##
* *Reflection: Developing a Conceptual Understanding
Definitely, Maybe - Section 1: Definitely, Maybe

When facilitating this discussion, I made the decision to create a rule that students could NOT ask questions that simply had yes or no answers. For example, I did not allow students to pose questions like, “is the picture showing a polar bear?”, “did two people exchange vows?”, or “is this a rectangle?” What this rule did was require students to think harder about the characteristics that would guarantee the polar bear was indeed a polar bear, for example, by asking “where does this creature live?” or “what might this creature eat?” As a result, students were able to get a clearer idea of the kinds of assumptions they can and cannot make based on what is given to them.

Because I barred questions with yes or no answers, something surprising happened when students got to the picture that showed a "square": some students decided to use rulers and protractors to measure. Some students even folded the rectangle along one of its diagonals to show that the diagonal was not a line of symmetry, therefore the rectangle could not be a square as well. This was an unexpected surprise, and I am glad that it came up because it continues to reinforce the transformational lens I want my students to use throughout their year in geometry.

*Important Decisions to Make When Facilitating the Whole Class Discussion*

*Developing a Conceptual Understanding: Important Decisions to Make When Facilitating the Whole Class Discussion*

# Definitely, Maybe

Lesson 1 of 8

## Objective: Students will be able to defend assumptions based on their reasoning. Students will also be able to define basic vocabulary needed for Geometry.

#### Definitely, Maybe

*30 min*

I use Definitely, Maybe to introduce students to deductive reasoning in an engaging way. In this activity, students separate given information from the assumptions they want to make as they must consider what information is needed to come to a conclusion. The task asks students to identify what they know to be true given a set of three images. Given each image, groups of four students write out what is given, what they can infer about each image, and what they might be able to conclude about each image if they had more information.

In the past, I have used a speech given at a wedding reception, a polar bear, and a geometric figure that appears to be a square but is in actuality, a rectangle -- all three of these images afford students many opportunities to have rich discussions about how to defend the conclusions they want to make.

I facilitate the Definitely, Maybe activity in three rounds:

- Pass out the same image to each group
- Have one student record on behalf of the group (a different student should record for each round)
- Facilitate a whole-class discussion with students sharing out their group's conclusion and how they know--this is an opportunity for students to share out their arguments and critique the reasoning of others (
**MP3**)

*expand content*

After our Definitely, Maybe discussion, I will pass out today's note taker. In my class, I ask students to maintain an organized binder. One of the sections in students' binder is strictly for maintaining notes such as these. Students begin to fill this section today. (I post an answer key for the notes on my class website everyday so that students who were absent or would just like to see my notes again can have access to them.)

I begin today's notes section by explaining the meaning of basic geometry vocabulary, and, teaching students how to write out information given in diagrams (like rays or line segments). I am also careful to demonstrate to my students how to mark diagrams. I like to establish conventions for using congruence symbols and congruence markings as early as possible. It is important to spend time on this because students need to attend to precision, as we begin developing the skills necessary for good proof writing (**MP6**).

**Teacher's Note:** I use the *Discovering Geometry* textbook from Key Curriculum Press for this Geometry course, so lessons denoted like "Lesson 1.1" refer to Chapter and Lesson headings from that textbook.

*expand content*

#### Practice

*20 min*

*Discovering Geometry* has lots of online resources to accompany each section in the book. The following PDF contains extra practice for the information covered in today's notes, along with other lessons in the chapter.

**Teacher's Note**: These resources appear to currently be available for free online, as I am providing them here. I contacted the publisher of record to confirm this, but I did not receive a reply.

#### Resources

*expand content*

##### Similar Lessons

###### Angles and Rotations

*Favorites(8)*

*Resources(17)*

Environment: Urban

###### Reviewing Geometric Models

*Favorites(7)*

*Resources(27)*

Environment: Rural

###### Circles are Everywhere

*Favorites(31)*

*Resources(24)*

Environment: Suburban

- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Definitely, Maybe
- LESSON 2: Who's a Widget? Making Sense of Definitions
- LESSON 3: Recyled Definitions
- LESSON 4: Investigating Special Quadrilaterals
- LESSON 5: Presenting Special Quadrilaterals
- LESSON 6: Special Quadrilateral Clean Up
- LESSON 7: Introducing Geometry Review and Group Test
- LESSON 8: Introducing Geometry Unit Assessment