Let's Talk Third Grade Fractions!
1. Begin by reading pages 3-5 of the Math Progression Document and look for new understanding and/or important aspects of fractions in the 3rd grade.
2. Watch the following video on standard 3NF1 from EngageNY Studio Talks located here: Click Here
(The discussion on Fractions begins at 11:00min if you want to fast forward to just that section)
3. Post One Comment about something new you learned, an important aspect of 3rd grade fractions that other grade levels need to know or an instructional strategy/model that you would use to help introduce fractions in the 3rd grade.
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 3rd grade fractions and what you have learned or can use in your classroom.
True confession: I was going to start at the 11 minute mark, but being the math geek I am watched the whole thing! Geez learning something new everyday!
ReplyDeleteHaving taught fifth grade for 18 years let's just say I was fascinated watching the video!
I caught myself thinking huh so that's how it starts. For example moving from fractions as part of a whole to fractions on a number line. I guess I figured they had to learn it somewhere because by the time they get to fifth I expect they will know that, but....I liked the way he showed the fractional pieces over the top of the number line - a nice visual connection.
Equivalent fractions using blank number lines. Again, most incoming fifth graders know (or remember) basic equivalent fractions. But having students - even fifth graders do this activity to remind them visually of the relationship between equivalent fractions as well as the relationship between 1 and 2/2, 3/3, 4/4, etc would be a great intro into reviewing equivalent fractions in fifth grade. It could also be used to show simplest form :-)
Loved the activity of comparing the unit fraction pieces to have students discover the denominator getting larger as the pieces got smaller. Again a quick and easy review for fifth graders - or at least those still struggling with the concept.
I was especially taken with the idea of understanding that the fractional piece depends on the size of the whole. Comparing 1/2 of a large pizza and 1/2 of a personal pizza - brilliant!!!
I also found myself saying "but what about" (then remembering it's 3rd grade not 5th). Watching the progression - where they came from to what they need to know when they get to me in fifth...wow!
I have not looked in depth at the 4th and 5th grade progression of teaching fractions. I am curious to see how the learning standards are taught and if the standard algorithms that we learned in school are still used. Perhaps they are taught after the students discover WHY they work?
DeleteBecky,
DeleteI agree with you about the activity of sorting the fraction pieces to see what happens to the denominator.
I also enjoyed the pizza idea. Kids love that. I remember teaching music notes with personal pan pizza.
Becky: I think you have covered it all!! AWESOME!! We will talk further about the ideas of fractions and relation to whole next week, this is one of the most important foundations and definitely requires more conversations!
DeleteJen P,
DeleteWhat a cute idea of teaching musical notes using a personal pan pizza. Please tell me more about this idea. When teaching fractions to the students, I always relate it to pizza. I ask the students, wouldn't you like the biggest piece (and what would that be)!
Joanne,
DeleteI would use the personal pan to teach note values. I would say to picture yourself at Pizza Hut getting a personal pan pizza. When it is served, how many slices are pre-cut for you....4. The whole note gets 4 beats, just like 4 slices of the whole personal pan. Then the half note is half of the personal pizza which is 2 beats/2 slices. If you eat a quarter of the pizza/quarter note, you would have one slice/1beat. Then the eighth note, I would saw picture 8 friends trying to share a personal pan...how much would they get....a half of one slice. So the eighth note is worth 1/2 beat. Then the 16th note...imagine 16 people at the table. They would get 1/4 of one slice.
It's for music, but does make use of fraction knowledge.
You can use music to basically teach any subject and memorize things through song. (There is my music advocacy for the day)
Great ideas Jen! Thanks for your explanation.
DeleteBeing new to teaching math, I gained many ideas from this video. I loved the use of the number line as I am a visual learner. I really loved the use of the line with comparing equivalent fractions.
ReplyDeleteI also loved the idea of paper folding to show fractions.
Through this video, I do see the benefit of looking at place value in addition. I have not seen "jumping" on the number line before.
I love number lines for teaching fractions and I love the "trick" that the 3rd grade fraction module uses to teach kids to break their number line into equal parts. Many times kids want to draw the same number of lines to represent the denominator, for example, if we are working with sixths, they want to draw 6 lines. The module teaches us that we need to subtract 1 from the denominator and then draw that number of lines. To represent sixths, we would then draw 5 lines and have 6 equal parts. Kids quickly learn that if they draw 6 lines to represent sixths they will have too many parts. This is a great way to help them with their visual representation.
DeleteI really like the "open number line" strategy for adding and subtracting numbers. It allows for multiple ways to solve and discuss how it worked (or didn't). It forces place value to be used, and a teacher can gauge the depth of understanding about place value. It helps develop the "mental number line". Mental math skills, number sense, ... I'd never seen it prior to about 2-3 years ago, but I see a lot of benefits in it...
DeleteI watched the whole video as well. I thought the absence of the addition algorithm in 2nd and 3rd grade was interesting. This year I will be getting 3rd graders that have been taught using the modules, so I wonder how they will attack these 3 digit addition problems. I think the dissection of the problem using place value knowledge to solve the problem leads to an excellent understanding of the problem, as well as great mental math strategies, however, it is a lot of work for the kids. I teach and encourage this strategy in my classroom, but I also teach the standard algorithm (shh...)
