##
* *Reflection: Grappling with Complexity
Each Orange Had 8 Slices - Section 3: Exploration-Posters Phase 1

As they work to represent the math on the page, I will be specifically watching for how students approach the problem. At this time I still have some students counting the objects by one's without using skip counting, students seeing the multiplication but representing it with the wrong equation, thus not understanding the "group size" concept, and many students understanding the relationship between multiplication and division. How they choose to model the math found in their poster will tell me several things about their understanding and approach.

However, since they are working in partnerships, listening in on their discourse will be just as valuable. It is during discussion time that many students grow their strategies, as they hear and see the thinking of their classmates.

*What do students do?*

*Grappling with Complexity: What do students do?*

# Each Orange Had 8 Slices

Lesson 5 of 15

## Objective: SWBAT demonstrate multiplication as equal groups inspired by the colorful riddles presented in Each Orange Has Eight Slices.

#### Engage

*5 min*

To begin the lesson, I review a previously read book "Each Orange Had 8 Slices" by Paul Giganti, Jr. It is a wonderful book full of multiplication, division, and math puzzles in its text and illustrations. As we have already shared the book as a piece of literature, I tell students our purpose today is to look for the math:

*Mathematicians, as you remember, last week we enjoyed this book, "Each Orange Had 8 Slices". We loved the illustrations, especially the one with all the quacking ducks! Today, we are going to do a really fun activity with this book. Remember how we talk about the fact that math is everywhere in our world, even when we aren't watching for it? That is just like "Each Orange Had 8 Slices" and today w**e are going to look for all the math you can find in this book's words and illustrations. Can you join me at the community area in a circle for your directions?*

#### Resources

*expand content*

#### Mini-Lesson

*10 min*

During the mini-lesson, I have chosen to use the teacher move of **fish-bowling**. The students will be in a half circle (the fish bowl). I will be in the center with another student. During this time, we will act as partners to model the activity.

*Okay boys and girls. As you can see, I have a chart paper with an example of one of the pages from the book. I also have some sentence starters and frames on the floor. My partner and I will work with all of these to come up with the math we see. First we will talk about what we notice. Then we will decide together how we want to display our thinking on the chart. Keep in mind that the other groups will be touring the room halfway through to see our work. We will want to be thoughtful and neat in our drawings and writing. *

*Okay partner, let's discuss what we notice on our picture.*

Use the talking moves and model responses during this part. Move through it quickly, but take time to hear the student's responses to guide them to careful and rigorous work.

*Yes, I see that there are 3 bikes with 3 wheels too! How should we write that on our poster? *

*Boys and girls, can you tell me what you noticed about our work? What did you see and hear?Wonderful noticing. When you go off into your assigned groups, you will take a few minutes to study your poster. Then decide together how you will represent your ideas. Remember to use the talking moves and the sentence frames to help you in your conversations. *

#### Resources

*expand content*

#### Exploration-Posters Phase 1

*15 min*

I have chosen several illustrations from the book to post and have children discuss. Student partnerships go to their spots to begin working. As students discuss the posters, using the sentence frames and talking moves that are posted throughout the room, I circulate using guiding questions and prompts to get students started (MP3 & MP4). I then step back and listen in on conversations.

You may want to insert comments here and there as students work. I try to stay out of their conversations, really watching for what they can do on their own in order to assess their level of understandings/misconceptions.

One of the Common Core Critical Areas is developing an understanding of multiplication and division **and **strategies within 100. This lesson has students grappling with both and gives them an opportunity to work specifically with the "equal group size" concept.

*expand content*

#### Exploration-Posters Phase 2

*15 min*

Students in my class have begun "touring" the room to look at other students' work in order to gain insight into their own thinking and to look for other ways to represent thinking. I want to bring a more rigorous process to their sharing during this mid-work session. I have the students turn to listen to my instructions, then I will send them off to tour the posters with a task to accomplish.

*Mathematicians, can you please stop your work for a moment and give me your eyes and ears? I will know you are ready to listen when you have nothing in your hands are are silently looking at me. Thank you. *

*In a moment we are going to tour the posters. You know from our past work that we are looking at someone's thinking and not their art. Your job is to act as a teacher and a learner. *

*You will take some sticky notes and make comments on the thinking work. There are sentence prompts on the wall for you to place your notes on. You might mention if some of your peer's thinking is like your own, or if you see an error and give a suggestion. Maybe you will mention that you learned something new from them. *

*We will not tour all of the posters, maybe just one or two. Please approach a poster that no one is at and begin your work. When you are ready to go to another poster, look for an available one. I will give you a signal when it is time to go back to your own poster to resume your work with your new knowledge and ideas. *

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#### Elaborate

*15 min*

I give students time to share their completed posters at this time to the group. We are still learning to share "thinking" as opposed to the art of the poster, so I will prompt and guide the discussion here. When a partnership completes their sharing, they will ask for one compliment and two questions (MP3).

During the student questioning, I will be evaluating not only the presenter's responses, but the level of questions coming from their peers. These observations help guide me in our next learning steps and define misconceptions and abilities that I need for planning lessons going forward.

*expand content*

#### Explain and Evaluate

*15 min*

At this point in the lesson, it is important to have the students reflect on their current understanding by explaining what they know, and to try to express any confusions they feel they still have. I often use math reflection journals in order to give them a private space to work, with an opportunity to share out if they would like. Obviously, I read and discuss them all.

Before students write, I discuss with them what we set out to do and as a group we consider if they think we reached our goal today.

*Mathematicians, what was it we were working on today? What was our goal? Did we accomplish our goal? Why or why not? *We use our math talking moves to guide our responses

*Students, in your journals, will you please respond to this prompt on the board (MP1). "What was one really important thing you learned today? Also, what kind of work did your brain do? Find a way to show me your thinking". In a few minutes, I will call on volunteers (only) to share. *

#### Resources

*expand content*

#### Wrap Up

*5 min*

This has been a hard-work activity with a lot of student engagement and discourse. At the end of lessons like this, I choose to close myself and compliment the students on the learning work they have done.

*Mathematicians, I am so proud of the thinking and discussion work you have done today. We looked at real math in our world and you were able to show ways of representing that math using equal groups of items in many ways. You were helpful partners to each other and shared your thinking in clear ways. Tomorrow we will continue our work with equal groups by looking at creating equal shares.*

#### Resources

*expand content*

*Responding to Maria Ruiz*

Wow! Â Thank you so much. Â I hope you found it helpful:)

Â

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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

- LESSON 1: It's As Basic As That
- LESSON 2: Naming Arrays
- LESSON 3: Variables
- LESSON 4: X Represents Groups Of
- LESSON 5: Each Orange Had 8 Slices
- LESSON 6: Creating a Word Problem Book
- LESSON 7: Equal Groups on a Number Line
- LESSON 8: Collections of Equal Groups
- LESSON 9: Explaining Multiplication
- LESSON 10: The Story Of Multiplication Day 1
- LESSON 11: The Story of Multiplication Day 2
- LESSON 12: Making Equal Groups Part 1
- LESSON 13: Making Equal Groups Part 2
- LESSON 14: Associative Property
- LESSON 15: Associative Property With Manipulatives