subtracting fractions. You will need to do the same approach as adding fraction with finding the same common denominator and then getting the numerator to be consistent and then subtracting the fractions and then simplifying. Here is a great video to show how to subtract fractions. 

Okay, not so bad right? Now things get a little easier! Let's learn how to multiply fractions, first, you line your fractions up and then you multiply the top and then the bottom and finally simplify. Your probably thinking, "That's it?" Yep! That's it! Here is a great video to show how to multiply fractions. 

Now, last by certainly not least let's learn about dividing fractions. First, line up your fractions, now here is where it gets tricky instead of dividing the fractions you are going to multiply by it's reciprocal, and then simplify. 

This past year I was a Teacher's Aide in Third Grade, and the time that I was able to spend in the classroom helped me see that students love to work with fun technology. In fact when we worked in the computer lab the teacher would often allow the students some time to work on Math games.  Here are some Cool Math Games that students will love and will help them understand more about fractions. Math is fun is also a great site that some of the students really liked, this site has many great other types of Math problems other than fractions. I had to also share this song from the Math is fun link. Singing this to all the students will help them remember the "rules" of the fractions. 

♫ "Multiplying fractions no big problem, Top times top over bottom times bottom,

"Dividing fraction, as easy as pie, Flip the second fraction, then multiply,

"If adding or subtracting is your aim, The bottom numbers must be the same!

"Change the bottom using multiply or divide, But the same to the top must be applied,

"And don't forget to simplify, Before it's time to say goodbye"♫

Positives vs. Negatives

This week in my online Math class I am learning about positive numbers and negative numbers. I can't help but remember when I was growing up and I was learning about these topics as a young student and my dad would try and explain it to me in "his terms" and I was SO confused. I look back on the techniques that he used and they were something that I understand as an adult however, as a young student I was confused out of my mind. My dad was trying to use his terms of a "visual aid" by standing in front of me and pretending to be at a 3 for instance and walking back 5 places and would ask me where I am now. Thinking about this I now know what I will NOT be doing to teach this topic to my students,  instead I will show them real visual aids. The photo that I have below is a line graph, which is one visual aid that I would use in a situation to show students how to add and subtract with positive and negative numbers. 

I was looking for some more resources that would be great to use for students learning about positive and negative numbers and came across a couple websites with games one is pbskids.org and the other is mathisfun.com both are fun and great for students of all ages. 

Students will be learning how to add, subtract, multiply and divide with positive and negative numbers. 

A great "real-life" scenario that would be great for students is a checkbook, I would start by showing the students what a checkbook is and how you can and would use it and then I would give them examples so they have to add and subtract in their very own checkbooks. It will be the students responsibility to keep track of their own checkbooks. 

Least Common Multiple and Greatest Common Factor

This week in Math we are learning about LCM and GCF. What on Earth are they, and what's so significant about them?? Well let me tell you, LCM is the Least Common Multiple, this is the smallest number that a pair or a group of numbers have in common. The Greatest Common Factor is the biggest number that goes into a pair or a group of numbers. This topic was a great review for me, I have learned it before but it has been a while and when I saw the topic come up I instantly had a brain block. I watched some videos that the teacher offered and I also found this video on my own. I think this video would be great for teachers to use for reference and also use if a student is struggling. 

Students love relating Math to the real-world, and I know that I do too. Any time that I can relate real-world with my Math examples I know I am able to help the students "connect the dots." Not only do I like to use real-world examples but I also like to help students "see" the problem, if I can use visual aids in a Math scenario I will. I like to be able to explain something and show something to help students really get what I am teaching. 

Here is a great GCF "real-world" scenario question for students:

Amanda has three pieces of cloth. One piece is 36 inches wide, another piece is 45 inches wide and the last piece is 54 inches wide. She wants to cut all pieces into strips of equal width that are as wide as possible. How wide should she cut the strips? 

Here is a great LCM "real-world" scenario question for students:

Jake runs every 10 days and Cleo every 6  days. Jake and Cleo both ran today. How many days will it be until they run together again?

