Adding and Subtracting Fractions!
We could spend a full two weeks on adding, subtracting, multiplying and dividing fractions. Therefore we are just going to briefly look at these processes and what we have learned to discuss a few ideas.
To begin, on scrap paper, solve the following problem WITHOUT using the traditional "common denominator" approach: 3/4 + 1/3
Now, watch the following two videos on adding and subtracting fractions:
(Yes, you can you this AWESOME piece of technology in your class that is used to model the problems!!)
Comment on some of the following things in your post for today:
How has the traditional way of solving fractions changed for the better and/or worse?
How could a student build on previous understanding of adding/subtracting whole numbers in order to add/subtract fractions?
Can you share anything new you learned or something you have tried that you find works well?
Is there anything you would like to add to the discussion of adding and subtracting fractions? Maybe a website, link, or video that you have found?
How has the traditional way of solving fractions changed for the better and/or worse?
ReplyDeleteAfter watching both videos, I really felt that it would be difficult for my special ed students to grasp. There are so many steps and visual components that might overwhelm them. For regular ed students it might be good. Sometimes I feel like we are trying to reinvent the wheel! My students usually do well with rote methods and are successful computing fractions. I'm willing to try a new approach, but I don't want to confuse them.
How could a student build on previous understanding of adding/subtracting whole numbers in order to add/subtract fractions?
I suppose using the number line and bar diagrams at an early age is key. Also by utilizing all the methods we have discussed so far we could see what works best.
Can you share anything new you learned or something you have tried that you find works well?
Out of the two videos, I thought the second one was a little easier to understand visually. I did like how they represented each fraction with a bar diagram and a comparison bar in between them. I did post a link below as well.
Is there anything you would like to add to the discussion of adding and subtracting fractions? Maybe a website, link, or video that you have found?
While looking around on youtube I found an easy way to add and subtract fractions that I thought might be helpful. It doesn't provide the visual methods we have learned so far. It is more of a traditional method.
The link is: https://www.youtube.com/watch?v=GFGlgSfQ-Gk
Joanne,
DeleteI agree with you about "reinventing the wheel". I go back and forth with this new approach. I do see the value in "understanding" their math, but in the long run, I believe they will just end up using the rote method. I go back and forth all the time.
Thank you Jen for your support. I felt bad posting first with maybe not such positive comments. I just know my students and their needs and capabilities. I am so willing to try new ideas, but I do have some reservations about how it will help them.
DeleteJoanne you are not alone! I think with everyone still transitioning for the next few years moderation is key. Especially for our special ed students. We need to be able to choose what works best and tailor our instruction to that. Thank you for being honest!
DeleteJoanne, thank you for sharing. I can appreciate where you are coming from and would like to add my thoughts. Developing/increasing number sense is important and adds to/deepens a students thinking skills and ability to reason. However, sometimes it also helps for students to, in a sense, work backward. Understanding fractions can be new and complex for a 7,8 or 9 year old brain. It can be easy to get lost in the process of thinking when the knowledge is at such a new and fragile place. I think that when students can answer the problem first, perhaps using more traditional methods, they are better able to then go back and explain their thinking.
Delete(Traditional way change for better/worse)
ReplyDeleteI do believe students will truly understand how they arrive at their answer. When I was a student, I just followed the steps presented to me on the chalkboard.
I will say that this method does take longer and there can be mistakes made.
(Build on previous understanding)
I completely saw this laid out in front of me during the first video. There was definitely a progression from K and 1st to 2nd grade and then to 4th grade with the use of diagrams to number line to mixed numbers.
(New I learned)
I loved the use of the number line to add and subtract fractions with common denominators just like the jumps.
Pinterest ideas...
https://www.pinterest.com/search/pins/?q=adding%20and%20subtracting%20fractions
Jenn
DeleteIt's interesting that you love the use of the number line to add and subtract fractions and I find it very confusing! Just like the kids in class I guess. That's why showing as many examples (and non examples) as you can in the hopes that one of those is good for each of the students in the class.
