Let's Talk Fourth Grade Fractions!
1. Begin by reading pages 6-10 of the Math Progression Document and look for new understanding and/or important aspects of fractions in the 4th grade.
2. Watch the following video on standard 4NF from EngageNY Studio Talks located here: Click Here
3. Post One Comment about something new you learned, an important aspect of 4th grade fractions that other grade levels need to know or an instructional strategy/model that you would use to help introduce fractions in the 4th grade. Try and relate your new learning of 4th grade fractions to what you learned about 3rd fractions from the video and/or progression document.
4. Post one comment responding to another participant in order to add to their thinking, suggest additional ideas or engage in a meaningful educational conversation about 4th grade fractions and what you have learned or can use in your classroom.
I really liked how jumps on the number line can be used. In 3rd grade, the demonstration used it for adding hundreds. In 4th grade, the demonstration started with a basic multiplication problem of 4x3 (which I know is 12 from memory) but it was shown in detail. Then he went on to do 4x1/3. I know to do 4x3x1, but cannot justify why. This visual shows why it works.
ReplyDeleteI also like the bar graphs and in particular the Grids for tens and hundreds. I remember struggling with unlike denominators. The grid visual is perfect to use for shading various scenarios.
I will say that there will need to be a lot of practice offered for the students to be able to do use these visuals fluently. But I do see the benefit of it building on understanding at each grade level.
What you say is KEY Jen, PRACTICE!! This visual way of learning and understanding can be a difficult step for most kids especially if they didn't have it in earlier years. This is where coherence comes into play because it must build off of earlier foundations of fractions.
DeleteI agree with you that it is even more difficult if they didn't have it in earlier years.
DeleteI think one major flaw with the common core math is not the actual methods, but how it was introduced. They should have started one year with just Kindergarten. Then the next year Kindergarten and First and so on. Don't change how students have already learned. I had trouble as an adult taking a math course recently and trying the new way.
I agree with the need for much practice for using the models. Some students take so much time to shade/color models in. These valuable activities need time!
DeleteThe concrete and pictorial need time/practice, like Heidi wrote. If we want the depth of understanding that leads to long-term success and application in novel situations, we have to invest the time early on in the types of foundational activities and conversations encouraged in the video. And this is where I find the greatest tension lies for me: taking the time to work with math when a curriculum is arbitrarily assigning a specific (short) amount of time with a concept, and missing the process, thinking, conversation, etc. that develops the concept in a child's mind. Practicing an algorithm doesn't necessarily ensure understanding of the mathematics involved... So hopefully, we will see a better balance of concrete and pictorial with abstract as common core implementation ages...
DeleteI was also impressed with the jumps on the number line to show first 4 x 3 and then 4 x 1/3. I felt that this method answered so many possible student questions before they would even have a chance to ask them; it was a very thorough explanation. I often use the term "groups of" when speaking of multiplication to help connect multiplication with repeated addition. However, I believe "jumps of" is a better term. Not only does it seem to better relate to the number line, it's also more fun!
DeleteThose jumps on the number line....had us all! It just really makes clearer what you are doing. But again I can see this taking time - and lots of it. I struggle with time as well. I am a firm believer in small groups for math - just like ela. It gives me the time one-on-one I need with some students, but sometimes even that isn't enough based on their lack of foundational understanding. It is frustrating for me as an educator, I can't even begin to imagine how frustrating it must be for those struggling students.
DeleteAfter watching the video, I enjoyed seeing a variety of methods that the instructor used to help students understand fractions, mixed numbers, and improper fractions. One suggestion would have been to explain that you could also put the whole number over one and multiply it with the fraction. I thought that this should have been included. I liked the lesson showing bar diagrams and how the students were asked to shade in each picture. I did like the "jumping method" that he used as well.
ReplyDeleteAll of these strategies will be useful when teaching these lessons in the upcoming school year.
When you suggested that you could explain the whole number over one and multiply it with the fraction, it made me think would it be beneficial to at least mention next year's learning? What if they just had a preview of the next school year, but it was not reinforced yet. Would that help with connections more or just be information overload?
DeleteThanks for your question and looking ahead to next years progression of skills. When working with special ed. students, sometimes less is more. In other words, using less steps for them to remember would be to place the whole number over one and multiply. Conceptually, the additional modifications are great for some, but may confuse others by utilizing too many things to remember. It is important to analyze our teaching strategies to increase learning for our students.
DeleteI definitely think that it is worth mentioning. Some kids will pick up on it and its a great way to get them thinking!
DeleteI also like the word connection from the multiplication symbol to jumps on a number line. In the videos, the continued reference of concrete-pictorial-abstract is great. When I think of struggling learners, this three stage learning presentation really reminds you that reinforcement for some students will need to be back at the concrete stage rather than just preparing more abstract practice. In fact there are time that you might even need to go back to the concrete activities of a previous grade level to meet the needs of a student with significant gaps.
ReplyDeleteI think this is a cultural shift that we need to help make for the upper grades especially. They need to be encouraged verbally and through modeling that using concrete and pictorial representations to fill in gaps or develop conceptual understanding is not just for primaries - it's the bright thing to do whatever your age. If we do it often enough, then they might even choose to break out the counting bears, unifix, Cuisinaire, bar models, open number lines, and so on, on their own, in order to aid their understanding or help a classmate. I smile just thinking about students taking charge of their math learning and problem solving like this. :)
DeleteI couldn't agree more with the both of you! I am honestly stressing to start with the concrete. I find a lot of the upper grade level teachers want to jump right to the abstract and they lose half the kids. They are NEVER to old to start at the foundation and work their way up. Great points made here!!