 Both of the examples that I have given are good ways for students to "visualize" the problems. Students will be able to think about these problems in the future as they work out greatest common factor and least common multiple problems. Like I mentioned before I like to be able to show students problems that relate to the "real-world" and both of these do that. 

Let's Multiply!

This week in my summer Math class we learned new ways to multiply. Have you ever heard of different multiplication techniques other than standard multiplication? Well this week we are learning about four different methods.

• Standard Algorithm (Standard Multiplication)
• Lattice Method which has also been referred to as shadow boxes
• Cluster Method
• Partial Products 

All of these methods provide you with the same answer, however, only Lattice, Cluster, and Partial Products are introduced to students who learn with Everyday Mathematics, which is what most of the schools I've been in use. So how do we calculate these methods? 

Standard Algorithm- This is the method that your mom and dad learned in school, this is the method that schools are not teaching. Why? I am not sure. 
To work this problem the numbers are set up with the smallest amount of digits is on the top. 

Lattice Method- This is a method that I learned when I was in fifth grade. I loved this method, it was easy to me and I was able to do it and get the correct answer, every time. This is set up like a box and then the diagonal line in the middle of each box is where the answer goes.  

Cluster Method- This is a method that I was not familiar with prior to this week. With this method, students are essentially using their own reasoning to figure out with the problems answer is. For example, if the problem was 25 x 13 students would break this down and figure out that 25 x 10 = 250 and then 3 x 25= 75 so 250 + 75 = 325

Partial Products- With this method students learn how to use mental math to calculate the answer. As you can see the problem is calculated with 10 x 8 and 5 x 8 rather than 15 x 8. 

Guessing Correctly

Everyday we use some sort of estimation or as I would like to call, guessing correctly. I use my techniques mainly in the kitchen on a daily basis, especially when I am tying to recreate a recipe of a main course, side dish, or snack that I recently loved. I throw a little of this and a little of that into the bowl and go to work trying to recreate something, sometimes it works out in my favor and others, well let's just say we won't be making that again. 

In general, Math has always been an "easier" topic for me, but this week, in my Math summer course, we are talking about estimation I am finding myself more and more confused and even more frustrated. I can't estimate correctly apparently. I don't know why Math needs to be a topic that is so complex.

The topics that we are discussing this week are on estimation and several different methods, such as, how to use front-end estimation to determine a correct answer for adding or subtracting several numbers together. Front-end estimation is a method used to round down or up to the nearest ones, tens, hundreds, thousands, etc to estimate the correct sum of several numbers.

(A view of front-end estimation)

In the classroom there are several different methods to use when teaching students how to correctly add or subtract several numbers together. Once students understand the whole concept of front-end estimation, it would be a great resource.


http://www.aasd.k12.wi.us/staff/boldtkatherine/MathResources3-6/Math_Rounding&Estimating.htm

Ready or Not, Here We Go!

This week marks the first week of my Summer Math class. I am finding so many things to be going well so far, despite the fact that I am NOT a huge Math fan. A lot of the Math I am working on is a review of what I have already learned. I am feeling confident and good about my start. 

With the beginning of this class I have been watching some new videos and reading some really interesting Math articles. I recently watched a video and learned that in America we often teach students several different ways to learn one topic, which I believe is where students can get frustrated, rather than teaching one way to do something and students mastering that one method and moving on to a new topic. On the flip side of this in China, students learn one way and are able to "master" this technique, maybe the reason that China is so much further than we are? 

As I have been working on Math problems this week I have found myself struggling with the word problems, which require a lot of reading. I have never been a reading fan, and so these problems have been making me find that I need to pay attention more. As I have been working this week I thought it would be fun to find a website that I could share with my students, who also struggle as I do with this topic. As I have been playing around on this website I have found that it would be great for any age, which would be great as a teacher for students who may be struggling or those who are excelling. 

http://www.ixl.com/promo?partner=google&phrase=Search%20-%20math%20problems&gclid=CIDv5oH3wbgCFRSVMgodpCgAig