ReplyDeleteNow for third grade fractions...
I really like how the fractions are constantly referred to based on the UNIT fractions (1/2, 1/3, 1/4...) I think this really helps students understand the meaning of 2/3, 3/4, and even 6/5 (although this is still difficult for them!)
Fractions on a number line is a great concept, but it is difficult for the students to make the number lines and put lots of fractions on them. The number lines get messy and the fraction marks end up not lining up. I will continue to use the number lines, but my students have had more success with fraction "bars" or tape diagrams, of course making sure the WHOLE you are comparing is the same.
As far as comparing unit fractions, we constantly refer to the WHOLE as our favorite candy bar and the "denominator" is the amount of people you have to share with. This helps them visualize that more people to share with means a smaller piece, and they may not want to share that favorite candy bar with the whole lunch table!
Lori,
DeleteI like how you commented that number lines do not always help as some students are "messy". I thought it was a great idea when I saw it, but then again from hearing your experiences, it may be the best approach for each student.
I agree Lori! I tend to use the fraction bars which transition to the TAPE diagram quite well and then try and show the fraction bars above the number line to see the connection throughout the introduction to fractions!
DeleteI agree that the number lines can be messy but I think it's important particularly for my fifth graders to work on that. They can be very confused and want to count the lines and not the pieces.
DeleteLate night random fraction comment: Fifth graders struggle with whether to make a circle model or rectangular model when demonstrating a fraction. Some will try to slip a shoddily split circle into 7 pieces. It's a wonderful lightbulb moment when they realize the model matters. But my thrill is when they seamlessly make correct models after a few days of practice:-).
Lori, I like your candy bar example! I think I would like to have a large model/image of a candy bar to hold up when ever I need to reference this concept!
DeleteBecky - I was about to type the same comment you have already mentioned. It has been my experience that students often want to count the lines and not the "spaces" even after practicing with a manipulative to "hop" from line to line. Messy, student-constructed number lines seem to add to this confusion.
DeleteI agree that when students use a number line that it, at times, can be very messy and tricky. Many do want to count the lines, just like when they are reading the clock, instead of the pieces. When I am modelling the jumps I like to use some kind of made up lyrics and body movements to help the children understand. [It's all about the 'jumps' (bass) not the lines (treble)] This is fun, especially since I cannot sing!
DeleteI can honestly say i have always been most afraid of teaching Fractions on a numberline, but now that i see the transition and understand how it is first taught, I LOVE the numberline for fractions and how visual it is. I do agree though, it may not work for all kids!
ReplyDeleteThe biggest take away here is how can you use these basic introductions to fractions in 3rd grade to help kids gain a greater understanding. Its great to be able to see now where your older kids are coming from and use some of these models to help remediate throughout the elementary years!
Im really enjoying your comments thus far, keep them coming!!!
I think a big hurdle that needs to be crossed for kids to be confident in their understanding of fractions is that they need to conscientious in their drawings and their level of neatness. It is much easier to use two number lines to compare fractions as opposed to trying to break one number line into two different fractions which is unfortunately addressed in third grade. This is the time when we begin to lose our most confident learners because at the age of 8, many kids aren't able to accurately draw two fractions on one number line correctly.
DeleteI agree Sunnie! I take a deep breathe each time we begin partitioning a circle, some just never get it!! They are so focused on making in perfect they lose what we are trying to teach.
DeleteI agree with you Sunnie. I wish tracing paper could be put through the copy machine so students could place one pre-printed number line on top of the other in order to compare fractions more accurately. I have had some success with really blowing the number line up (11x17 or at least 8x14) and using different colored pencils to give students an appropriate amount of space to help them differentiate between fractional parts on one number line. The workbook space provided by Pearson is a joke even for the students with the greatest fine motor skills.
DeleteWhen teaching fractions at any grade level, the most important point that I try to get across to the students from the beginning is that a fractional part is smaller than a whole number. Initially, I have a conversation relating to pizza, but I also incorporate using the measurements on a ruler that are less than an inch as another example. These conversations also lend themselves to a discussion about decimals and percentages as well. I do use the number line with fractional representations (in large scale so you can fit the numbers on the line) and tape diagrams. The introduction of fractions in third grade needs to be reiterated in the upper grades each time you approach the topic to solidify recall, comprehension, and application.
ReplyDeleteI couldn't agree more Joanne. Later we will discuss fractions greater than 1, so i will be interested in hearing your take on that too!
DeleteI have spent the last two years focusing on 5th grade math. One way in which I saw many kids struggle was with individuals that had a weak conceptual understanding because they needed additional hands on opportunities to master a concept. In the video, I liked the simple activity of lining up the fraction manipulatives. I think I could set up a math center activity with a variety of similar objects. This would be a great way to give some extra hands on opportunities.
ReplyDeleteGreat though Heidi! Going back to the basics is so important and so many teachers dont do this due to lack of time and individual attention.
