##
* *Reflection: Rigor
To Be a Fraction, Or Not To Be, That is the Question - Section 2: Active Engagement

Using sentence frames for the videos would have helped raise the rigor of the activity. The students did a good job explaining what was in their art, but they could have described why the pieces were or were not fractions. Had I given a prompt for them to use, all of us would have dug deeper into understanding. Students understanding of fractions, mine of what my students know and what might still be challenging.

If you try this activity, supplying your students with sentence frames such as:

I cut________ into _________equal pieces and that is why they are named ________________.

These pieces are not fractions because___________________________.

For some students shorter or more explicit sentences, with one statement at a time, might be more effective. For example, the first sentence frame above could also be done this way:

I cut (name of shape) into _______ equal pieces. I counted all of the equal pieces. I have _______ equal pieces. I know that when a whole is _______ pieces, the pieces are called ____________.

*More Organization*

*Rigor: More Organization*

# To Be a Fraction, Or Not To Be, That is the Question

Lesson 2 of 3

## Objective: Students will be able to communicate their understanding of what a fraction is and is not by creating a video using their artwork as examples.

## Big Idea: Using technology and art to engage students in the concept of "equal parts" of a whole as a fraction is the goal of today's lesson.

*60 minutes*

#### Mini-Lesson

*10 min*

To begin the lesson today, I ask the children to put out the artwork they created as homework the night before. Their task was to use whole, halves, fourths, and eighths of the same size circles to create an image.

Students take a minute to organize the display of their work, and then tour the classroom to view everyone's "art". I remind them that this is art, and they need to look not only at the art, but to think about the fractions. After 2 minutes, I ask the children to gather.

As they finish and return to their seats, I choose two different student pieces to discuss as a whole class. One of the art pieces, while beautiful, is made of various shapes, none of which are fractions. This lesson is all about attending to precision, which is Mathematical Practice 6. That is why I spend so much time in this discussion.

The other design has some fractions and some "pieces" of a whole.

I ask the students to think about these pieces of art, and then discuss and defend their thinking with the class. The student in this video is explaining how he understands halves.

I also interview the artists in order to give them the opportunity to revise their thinking, as you will see in this clip. The opportunity to revise thinking and communication is the best learning there is. If we don't supply this time for students, the chance to learn deeply in a meaningful way is lost.

(Don't be distracted by the SlideStoppers on their desks. Those are an invention of mine to help organize and prevent supplies from falling off the lift top desks.)

*expand content*

#### Active Engagement

*25 min*

Discussing, and showing examples, of what is not a fraction is just as important as thinking about the criteria of a fraction. I challenge my students to use their own artwork to think in that way as they teach others about fractions using the application ShowMe.

This is a video for you on how to use the ShowMe app. If you have not had your students do this, I create an account that they all sign into so I can access their videos. I also have the students take photos of their work with their iPad, and then access it through the ShowMe app. That way, if there is a mistake, the photo is not lost.

In this project, I am looking for students to be able to explain why their pieces are fractions, or why they are not fractions. Understanding the equal parts and unit fraction is a fundamental phase of understanding fractions and is critical to future work with this concept, so don't go too fast through this seemingly simple step.

In this ShowMe, the student is teaching us that his piece is made of all fractional pieces. I am glad he drew the other half of the whole and explained that fractions have to be equal.

The student in this video figured out how to create 16ths and used them in his project. This is a great assessment for me and discussing with him how he did it will be my conferring topic with him in the next session. I also love his new word, "unfractional"!

*expand content*

#### Journal Response

*15 min*

As students complete their ShowMe video and are waiting for a partner to share with, I ask them to record in their journals what a fraction is and is not. This record includes words and pictures. Writing to convey understanding in math is a critical skill, set as well as another way to communicate understanding and to use the vocabulary in a different way.

*expand content*

#### Wrap Up

*10 min*

In order to celebrate their videos and the learning of equal partitions of a whole to create fractions, I have students share their videos with each other in a casual way. Sometimes just letting them share without an assignment frees them to revise as they see fit.

In our next lesson, I will have several students share their videos with the class and we will discuss what was helpful in learning the concept of fractions, and what could have been done to improve the video as a teaching tool.

We will also ask other second and third grade classes to view our videos and let us know what they learned.

*expand content*

*Responding to Sara Mangan*

Hello Again!

Yes, you absolutely can use any of my materials and thank you for citing!

There are a few things I would suggest about the "talk" in math class. I actually spend time "teaching" it. I walk students through different situations modeling just talk, math talk, and explanatory talk. I promise you if you walk around with a recording device, or better yet, let them record their thinking...their conversations will lift.

I teach parts of a whole first, then parts of a set, then comparing and equalizing fractions, then converting. My lesson plans-units 5 through 8 run in the order I teach. I also have some assessment ideas in Unit 8.

I hope this helps

| 24 days ago | Reply*Responding to Michelle Marcus*

Thanks for your quick reply. I have a few more questions for you if you don't mind. I have been looking through your lessons and there are pre-test, worksheets, etc. to download. Can I use those in my future classroom and for school assignments? I would cite my source of course.

Right now I am a para in a 6th grade math class. I am constantly asking my students questions. I want them to be able to explain to me WHY they got that answer, so watching these videos is so great because I believe so much that this is how students really learn.

One final question, when you introduce fractions do you teach parts of a whole first? If so do you then teach parts of a set or fractions on a number line? I am trying to figure out which concept is hardest for students to grasp so I can introduce that last.

I a working on an assessment project and we have to plan one week of lessons for anything we choose. I am probably putting too much thought into this but I want it the best it can be so I can use it someday in my future classroom.

Thanks again for your time.

| 24 days ago | Reply

*Responding to Sara Mangan*

Hello Sara! Thank you for the kind feedback. I spend about 25 days on fractions. Yes, the students are able to speak well about their thinking and learning. I make discourse the most important part of our lessons.

Good luck with your grad work...I know how consuming that can be!

| 24 days ago | Reply*I enjoy all of your math lessons on fractions. I am currently in grad school to get my teaching license. How many days do you spend on your 3rd grade fraction standards? I feel like fractions are very difficult for students to grasp. I am amazed when you video your students how good they are at figuring out fractions and explaining concepts back to you. | 24 days ago | Reply*

*expand comments*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities