Section 2 - Construct Viable Arguments & Critique the Reasoning of Others

What does this look like with students?

This section helps the facilitator teach the skills of constructing justification of work and thinking and critiquing the reasons of others in more depth. Teaching techniques are used and students have non-math and straightforward math examples to practice these skills based on their grade level.

Below is a collection of activities separated by grade band to show you how you might begin developing these practices with students. There are both non-math and math-specific activities included below.  These are great activities to select from and practice with your students.  The skills in the lesson have been created to not cause great challenges for students, and instead focus on the Math Practice Standard.  If students are struggling, feel free to select a different activity or move to a different grade band. 

Grade Band Kindergarten - 5th Grade

In this section, for grades K-5, you will find several activities that promote the general practice of constructing ways to share and justify work & critiquing the reasoning of others.  While the activities may have solutions to them, they are designed to promote problem-solving, thinking, developing justification, and giving and receiving usable feedback from peers and the teacher/facilitator.  These are the characteristics that Math Practice (MP3) emphasizes.  Use these activities with this focus in mind as the learning and practice targets.  Each activity can be completed in a 5-10 minute lesson as a warm-up to generate thinking and discussion.

Grade Band 6th - 8th Grade

The activities for Middle School students allow them to practice making and defending choices. They justify thinking using actions, diagrams, drawings, speaking, or writing. Students listen to and read the ideas and work of others and decide whether they agree or disagree.  As students critique the reasoning of others they focus on what makes sense and what doesn’t. They provide examples and counterexamples.

Consider incorporating daily or weekly practice of these activities. Each of the following activities works well as a 5-10 minute warm-up and discussion.

Grade Band 9th -12th Grade

The activities in this HS section have the students thinking about constructing, justifying, and communicating ideas and listening, comparing findings, and identifying flawed logic. It is intended that the students will also ask questions for clarification or improvement of another student's work. Several activities promote these skills. The activities do not necessarily have ONE right answer, and rely on the students to justify their standpoint.

Please go to Part II: Student Practice

This part of the Math Practice Standard toolkit provides math-based activities to practice justifying and critiquing skills at the different grade levels. Students will have learned and practiced this skill in Part I and can now formalize their knowledge in Part II with specific math practice