I will be honest, when i first started this job number lines scared me and the thought of trying to teach others how to teach them made me sick! I found that by practicing and teach my brain to undue what i have previously learned definitely helped. They still arent my favorite but i see their benefits. I tend to stick to the TAPE diagram or area model.
DeleteI did find this site as well using the number line. The students actually walk the number line...
ReplyDeletehttps://www.pinterest.com/pin/211317407488839348/
After viewing video 1 for the first time, my eyes glazed over and when it was over I laughed aloud and said, clear as mud!
ReplyDeleteThe second video however had me jumping in my seat!!!!! This is so stinking cool. I love it and can't wait to leave this post and go practice it:-) Seeing the model was huge. I still think the number line is good, but way more difficult to work with.
I am so guilty of just showing students what to do when adding and subtracting fractions - the old fashioned way. I do like seeing what this represents but again the darned time is an issue. So I say does it really matter? If students know HOW to add and subtract ( and they understand the basic concept of adding to get more and subtracting to get less) do they really need to see the "underneath" parts?
I agree that time is such an ornery issue. And understanding for probably half or more of our classes can take quite a bit of time... But I can't help but feeling that the reason every teacher feels like they have to re-teach something that the previous grade supposedly taught is because we keep showing how to do something (an algorithm) and students either forget as soon as the test is over (raise your hand if you ever did this yourself :) ), or they know the algorithm but are presented with a problem in which the algorithm that could solve it is not readily apparent. If we make sure that the majority of our class knows the why at least as well as the how, might we eliminate some of the time subsequent teachers (and we ourselves) have to spend re-teaching?
DeleteThis comment has been removed by the author.
DeleteI think at this point it is best to show both to our students and allow them to decide what fits best. The idea of the old fashion way makes it hard to have a conceptual understanding and makes it difficult for them to explain their work, but i definitely see how time is a HUGE issue. My only hope is that as time goes on students will come in with a deeper understanding to begin with and give you more time to build off of that.
DeleteI went to my go-to place - Teachers Pay Teachers to look for adding and subtracting fractions using models and number lines and found a few things that I might consider. Again, I'm just not sure how much time I could devote to this. I am thinking of starting a math club in my school so this is something we could do after school in the club.
ReplyDeleteI think that if we use more concrete and pictorial methods to help students understand, then both teachers and students benefit. Rather than go with the "ours is not to question why, just invert and multiply" mentality that contributes to our societal "mathophobia", we might actually help people to see that we are wired for math (at least the basics, which includes fractions), just as we are wired for language. So if common core pushes us in the direction of better understanding, then I think it's a a very positive change. Now, how the logistics (esp. time) work out, I'm not sure, but other countries seem to have figured it out, so it's possible, right?
ReplyDeleteAs for websites, I love thinking blocks from the second video.
Greg Tang math also has some cool math games that are really math and kids like them:
http://gregtangmath.com/games
Also this is an intuitive, non-verbal way to do fractions that I have had a number of AIS students really like - enough to do in recess even:
http://www.mindresearch.net/demo/game/
Finally the following site has some good math practice activities. Some you have to be a paid member for, but many are free. I really like the free number line game for those students who struggle with a mental number line. It's a fun practice to strengthen that visual-spatial concept:
http://mathsframe.co.uk/free_resources.asp
I have a couple of books that have good ideas, but I'm traveling currently, so I don't have access to the titles and can't remember enough to google them... If you are interested, you can email me and I will send the titles after I return home...
Thanks for a great share Dana!! I LOVE Greg Tang, if any one can get the approval he is coming to ERIE 1 BOCES this fall, definitely worth the day out of the classroom to work with him.
DeleteHow could a student build on previous understanding of adding/subtracting whole numbers in order to add/subtract fractions? Students can use the number line in the same way the did for whole numbers. Using the unit fractions they have previously learned they can count up for addition or back for subtraction.
ReplyDeleteHow has the traditional way of solving fractions changed for the better and/or worse?
