When we were asked why the numbers we chose were fractions, I tried to create a general definition that could be applied to every fraction. There is a numerator (the number on the top), a denominator (the number on the bottom), and a line between the two. This seemed to be the general definition for most students in the class.
However, most of the fractions created in the class were different. I started to notice that some students had created fractions that were a lot different than the one I created. The lesson then progressed into the types of fractions.
The first type of fraction that we looked at is called the Proper Faction. This fraction equals less than one. The fraction 3/4 is an example of a proper fraction.
Another type of fraction is the Mixed Numbers Fraction. This fraction equals more than 1. The fraction 1 and 2/4 is an example of a mixed numbers fraction.
The third type of fraction is called a Unit Fraction. This fraction is similar to the proper fraction as it equals less than 1. The difference is that the numerator is the number one.
One of the tools used to teach us about fractions is a book called "The Hersey's Milk Chocolate Fractions Book". This book uses a Hersey's milk chocolate bar as a manipulative to help students grapple with the understanding of fractions. Each table was given a Hersey's chocolate bar and was asked to break up the bar into twelve pieces. One of the reasons why I really liked this activity is because I think it will be effective with Junior/Intermediate students. Most students, if not all, know what a chocolate bar is and dividing it into twelve can help them understand how a portion of something (such as the chocolate bar) can be represented by a fraction. As the book was read to us, we were asked to group the chocolate in several ways that represented fractions. The book also uses pictures to help demonstrate how the chocolate pieces should be divided.It was also beneficial to understanding fractions when we were asked to fill out a graphic organizer on fractions. This organizer was a chart we had to fill in that helped us to define what a fraction is and give examples and non-examples of fractions. This chart could be filled out by students as an activity either before they are introduced to fractions or after they are taught. It can be used to help the teacher understand what students think of when asked to define a fraction and guide students.
I can see the various manipulatives used in class being extremely beneficial to teaching students about fractions. While the chocolate bar and book are extremely helpful, we were also given various shapes, egg cartons, and several informative sheets that broke down fractions. As I continue this class, one of the key elements that I am noticing is the use of several manipulatives. One type of activity may help some students to understand what a fraction is, but others may need a different manipulative to help them. Activities that engage students and promote collaboration is another important element to teaching. The Hersey's chocolate bar activity allowed us to work in groups and got us excited. The presentations that followed the lesson also promoted the use of manipulatives and collaboration amongst students.
Hi Brandon,
ReplyDeleteGreat post this week! You highlighted some key concepts that I picked up as well from this weeks math class. I liked how you summarized what we did at the start of class. Stating how everyone had to come up with a fraction and every student had a different answer. However, when we all came together we had a similar definition of what a fraction is. It's interesting how some students did proper, improper or mixed fractions yet we all had a similar definition of what makes up a fraction. I like how you provided examples an definitions of the different types of fractions students work with. As well, you noted the Hershey's chocolate book of fractions. I think this was a real hit within our classroom and I agree with you in thinking that junior/intermediate students would love this. Furthermore, you highlighted the use of a graphic organizer, which I would think is used for an English or history class is an exceptional tool applicable for a math class. This organizer allows students to see what a fraction is, is not, it's definition and it's characteristics. This is key to providing an informative background to any math subject. Lastly, you touched upon the subject of manupulatives and how you see a pattern within this course. I fully believe manipulatives are the key to success in math. Even if a student states that they do not need them, I still think it's important to provide them to every student. As you said above, each student learns in their own way and that's why we use so many different manipulatives. I agree it is key to provide our students with whatever resources they need in order to be successful. Great post this week Brandon.
Cheers, Courtney
Thanks for this post Brandon! I would almost use this as a reference for when I need a fraction refresher. You explain them extremely well and then give us the visual representations, which is very useful. You laid it all our very simply and intuitively. I loved the diagram at the end of your blog that illustrates the graphic organizer - thanks for posting this! I was wondering if you would, on your next blog, potentially introduce ways in which you maybe struggle or see other students proposing alternative solutions. I know you are a math whiz, so I guess this is a bit of my trying to gain an understanding of how you manage to solve problems quickly and efficiently. Great post and thanks again!
ReplyDeleteGreat post Brandon!
ReplyDeleteSometimes its hard to come out of a lecture and be able to recall all of the information that was presented. You created a really awesome recap for the fractions lesson - this will definitely be something I look back on if I end up having to teach fractions! I noticed you talked a lot about manipulatives, I too have noticed how often manipulatives are used. I'm finding it very helpful, but having a hard time remembering using them when I was in the elementary grades. Do you feel like they are used more often now then they were when we were learning? Do you (personally) find them more helpful or do you think the way we learned was just as efficient? It's always interesting to see how different learning styles respond to different teaching techniques!
Sometimes I got confused with types of fraction to kinds of fractions. There are several terms for fraction where I am confused to where they should be categorized to. Proper fraction, improper fraction, mixed number, whole number, equivalent fractions, like fractions, and unlike fractions are terms that should be categorized properly to avoid a confusion.
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