Simplifying Fractions...oh boy

Nothing mind blowing today.  We went back to school after a 3 week break and spent a lot of time reviewing.   It is amazing how much knowledge can leak out of a brain after 3 weeks of vacation.

Anyway, we set out to tackle fractions....simplifying fractions to be specific.  I thought I would share with you the little "trick" I use to teach the kids how to do it.  You see, when *I* was in school, the teacher just said to find the number that they both had in common and divide.  If it could be divided again, do it again.  So I was stuck with dividing my fraction by 2/2 several times before it was as reduced as possible (oh yeah, they called it reducing back then too)

Now, I am pretty good at math (which, incidentally, is why I REALLY, REALLY hate teaching math...I was good at it and can't understand why *they* aren't....)  And even with me being pretty good at it, I spent a great deal of time as a youngster trying to find the perfect number that would reduce the fraction down to the simplest form.  It was agonizing.

So as a teacher, in an effort to combat this, I started teaching my students how to simplify like this.

And that is that.  They don't have to do any of the re-simplifying because they didn't guess the GCF wrong.  They just get it right the first time.  It is something that I wish *I* had as student.   So now, when students complete their work, even a boring old practice workbook page, this is what it looks like. (and you all know how I love when the kids show evidence....this just makes my heart happy!)

What little tricks do you teach your students to help them with fractions?

1. Good idea! It's a concept that they are still having trouble with, especially when they *still* need to divide again... and don't realize it :-/

2. That is a great idea Stephanie---And... I felt the same pain that you did today. The kiddos came in tired, sluggish, and I wondered if they even remembered what a fraction was :)

1. Yeah....we went over topic sentences for about 30 minutes today (I know, not math, but it just gives you the overall feeling of how things went today)

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4. yet another helpful idea :)
my math class (we switch from homeroom for math) struggles with essentially every concept. We're going to talking about adding fractions with like denominators tomorrow. I look forward to using your trick once we get to simplifying!

5. We combine prime factorization with reducing fractions. Just cross out all the common prime factors as "one" and what your left with is the reduce fraction. Using your first example, 5/10 becomes 5/2x5. The fives are turned into ones (slash through each making a one. So you have 1/2x1, which is 1/2. It does great double-duty to have them practice with primes.

1. This is how we teach reducing fractions as well and it really helps! My students really love this method as do I.

6. I love this so much! I learned it from you back when I saw your detailed and wonderful Calendar Math explanation. It has been a big help for my students this year during Calendar Math and we are coming up on fractions soon. Thanks, as always, dear Stephanie!!!

7. Wow! This is perfect for what some of my children need right now! Thank you so much for sharing another strategy to help children understand how to reduce fractions! I can't wait to try this in my small group tomorrow. I'm one of your newest followers. Feel free to check out my blog (constant work in progress) at: http://elementaryteacherfiles.blogspot.com

Thanks!

~Amanda

8. This is so needed for my kiddos right now. I have the extremes when it comes to math this year--high fliers and low bunnies, nothing in between. My strugglers could benefit from this strategy nicely.

9. Yes...I teach it this way too! I also call the fraction that we divide (or multiply) by a "giant 1". Because of course 5/5=1 and the Identity Property says that when we multiply or divide anything by 1 we still get the same number, thus equivalent fractions!

1. I like the "Giant 1". I am going to have to start using that ASAP!

10. I teach my 4 Simple Rules for Simplest Terms -- for Proper Fractions
1 If the fraction is a unit fraction (n = 1)...
2 If the numerator and denominator are consecutive counting numbers...
3 If the numerator and denominator are both prime numbers...
4 If either the numerator or denominator is prime, and the other is composite, and the numerator cannot divide the denominator...

...then the fraction is in simplest terms!

If the answer to all of the above tests is no, start applying Rules of Divisibility checks:
both parts even? divide by 2
both end in 0? divide by 10
both in in 0 or 5? divide by 5
multiple of 3 or 9? etc

11. There is a much simpler method that i use...

Eg: 60/30 = 6/3 = 2
230/240 = 115/120 = 23/40
32/46 = 16/23
64/72 = 32/34 = 16/17
You could directly reduce it there and then, starting by dividing with 2.

12. There is a much simpler method that i use...

Eg: 60/30 = 6/3 = 2
230/240 = 115/120 = 23/40
32/46 = 16/23
64/72 = 32/34 = 16/17
You could directly reduce it there and then, starting by dividing with 2.

13. I wanted to add that I purchased your calendar math for 4th and 5th and am going to get myself together to implement before the end of the month. How smart are you?! Keeping these skills alive on a daily basis, regardless of the unit at hand, makes so much sense. I'm really looking forward to it. Thank you!

1. What an email to open today! Thanks for that compliment...you just made my day! :) Let me know if you need help setting up your calendar, etc...

2. I wanted info in your calendar math!! I am a new follower!! Very interested!!

14. I wish you had been my elementary math teacher...

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16. Good one. You might also consider telling a story (my students love this one - I need to get part 2 out this year): http://wp.me/p1Dq2f-us

17. I tried your strategy with my two strugglers and it worked wonders! Thank you again for sharing! :)))

~Amanda @elementaryteacherfiles

18. I just Googled different ways to simplify fractions. This came up and I immediately taught it to my students. They love it and are doing a great job with simplifying now! I'm also teaching it to my fellow 5th grade teachers! Thank you for sharing it! You rock!

19. I stumbled upon your site looking for an alternate way to teach simplifying fractions to one of my clients/students. WOW! You helped me out a lot!ll Not only did my student understand this method, but he actually likes simplifying fractions. Thanks! BTW, I'd like to feature your blog on my blog and recommend people visit your site, if that' s ok with you! I'm going to feature it on Wedenesday Morning!

20. Great idea! I'm going to try this ASAP!

21. This is perfect! Going to use it today. It should really help my kids :)