From the first video, I thought the way to show a mixed number on the number line was confusing. I am a visual learner, but still thought this. I am not really a fan of the dividing the the bars into twelfths as there is a greater chance for error. This would be okay for smaller denominators, though.
The second video was using the Singapore methods. I use Singapore at school and really see the value in it. As the students gain understanding of the concept being taught, I begin to hear comments from them on why do we have to do all these steps when we could just....
I think the newer ways of teaching fractions are all valid and can be shown as another strategy to be used. If the student understands what, why, and be able to explain why they are doing the steps, then they should be able to do it the traditional way.
I agree that if students understand why an algorithm works, they will ultimately be able to use it. I like that they get to draw and explore before they memorize. They will also have some background knowledge to fall back on if they forget the algorithm!
DeleteWhen I taught middle school, I did a lesson with my resource room students using circles and string and we found out WHY the equation for the circumference of a circle works. We discovered where that number Pi came from. That was 20 years ago. I feel like middle school students would all be able to explain why that equation works now.
I have found a couple of interactive websites that I would like to share:
ReplyDeletehttp://interactivesites.weebly.com/fractions.html
This website has many games for students to play.
http://www.learningreviews.com/Fraction-Games-Websites-for-Kids.html
This website has many websites listed and they name the author of it and give a short description of what the site offers.
Adding and subtracting fractions has certainly changed from when the parents of our students went to school. Parents are used to memorizing an algorithm and solving a problem. I think the new learning standards and the modules lead to such a deeper understanding of math! However, the teachers have to sell the program. If the teachers are not comfortable with the "new deeper understanding of math", then the students are not going to feel comfortable with it. Hence, they try do do their homework, parents get frustrated trying to help, kids tell the parents they are doing everything wrong, and everyone ends up hating the Common Core! I frequently tell my students that their parents may know another way to solve a problem and they are correct too! There are SO many ways to solve a math problem! I, personally, love knowing "Why" everything works. I try to convey this to my students. I love asking them to "prove" their answers with a picture. As I got more comfortable with the common core, so did my students. Almost 90% said math was their favorite subject at school. I also think that now that younger grades are teaching using the new standards and modules, it is going to be easier for us at the intermediate level. They are becoming more familiar with proving their work with pictures and number lines, so fractions is a natural extension of that!
ReplyDeleteI couldnt agree more with your post Lori! Great job!!
DeleteHow has the traditional way of solving fractions changed for the better and/or worse? I think starting with models makes it better. I am of fan of starting out with concrete, and then models as a foundation for reaching the abstract level. I love using my fraction tiles with kids. Putting those brightly colored lengths of plastic in their hands gets them going! Those tiles can be lined up for number line activities and tape diagram models. Having that tactile experience is so valuable. The common core does not call on the tiles as lesson materials but they should. Think of the kiddo that struggles to draw a model, you could have him build a model instead.
ReplyDeleteI really like this post. I think the fraction tiles and fraction stackers are great manipulatives for the students. Firstly, they love to play with them, and they can more easily see the sizes and how they relate. Finding equivalent fractions is great with them too!
ReplyDeleteHow has the traditional way of solving fractions changed for the better and/or worse?
ReplyDeleteI think providing students with various strategies that can be used to solve fraction problems is helpful. It hopefully allows each student to take ownership of his/her learning and focus on the strategy that best allows them to be successful.
How could a student build on previous understanding of adding/subtracting whole numbers in order to add/subtract fractions?
When students are adding fractions with like denominators, they are focusing on the numerator. The numerator can be considered what they "have" to add together. This is similar to adding whole numbers and should provide the student with some comfort.
Is there anything you would like to add to the discussion of adding and subtracting fractions?
I have found that it is extremely important for students to know their multiplication facts "in a snap." Finding the LCD by way of multiplication forces students to keep flexing their multiplication muscles throughout the year. It is my hope that by presenting students with other means/methods of adding and subtracting fractions we are not taking away from much needed work with multiplication facts.
Had to share this fun video:
https://www.youtube.com/watch?v=LPVfV_EZe1A