Constructing Viable Arguments

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SWBAT construct viable arguments and critique the reasoning of others.

Big Idea

In this lesson, students will engage with Mathematical Practice 3 by investigating how to best arrange trapezoidal desks in a classroom.

Do Now

5 minutes

Based on conversations with students, the most important expectation they have from a teacher is respect. However, when I ask them to describe what this means, they have difficulty verbalizing what respect means. In this Do Now, students come up with their own definition of respect. They also describe suggestions for ensuring that all students and teachers in the class are respected. Each student writes his/her answers on an index card.

This discussion is important to have in order to set up a classroom where students feel safe voicing their opinions and comfortable critiquing other students ideas and work.


8 minutes

In this part of the lesson, we discuss Mathematical Practice #3: Construct viable arguments and critique the reasoning of others.  We break the practice down into its components and define each word. The word construct has several meanings, especially in mathematics. In future lessons, students will learn about geometric construction; however, in this context, constructing means something different. Constructing viable arguments involve taking a stance on a topic and providing evidence for reasoning.


I then ask students what it means to critique something. We discuss how to evaluate someone else’s thinking in a respectful way.


In this lesson, students investigate different ways for arranging the desks in the classroom. They have to design a seating plan and then explain why their plan is the best for the classroom. At the end of the lesson, students will critique other students’ plans.


To begin the activity, I show a short video explaining the task. Then I instruct students to choose a group of students to work with. Since this lesson is early in the year, I prefer for the students to make their own choices about who to work with. This way I am able to see which students are friends and how well they work together. In the activity section, I give an explanation of the specific task.



22 minutes

Students begin the task with their group. Since the desks in the room are trapezoids, I give students trapezoid pattern blocks to help them with their plan. They try out different arrangements and draw a rough draft of their plan. After about 10 minutes, I give students poster paper to draw their final design. 


Because this is a quick activity, I instruct the students to take on different roles. Two group members draw the final plan on the poster paper while the other students work on writing the explanation of why they chose their design and why it is the best arrangement for the classroom. Since the space on the poster is limited, I give students a piece of loose-leaf paper to write the explanation, which will be taped onto the poster later.


After 10 minutes of working on the poster, students are told to hang their poster on the wall. I usually give students a 2 minute warning before they have to hang the poster.


10 minutes

Gallery walk: Each student looks at another group’s poster. They write down two positive aspects of the group’s seating plan and one way in which the arrangement can be improved. This is the part of the lesson where students critique other students’ plans.