# Thinking Some More

I’ve been doing a lot of thinking about my fraction activity plan for tomorrow. There are many things that I want the students to be contemplating and discussing before they complete the assessment question.

• I want them to understand how fractions compare to each other (e.g., creating fractional amounts that are more or less than a half, and being able to explain how they know that they’re correct).
• I want them to understand the part-part-whole connection (e.g., knowing that the one big piece of lego is made up of three small pieces of lego).
• I want them to play with and understand different fractional amounts (e.g., I want them to realize that 4 out of 8 items is still half of the total amount).
• I want them to understand that fractions can be part of a set or part of a whole (e.g., there are 6 out of 8 brown animals in the collection of animals or there are 4 out of 6 pieces of pizza with pepperoni on them).
• I want them to start using the math vocabulary associated with fractions (e.g., halves, thirds, quarters, etc.).
• I want them to see how fractions can be used in different contexts (even seeing the overlap with our current measurement unit).

It was with all of these thoughts in my head that I created these activities this morning.

I don’t know if these activities officially count as provocations, or if they’re more math problems. Either way though, I think that they’ll get the students thinking about fractions and beginning to show me an understanding of proportional reasoning as well. They’re open-ended problems that will hopefully give all students an entry point. I’m also encouraging the use of discussion, with the hope that students can build on the ideas of their peers, and help create understanding for more difficult concepts.

As students complete the assessment question, they can also go back to these centres to explore alternate solutions and to continue working with the concept of fractions. Then when everyone finishes the assessment, we can discuss different solutions as a class. I’m hoping that this sharing piece will help consolidate the learning and build a better collective understanding of fractions. What do you think of this plan? How would you modify or change these activities to better help get students thinking, playing, and working with fractions and proportional reasoning? I’d love to hear your ideas!

Aviva

## 15 thoughts on “Thinking Some More”

1. I really think that your students will enjoy this activity. The questions are fun, and hands on. Influences the students to explore the unit.
I personally think it would be better if you added some independent work as well. If they rely only on peers, they won’t be doing anything for themselves for the assesment. I have some questions for a small survery I am doing, would you mind answering?
§ To conduct provocations, what are the needs? Are muniplatives needed?
§ What are the extreme feelings you have when a student doesn’t understand, even when you have explained everything so throughly?
§ Most of all, do you always WANT them , WANT them, and never just let them? What is your preference, to want or to let?

I hope you get the chance to answer these questions, perhaps in a post if it is too much in a comment !! 🙂

• Thanks for your comment, Yusra! I guess that I wasn’t that clear in this post (I blogged a bit about this activity yesterday as well), but the assessment itself is independent work. These activities are just the lead up. They’re to get students thinking about working with the topic, so that they have an understanding of it before they complete the diagnostic assessment. Does this help?

1) Provocations can be anything. They can be a book or an article, a quote, a collection of objects, or even a song or a podcast. They’re items that will get students thinking about the topic and asking questions to hopefully connect with the bigger idea or concept. Often with a provocation, a teacher wouldn’t actually divulge the topic. They would actually get students to uncover the topic just by the items that are chosen. I hope this helps!

2) It can be hard when a student doesn’t understand. I often question if I’ve done things well or provided enough opportunities for that student to learn. I often re-look at what the student doesn’t get, and then consider another way to present it. That’s when I try again. I try again a lot, but usually, one way or another, all students end up understanding the concepts (as long as I provide different ways for them to learn).

3) This is a hard question. I used the word “want” because as I planned for tomorrow’s activities, I wanted to keep in mind the big ideas that I need students to understand. I want to let them understand these ideas though, as they explore the activities, talk to each other, and talk to me. Maybe this is a combination of “wanting” and “letting.” Does this help?

Thanks for the great questions!
Miss Dunsiger

• Mrs.Dunsiger, Thanks so much for your time! Thanks for letting me have some info on your opinion of these questions, and the last one was beautiful 😉 !
I am sure you are a great teacher because you never hesitate to do anything!

• Thanks Yusra! That’s very nice of you to say. I really appreciate all of your great questions that always get me thinking!

Miss Dunsiger

• No problem! I am glad that you make daily posts so I have thinking in my daily routine 😉

• I try, Yusra! I’m not always daily, but I do tend to blog a lot. 🙂 I appreciate you always getting me thinking!

Miss Dunsiger

• Makes you feel any better, you sure do it way more than me! 😉

• Thanks Yusra! I tend to blog as part of my reflection process. I guess that I’m doing a lot of reflecting! 🙂

Miss Dunsiger

• Sure thing!

