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Graham’s Progression Videos

Today, I’ve got Graham Fletcher here today to help us think about how we can be teaching fractions with understanding. Before I actually hand it over to Graham, I don’t want you to forget that everything that Graham mentions, you can find links to above. One of the things that Graham mentions are the fraction subitizing cards.

Now, these are being sent to anyone who registers for Graham’s training, Demystifying The Fraction Rules We Teach. So if you want those fraction subitizing cards, get registered for that training, we’ll send them on out to you and you’re going to need them because in the training Graham’s going to talk about some ways to use those fraction subitizing cards.

So, without further ado, take it away, Graham.

Hi, my friends. How are you? I’m Graham Fletcher, and before I even get started, I just want to say thank you for taking time out of your busy day to come to hang out here for the next few minutes. And I also want to say thank you to Christina Tondevold for asking me to be a guest vlogger in her virtual space here.

Fraction Progressions Video

If you’re familiar with me and any of my work, I’ve spent a lot of time here over the last few years really diving into the progression of learning for lots of different domains. Because I think it’s really important in order to know how to move student thinking forward, we need to know where it’s coming from, where it is actually when we’re working in our grade level, and then also where it’s going to. Like the understanding that we’re building in this year, where is that learning going to be in the next few years? So in an effort to kind of support my work in terms of my understanding of progressional thinking, I created a series of videos and I’m sure quite a few of you are familiar with those videos.

There’s five of them right now that are out there. But there’s one video, that for me, has kind of remained incomplete. And it’s the progression video that I released back in 2016. It’s the progression of fractions.

[WATCH THE VIDEO AT 2:49 TO SEE THE VIDEO]

In this progression video, I talk about what fraction understanding looks like in first grade, second grade, all of the third grade, and the beginning of fourth grade. Where we’re tackling the meaning of a fraction. We’re talking about the comparison of fractions. And last but not least, we’re also talking about the equivalency of fractions. And so as I’ve started working on this video, it really helped me make some solid connections about what we learn with whole numbers and how we can apply those to fractions.

A lot of the time, whenever we tackle fractions, we basically throw the baby out with the bathwater and everything that we’ve learned about whole numbers, we just say forget it. Let me just teach you these rules. And I’ll be honest, the way that the fraction progression video is set up, is not the way that I learned fractions at all. It was rule after rule, after rule, after rule. So kind of pushing my understanding so that I can better support students.

So, since that progression video that I shared back in 2016, and trying to make those connections to whole numbers, I’ve released these subitizing fraction cards. And really, they’re just fraction cards, but what I wanted to do when I shared these cards was begin to make the connection, just like how we built number in kindergarten should be the exact same way, or similar way to how we begin to build our fraction understanding in grades two, three, and four.

But then also there’s something else that came from that progression of fraction videos. And it was your feedback. Lots of the feedback has been really good in terms of how you’ve been able to build your own understanding, whether you’re a coach, how you can take that information and support your teachers in your building. Or whether you’re a teacher, and you’re like hey, I now understand this, and I can now better support my students in my classroom. And so, our thinking and student thinking has really been able to push forward.

An Example Of How Rules Can Be Misunderstood

Now, you’re looking at this and you’re like, what? What’s going on here? Like you see 2/3 and 5/6, well, those are not equivalent to one another. But then I start thinking about this rule that we tell students. And it’s a rule that I don’t directly say in the progression video but I want to go ahead and bring it back because I’m pushing my own understanding and growing as well, just the same way that you are.

So, I want to kind of share the last 30 seconds of that progression of fractions video.

[WATCH THE VIDEO AT 5:49 TO SEE THE VIDEO]

Here this area model helps students visually see equivalent fractions.

Now, after students have explored with fractions lots of times, they begin to see this pattern in numbers. And I think it’s our job as the teacher to kind of allow them to see this. So students begin to see that whatever we do to the numerator, we do to the denominator. But I think that it’s important that kids come up with that understanding, not just us telling them. Did you catch it? I said whatever we do to the top, we do to the bottom. And so when I start looking at this student work, I can see that the student added three to the top, they added three to the bottom. They added four to the 3/4, and then added to the denominator of 3/4 another four. And here’s this rule that I can’t help but think that I might have maybe contributed to.

I’ve received lots of emails from middle school teachers wishing that I would have gone just a little bit farther with that progression than what I did. And what they were looking at was that we don’t necessarily teach the rule of what we do to the top we do to the bottom, but what’s actually happening when we find equivalent fractions.

Connecting The Learning Of Whole Numbers To The Learning Of Fractions

Well, say we were to multiply seven times one. Well, I think every single one of us on the other end of this video would know that seven times one is seven because of the identity property. Well, what would happen if we leveraged what we know about the identity property and applied that to equivalent fractions?

Typically, when we go ahead to identify equivalent fractions, we would say we’d multiply the top by two, multiply the bottom by two, and we get four 4/6, and we have the right answer, and we call it a day, and we move forward. And so what’s really happening here is we’re not multiplying the top and the bottom by two separate numbers, what we’re actually doing is leveraging our understanding of the identity property. What we’re doing is we’re multiplying 2/3 times one whole in the form of 2/2. And now, you can see that because we’re multiplying 2/3 by one whole, we actually don’t change the value of 2/3.

In a couple of weeks, I’m going to be releasing the progression of addition and multiplication of fractions and then I’ll be releasing the progression of subtraction and division of fractions. And one of the things that I’ve realized, as I’ve been creating these progression videos is that we teach a heck of a lot of rules. And so my goal is to kind of unwrap and unveil, or demystify a lot of the rules that we use when teaching fractions. So as I’ve uncovered some of these rules, what I wanted to do is I asked Christina if I could come back around and host a webinar. And what I plan to do in this webinar is I’m really trying hard to avoid and unpack the rules that we teach with fractions.

What I plan to do is share a couple of the rules that I’ve uncovered and unveiled as I’ve been creating these progression of fractions videos. And so, I hope that you can join us. Christina has a little bit more information about the webinar, the dates and the times. Thanks and all the best, and hopefully you’re walking away just pushing on your understanding, just a little bit more. And thanks for hanging out.

Back to Christina.

Thank you so much, Graham. Now, personally, I am excited about Graham’s training because, although it’s uncomfortable to admit it when we’ve been doing something maybe incorrectly, it is really great to learn better so that we can do better, right? That’s my whole philosophy. I know that I do a lot of things incorrectly. But I want to learn so that I can do better. And if you want to join me, then get registered for Graham’s training so that we can learn how to teach fractions with understanding and really demystify those rules that we’ve been teaching without understanding those rules ourselves.

So, use the link below to get registered for Graham’s training. All right, I hope that this has helped you build your math mind so you can go build the math minds of your students.

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