DeleteI totally agree that hands on activities are the way to go. I teach remedial math where I push in 2x a week and work with the whole class on either Singapore Math or Problem Solving/Common Core. I pull out in groups of 7 students max. This is where I use manipulatives all the time. I see many classroom teachers getting rid of their manipulatives at the end of the year because they say with class size, behaviors, time constraints, etc.they do not have the time to teach that way. So disappointing to me.
DeleteOne of my favorite quotes about fractions is, "Did you know that 5 out of 4 people have a problem with fractions?" :)
ReplyDeleteRegarding our task, I read somewhere before that one of the prime indicators of success in mathematics (at least early on) is having a "mental number line" - being able to accurately place numbers in relationship to benchmarks and each other. I noticed that my weakest AIS math students really struggled with this - seemingly placing numbers willy-nilly, or breaking a blank number line into parts that were not anywhere near proportional [like having all the numbers 1-9 bunched up, with 10 a big leap to the right of 9]. It seems that any work with number line representations will help strengthen a child's number sense. So (as I replied to Jen's post), I really like the open number line strategy that was shown before the 11 minute mark. I also liked the number lines that were used to show equivalent fractions, and the one that was used in conjunction with the bar model to show how each additional fifth was represented numerically. As some commented, developmental adjustments may have to be made due to the fact that number lines can be difficult for some to draw and label.
I also liked the fraction manipulative activity. We spend far too little time on concrete and pictorial representations of math, and rush right into abstract representations, and we lose so many kids that way...
In the Math Progression Document, I was struck by the area representations of 1/4 side bar on page 3. That looks like it would be a powerful activity if it was translated to a manipulative, or if it was repeated with pictorial representations of other unit fractions...
A question that I would have is whether or not the kinds of activities and conversations that we saw in the video are being engaged in in most (all) 3rd grade classes?
Great post Dana!! That quote at the beginning is definitely the truth. In some schools i see teachers struggling to understand more than the students. If they are taught this way from day one, they know no different. Us teachers almost have to undue what we have already learned to gain this deeper understanding of fractions. As you said, we have to start thinking visually and its a tough thing to do sometimes. I found the key is modeling, practice and TIME!
DeleteAs far as what is happening in the 3rd grade classroom i find that it is quite the mix. First it depends on the district and second on the teacher. A lot of teachers have begun to make the shift to more "common core" teaching practice, but many are still scared. I could never stress enough how important it is to start at this early age!!
My first comment is - where can I get a large piece of glass/plexi-glass/plastic that I can write on and FACE my students instead of forever turning around (or to the side) when writing on a white board or Smart board. It's genius and I want it in my classroom!
ReplyDeleteI was struck by the function and simplicity of the paper folding activity (3.NF.1) to introduce students to fractions. I think I liked it so much because the paper truly begins as a whole for the students and that whole will not change even when folded additional times. I felt that it correlated well with the later fraction size sorting activity (3.NF.3) by reinforcing that when the denominator increases, the amount represented is decreasing. I also support the idea of connecting fractions to the number line early on. (3.NF.2) I have always believed that in some ways, place value is to math what the ABC's are to reading. I feel students need a deep understanding of place value to really see the bigger picture relating to numbers and math. Finally, I am going to make an effort to call fractions "numbers" instead of relying on the idea that they are simply "parts of a whole." Nice video, Jessi. Thanks for selecting it.
Haha wouldn't that be great to have Carrie! Its actually some sort of mirror that works with the camera. I am fascinated by it every time i watch these!
DeleteGreat comments on what you have read and watched, it is o very important to see fractions as more than just a fraction!
I think Singapore math expressly teaches students that fractions can be viewed a number of different ways, only one of which is part-whole. So, I've tried to use that reality in my explanations when I remember. Sometimes I preview (or review) other ways to look at fractions: as a division problem, as a ratio, as another way to write a decimal or percent... I just recently came across an older article from Teaching Children Mathematics called, "13 Rules That Expire", that doesn't list this part-whole rule as one of the 13, but it could have. (There were some other noteworthy ones listed that are related to fractions, though, like "addition and multiplication make numbers larger", "division and subtraction make numbers smaller", and "always divide the larger number by the smaller" [So we can't do 1/2 divided by 2?].)
DeleteOne of the things that caught my attention is that I have never explicitly said to my students that you must consider a fraction in comparison to what size the whole is. For example, 1/2 a cookie is much smaller than 1/2 a pizza. I will definitely be making sure to point out this concept in the future. I really liked having the students take the fraction pieces and order them themselves, instead of having them do it on paper. I have used the number lines to show equivalent fractions in the past. This has really helped my students to see what is equal and not equal. Fractions are so hard for our students to understand that any ideas that can be shared are soooo appreciated. I have also taken many classes in Singapore Math. A lot of the Common Core does use these strategies as did parts of the video. What perplexes me the most about it is that Common Core has had to change the names of models, concepts, etc. Why? Tape diagrams? Bar models? Very frustrating for our students. Sorry, just a pet peeve!
ReplyDeleteOne thing that I like to share with my students is that fractions with like numerators follow the same rule that unit fractions do. So, 4/4 is greater than 4/5, which is greater than 4/6, etc. This helps them when ordering the fractions.
ReplyDelete