DeleteI also believe the points brought up by Heidi and Dana are excellent. I will add this quick anecdote. A few years ago, I was speaking to a kiddo about fractions and she told me that she had loved fractions last year but "not as much this year." When I asked her why she thought that was, she told me that in 3rd grade, she had made done more "art projects" with fractions and that had made it easier for her to understand. I took it to heart that perhaps I was not encouraging enough "play" with the manipulatives and the concept in general. So, I admit to being guilty of transitioning to the abstract too quickly!
DeleteOne thing I like about the models with fractions is that it helps steer away from some of the common mistakes that are made with fractions. For example, when you have a bar model with fifths, as shown in the video with 2 2/5, when he decomposed it, a common error when adding the fractions would be to add the denominator as well as the numerator and end up with 12/15 as the equivalent fraction. However, by using the model and referring to the unit fractions that composed it, it was difficult to make that kind of error. The correct thinking is more natural with a model than just the fractions lined up to be summed. For me, it was a good reminder, not just to use models, but to make sure I use the appropriate math terms consistently...
ReplyDeleteThe way that whole number times a fraction was modeled was a great way to use what students (should) already be familiar with: skip counting and grouping for multiplication, and apply it to something intimidating: fractions. I think it sets students up for success when they can see multiplication of fractions and whole numbers is just a variation on a theme and not something totally different.
BTW: Is anyone else impressed by how fluidly the video presenter is able to write his numbers in reverse on the glass? Maybe I'm just getting tired... :)
Dane, great comment. This truly is one of the important concepts here and we are definitely trying to work away from those common mistakes. I've heard it several times... if we know fractions are the hardest, kids are scoring the worst on fractional concepts, then why do we keep teaching them the same way? This SHIFT has to happen in order to see better results and deeper understanding of fractions!
DeleteOh and when i first watched a Studio Talk that is all i could focus on was how was he doing this???? lol. State Ed. told us he is writing on a mirror, not backwards!! Haahaha
DeleteWhew thanks Jessi! I kept watching and saying, "there must be some trickery going on here!" A mirror - who knew!
DeleteI agree, Becky, that these strategies will help with clarifying the common mistakes that students make. Using the correct math terms is also important, but as I said in the 3rd grade comment, it is perplexing to me why they change wording and expect the students to know that they can all mean the same thing.
DeleteI agree with all of what has been mentioned thus far in the comments. In regard to the modeling Nick did with comparing factions (4.NF.2), I thought he might have mentioned that several students might be able to use multiplication to change both denominators (in this case to 12) more easily than "splitting the unit fraction." His model provided an excellent visual but I think many students would struggle to divide each third into fourths and vice versa. I wonder if it could also be done using magnetic fraction pieces instead of having the students divide the space by drawing so many lines.
ReplyDeleteMy students in third grade struggle with drawing so many lines as well. They lose track of how many they have drawn in each space. I also think that when we are asking them to do so many important pictorial models, quality vs. quantity should be considered.
DeleteYes definitely Carrie, they struggle with drawing multiple models so hands on manipulatives are best!
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ReplyDeleteFourth grade holy cow, what a difference from third grade! I felt so comfortable with the gradual release from concrete to pictorial to abstract. Having said that, I wonder how many teachers realize how to do this?
ReplyDeleteUsing models is such a good visual way for kids to see what is happening.
When talking about equivalent fractions and the fact that you can multiply the number and denominator by the same number to get an equivalent fraction he didn't specifically say what you are really doing is multiplying by one and reminding students about the identity property for multiplication. I do it in fifth grade and all of a sudden those darned lightbulbs start to click on. Perhaps because this is all so new students can't /don't see it?
4NF2 I think decomposing the fraction bars when comparing fractions could be confusing to fourth graders at first and would require lots of examples and "doing" to get clear. Especially when you consider where they came from in third grade.
4NF5 My inside voice is saying, "so this is where the decimal thing gets started:-)"
When I think of all we do in fifth grade based on what has happened in fourth grade I thank goodness for the awesome fourth grade math teachers of the world!
Becky: Its very powerful for you to be able to "see" what they now come in with and use it to tailor your instruction or use for remediation. Great comment!
ReplyDeleteThis video was very helpful to me. I really liked the strategy of breaking up the bars into the denominator so that the students would be counting the unit fractions. Anytime that you can make a concept more visual for students is a bonus! I think that there is a big jump from what the video was showing for the 3rd grade and what they are expected to be doing in 4th grade. Students have a hard time understanding fractions so this will have to be a slow, in-depth process. It would be a good idea to really reinforce fractions at the end of 3rd grade after the NYS testings. Then do spiraling of those concepts in the beginning of 4th grade before they start these new concepts.
ReplyDeleteI thought it was very interesting to see how much more fraction learning takes place in 4th grade and how important it is for us to lay the foundation in third grade! Some things that caught my attention were the need for the strong understanding of the fractions that represent 1 whole (2/2, 3/3...) I loved the idea of transferring the multiplication language of "groups of" meaning the same as "jumps of". I am definitely going to use that this year! The splitting of the unit fraction bar pictures can be tricky for kids. They have to be so precise and really pay attention to their groups... My friend Heidi Topolski always made such a big deal about picking out a "math artist" of the day whose work clearly showed the problem to any onlooker. The students all aspired to the challenge!
ReplyDeleteOne last comment... I heard him refer to writing and drawing the fractions in a graph paper notebook. What a great idea!
Yes! 4th grade is key! It takes the basic understanding of fractions and builds the conceptual knowledge so that 5th grade teachers can then teach students operational techniques with fractions!
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