2. Aviva, I am a sucker for fractions as I have spent most of my math career studying it. Love the activities that you have introduced. I think a lot will come down to the questions you ask to bring out the main ideas. Part-whole relations is the main thing that holds students back. They often think of a whole number system versus a rationale number system (see 1/2 as 1 and 2 not a relationship). This is hard for many students. I found the Mariyln burns fraction kit to be the best to start the ideas flowing but have the kids build the kit. It brings a lot of concepts that you mentioned. Also by building it a lot of miss conceptions come out. When I taught I would spend two days just building this kit and then play the games associated with it. You could do that then your activities you have here or the other way around.

You also want to think about the stages of development. Students go through about 5 stages. 1) students develop a sense of breaking things apart (division is related to fractions) it’s not even or close but if I have one thing and three people I have three pieces. 2) understand fair sharing 3) use the half to do other fractions- if I half a half I get 1/4- they will also attempt to do this with odd denominator fractions and realize they can’t 4) measure for odd denominator 5) realize that you can divide and multiply.

Sorry for the long ramble. Overall your ideas are great as usually. I would play some games and keep asking those great questions.

• Thanks for the comment, Jonathan! As usual, you’ve REALLY got me thinking. I’ve never even seen the Marilyn Burns fraction kit. I just Google searched it, but I’m not getting a good link for what’s inside. Do you have more information that you can share? Since you said that you’re a sucker for fractions, I thought I’d ask. 🙂

I’m really stuck here, as I’m trying to complete a diagnostic assessment for fractions by Tuesday (tomorrow’s Monday :)) and I’m not ready to start fractions yet. My original plan was just to give the students the assessment, have them do it, and then move back to measurement. The problem was that I felt as though I was setting the class up for failure. That’s when I changed my plan and created these activities. My hope is that they’ll get the students thinking about some of the main concepts associated with fractions before they complete their independent assessment. I want to be able to walk around, listen to the students, and ask questions to get them thinking more in terms of fractions and seeing where each of the students are at. Could this work?

Based on timing, I’m thinking that this is my best plan for tomorrow, but then when I get into fractions later, maybe I should be looking at the Marilyn Burns Kit first, followed by more real world problems to get the students applying what they learned. Hopefully by then I can find myself a Marilyn Burns Kit to see. 🙂 What do you think? What would you suggest?

Thanks Jonathan!
Aviva

• The u it I sent you starts with it and provides the questions, big ideas, possible problems. Like I said I really love fractions. The kit is pretty much five strips of construction paper maybe 10cm wide and 30-40cm long. I have them in different colours (need whole, 1/2, 1/4, 1/8, 1/16) I also do ones for 1/12, 1/6, 1/3, 1/9, 1/5, 1/10 because in fives we do that but they will not work for the games. Of you have the Mariyln burns fraction book all there, I can scan some for you on Monday. I also had some great pre and post questions in the unit.

Have you done division? I would do that first but it also ties into measurement nicely, especially the idea the idea if iteration (breaking a whole into consecutive equal parts).

As for teaching before the pre test it all depends on what you are doing. Are you trying to see what they know? (Probably not much: the problems are always the same, which I think is quite funny’ another debate and topic). If that is the case let them do the pre without instructions. If you want to give some provocations first, don’t say anything and then give the pre, might be interesting. Would then have a talk afterwards.

I do love the fraction kit though, I have had such rich talk with it that I just do it. It’s also my whole thesis.

Does that help?

• Thanks for the help, Jonathan! I didn’t realize that the unit that you sent me was tied to Marilyn Burns. Thanks for sharing some more of what to include. I’m definitely going to need to investigate this more before we do fractions.

We’re moving to multiplication and division next, and I really want to do these units before fractions. I agree with you that they’ll be helpful.

As for the assessment, it is a diagnostic (of sorts), but it’s as much about proportional reasoning as fractions. That’s why I want to give some context. I’m thinking that I’ll use the problems as provocations, then do the assessment, and then follow-up with a discussion of the problems (and a consolidation of learning). I know that we tweeted a bit about this, and I think this plan will work. What do you think?

Thanks again!
Aviva

• I think that will work quite nicely. I think the importance is in the discussion. If you need the data for other things then so be it.

• Thanks Jonathan! I think that the discussion piece is important too.

I’m excited to see how tomorrow goes!
Aviva