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My students have the hardest time comparing and adding/subtracting fractions with different denominators.  They can tell me how to change the denominator but the consistently forget to change the numerator when they work alone. It is crazy how they can fully understand it together or in groups but alone they lose it all. I have tried interactive notebooks to start the lesson. We have discussed equivalent fractions, which they seem to understand. But ask them to do a multi-step problem and they get lost.

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My students are great at making models of fractions, however they freaked out when I went back to showing fractions on a number line. It was like they had never saw it in their life. I know that they used numbers lines in third grade. They also had trouble with understanding what a whole was in numbers and not a model. I definitely need to use number lines a lot more often with them. It probably would have helped them understand adding and subtracting mixed numbers a lot better.

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I have placed a blank number line in a number of classes recently. I have found that they were able to place benchmark fractions without prompting. When having to place fractions that have a larger denominator they struggled. Having the blank number line, with a focus on if the fraction is closer to 0, 1/2, or 1 has really helped. They have been able to talk through it with their peers as well.

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My students struggled with seeing fractions on a number line if the fraction is greater than one. If the fraction is written as a mixed number they had a easier time with it, but if it was written as an improper fraction (or a fraction greater than one) they had a little easier time.

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My students struggle with comparing fractions. They can understand relatively easily that when comparing fractions with the same denominator, that the fraction with the larger numerator is the greater fraction. However, when comparing fractions with the same numerator, but different denominators is still difficult. The concept seemed to be a little easier once they consistently drew models that were the same size and could be compared.

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My students understand fractions as parts of a whole, but had a difficult time understanding fractions on a number line. Most of them were completely lost when deciding the size of a fraction and where it would belong on the number line with only 0,1/2, and 1 noted. I had to teach and reteach fractions as measures, or points, on a number line. Finally, the number line did help some of my students understand size and transition to equivalent fractions.

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Initially students struggle to understand the difference between whole number words and fractional vocabulary. (For example four vs. fourths.) When students can better differentiate between the two they are able to equally partition, etc. A solid grasp of multiplication and division really helped students to dive deep into fractions this year. The foundational knowledge of equal groups, etc.

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My students have struggled with using number lines to compare fractions and find equivalent fractions. They can tell you that both wholes need to be the same size, but when they draw a model or a number line, they rarely draw it to scale. This makes it difficult for many students to actually compare and find equivalencies. When I draw it on the board, or if they use fraction strips, they can find the fractions and compare.

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My students really, really struggle with seeing the WHOLE when talking about fractions. They see a whole number above a line and a line above another whole number.
I implemented a fraction numberline/fraction of the day. I used note cards and yarn to create a number line along the cabinets. I started with a '0' and '1' and gave the class a fraction. They'd find the fraction on the number line, we'd label it and move on. Over time, I'd move the numbers so that it'd range from 0-2, then 0-3, then 0-4 and so on. They started using it in conversation about fractions. (Thanks for the idea Ashley Strode!)

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My students struggle with comparing fractions. They continue to draw the wholes different sizes. Both on a numberline and model. I think we have worked through the model issue. I encourage them to draw the wholes underneath each other to make them the same size. However, we are still working with the numberlines being the same length. I also think showing them fractions in different ways is so important. I never thought to use the geometric shapes to show fractions, but after training today, I can't wait to try it with my class. Especially, showing them that the hexagon is the same whole as the trapezoid and three triangles. Looking at wholes in different ways is tough for them.

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My students seem to really have a hard time with equivalent fractions. They can not wrap their brains on how they are equal. We have worked really hard on flip chart books, number lines, pies, hands on manipulative, etc. They still have a hard time with it. I have also shown them other ways....it blows their mind, every single time.

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Most of my students understand the concept when working with shapes and manipulatives. However, moving to the number line is ALWAYS a struggle for them. Then carrying the number line beyond 1 is really tough. While they can understand equivalence in shapes, it's really tough for them to label on the number line. If the line is broken into sixths, then the fraction is 2/6, not 1/3. The only exception to this seems to be 1/2. They will almost always label it 1/2, since this is often where they start with labeling. I think if their number sense was better developed it would be easier for them to understand. I totally agree with those who have shared the need to remap their thinking. If I'm being honest, it also requires me to continue to remap my teaching!

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My students really seem to struggle still with identifying the numerators and denominators. They don't see that they are related to each other, for example that 3/4 means that there are 3 pieces out of the 4. When we moved into mixed numbers, they also had a hard time understanding improper fractions. I think it's because they have a hard time thinking of fractions like 5/8 and 4/6 as less than 1. They haven't seemed to make that connection. So when we saw fractions like 15/8, they weren't (and still aren't) always readily able to identify that as an improper fraction. When asked to create a visual to represent the fraction, they put 15 pieces into a whole, relating back to their struggle to identify numerators and denonimators. We created so many visuals together using number lines and basic rectangles, even using fraction strips, but I still have some who have a long way to go.

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So many! Students have a difficult time understanding that a proper fraction is really less than 1. I’d guess that it is because they are not used to working with numbers that are not whole numbers.

Another area of difficulty is not understanding that when 2 fractions have the same numerator the larger fraction is the one with the smaller number for the denominator.  Ex- denominator of 16 is smaller than a denominator of 4.  In their minds- bigger number= bigger fraction.

I agree with the other teachers as well about understanding fraction until they had to place them on a number line. I noticed that we got to where I thought, "ok. we got this down." I introduced numberlines and then, all of the sudden we cannot figure out the denominator on the numberline!  I think having actual pieces to manipulate helped them with parts of a whole and parts of a group. The numberline just threw them off though. They would often forget the whole number. Subtracting fractions on the numberline was extremely difficult for them as well. We practiced taking the numbers off the numberline and subtracting as well as counting steps backwards on the numberline, but it never seemed to click as well and other fraction lessons.

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I am going to piggy back on to what Elizabeth said in her post. When we first introduced fractions as partitioning shapes, the kids seemed to really understand fractions. The moment that we began talking about comparing fractions and placing fractions on the number line, their minds were blown. I tried using the same manipulatives I used to partition shapes to show the difference in size and I placed them on the number line.  This helped them see the differences between the fractions. We also created a giant number line in the hallway, fraction strips, and fraction flip books in order to further support the concepts. I agree with Elizabeth that it is difficult for students to understand fractional values based on their previous number sense. We are having to remap their thinking and understanding which is a huge hurdle for some.

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Based on observations I've made within my classroom, my kiddos minds were blown when we made the connection of fractions to measurement.  It was surprising to me that over half of my class was perplexed that we can measure everyday things fractions.  My class made a giant, interactive number line in which they used a tape measure to measure where each fraction belongs on the number line; this helped my kids see how we can measure distance with fractions.  The number line leads into another fraction concept that I see my students struggle with. Students struggle with the concept of fractional values. It's challenging for many  students to understand that the bigger the denominator, the smaller the piece. We made fraction strips, fraction flip books, etc. to model halves, thirds, fourths, sixths, eighths, and twelfths so that the kids could have a visual representation of each fractional value. I believe it is hard for kids to grasp fractional value because when they order fractions from greatest to least they need to put the fractions with the smaller denominator first, which throws many of them off. For ex: (1/2, 1/4, 1/8) --> many kids think 1/8 is the biggest fraction simply because they see an 8 and it bigger than 4 and 2 as denominators...