## Tuesday, February 4, 2014

### FRACTIONS

With the start of the second semester, the focus in math has shifted from working with whole numbers to numbers that are less than one whole; also known as fractions.

The main learning objective currently is the Common Core State Standard 4.NF.2:

4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols less than, greater than or equal to, and justify the conclusions, e.g., by using a visual fraction model.

To make the concept a little easier to understand, students are using fraction models.

These models allow students to better visualize the fractions being used and to think about their size relative to other fractions and to one whole. This is especially helpful when students are asked to compare fractions or find equivalent fractions.

This particular web based model is really nice because it allows students to move around on the number line. It automatically shows when there are other fractions that are equivalent to the one a students lands on.

Here is a picture of it. Click on the picture to try it out.

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You can easily see at the top of the image that the student has chosen the fraction 2/3. Then if you follow the green line down, all of the equivalent fractions to 2/3 on the chart are indicated.

Comparing Fractions
It is easy to compare fractions with the same (or like) denominators. Let's use this example:

When comparing fractions with like denominators, the focus moves to the numerator. In the example above, both fractions are broken into 7 parts. The fraction with 2 parts shaded in is clearly smaller than the one with 5 parts shaded in. Therefore two-sevenths is less than five sevenths.

When comparing fractions with unlike denominators, one must really think about and try to picture the fractions. We don't always have pictures in front of us. It is okay to represent the fractions with a picture model, but it is also importnat to have mathematical strategies other than pictoral.

One strategy students have been taught is to compare fractions to the "benchmark" of 1/2. A benchmark fraction is an easily identifiable fraction students can use to help them identify or mark other fractions.

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By representing the fractions with a model, students can easily draw both fractions and clearly see that the two fractions are equal to each other in size. When different fractions are the same size, we call them equivalent fractions. We will be discussing these more at a later time.

In addition to representing fractions with a model, students should have a mathematical strategy they can use to solve problems. In the above example, one would first look at the denominator, or bottom number. Then, one would think about the numerator, or top number.

The question one should ask is "Is the numerator more than half, less than half or equal to half of the denominator?" In this case, 3 is half of 6, so that tells us this fraction is equal to half. Let's look at another example...

Students can use pictures models or use mathematical strategies to compare fractions to one half. If a student is comfortable with these strategies, she or he can now use them to compare fractions with unlike denominators.

Here is a video showing how to use these strategies to compare fractions with unlike denominators.

Please comment! How is Fractions going for you? What have you learned? What are you still trying to learn? What strategy works best for you when comparing fractions?

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1. Dear Mr.Pahl
I improved my fraction. My mommy told me a strategy I can use for fraction if I have trouble
Sincerely Dyna

2. Dear Class,
I think Fractions are really fun to solve and to learn about. But if you learn a new method it is kind of hard to understand but you get use to it after a while worth practicing:)

From, Karoline

1. Dear Karoline,
I also think learning new can be tough but can get used to it by practicing the new strategies you find out about.
From,
Sophia

2. Dear Karoline and Sophia,
This is Beth from Mr. Pahl's class at Western. I am so glad to see you using different strategies for working through and understanding fractions. What have you found to be the most helpful trick or strategy for understanding fractions?
Sincerely, Beth

3. Dear Mr. Pahl
I like fractions and I am trying my best but I am not doing so well.
From.Micah

1. Hi Micah,

Thanks for letting me know. Can you identify what it is you don't understand? We'll work on it Thursday. You are a very good student, Micah. Don't worry about it. We'll get it figured out and you will think fractions are easy peasy.

Sincerely,
Mr. Pahl

4. Dear Mr.pahl,
I really like learning about factions. I hope at the end of the year I know everything about factions.
From Kayden,

1. Hi Kayden,

Thanks for writing. I am glad to hear you like fractions. I like them, too! You will learn a lot about fractions this year, but probably not everything. We have to save something for 5th grade! Thank you for being such a good student!

Sincerely,
Mr. Pahl

5. Dear Mr.Pahl,
I love to do fractions. My favorite part is when I subtract mixed numbers and the denominators are different. I thought it was hard at first.
From,
Tori

1. Dear Tori,
I agree, I also like fractions. I thought subtracting mixed numbers, too. I admit, it was pretty hard, but now we know how.
Sincerely
Charlize

6. Dear Dyna,
What is the strategy that your mom taught you for fractions when you are having trouble? My name is Julia and I am in Mr. Pahl's class at Western and am in a fraction class too. I would like to hear your strategy!
From,
Julia

1. Hi Julia,

Dyna is in 5th grade now, but I will ask her for you!

Mr. Pahl

7. Dear Mr. Pahl,
I love doing fractions I thought subtracting fractions with different denominators would be hard but it really isn’t now.
From Sarah

1. Dear Sarah,

Thanks for writing! That's terrific! I am so glad to hear that subtracting fractions isn't too hard for you now. What do you think made it easier? Is there a particular strategy you use or did you just keep practicing until you remembered what to do?

Mr. Pahl

2. Dear Mr. Pahl,
I don’t think I had a special strategy I used. I guess I just kept practicing till I remembered how to do it.
From
Sarah H.

8. Dear Mr.Pahl,
The one thing that was really hard for some of the kids in fourth grade.
Is borrowing fractions I think that we need to practice on it more.
Sincerely,
Eric

1. Eric, I agree. We will be practicing that more soon. Thanks for telling me your thoughts.
Mr. Pahl

9. Dear Charlize, I really loved you’re video. I think that I even learned something, the point is you worked hard to explain everything and you had to do math to help people who did not understand so thank you very much. Also thank you for teaching me that strategy now I’ll be better in math! Happy Valentine’s Day, Hannah

10. Dear Charlize’s,
Your video helped me understand more about fractions. You did an excellent job on this video. I hope that you can make more videos about fractions to help kids who don’t really understand them.
Sincerely, Amaya

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