Series: Engaging All Students in Common Core Math


Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP3:  Construct viable arguments and critique the reasoning of others.

    Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and--if there is a flaw in an argument--explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Download Common Core State Standards (PDF 1.2 MB)

Using Extroverts
Lesson Objective: Engage students in constructing and critiquing arguments
All Grades / All Subjects / Engagement

Thought starters

  1. How does Mr. Pack use his knowledge of students to inform his teaching?
  2. How does this strategy engage students in constructing arguments and critiquing the reasoning of others?
  3. How does Mr. Pack adjust his teaching for both extroverts and introverts?
Mr. Pack's choice of students goes beyond looking to those who are "on Stage" and it should be emphasized that it is not uncommon to find introverts on stage. That is, often people misunderstand introverts as those who are shy or uncomfortable in public settings. Shyness has nothing to do with being an Introvert. Introverts are not necessarily afraid of people. What they need is a reason to interact. They don’t interact for the sake of interacting. I share this as an introvert who is both teacher and former international musician who has performed in front of groups well above 5,000 people; including solo performances with no band to hide behind.
Recommended (2)
I certainly see the benefit of channeling the energy of the more lively students in class. I am curious however, as to how I can go about doing this with a select few of my extremely energetic students who love to speak in class, but for the purpose of turning the conversation towards off topic subjects and buffoonery.
Recommended (1)
Good strategy. It seems to make the class more fun, while staying with the topic.
Recommended (0)
I can see this working in kindergarten. 5 year olds love to be either a "here I am" person or "leave me alone" person. In differentiated learning since I am working with small groups, the quiet kids are apt to speak up knowing there are only 5 kids in a group. In time, maybe they will feel more comfortable speaking in larger groups.
Recommended (0)
Yep, the extroverts really are a lot of help. They're willing to help in order for a class discussion to move along.
Recommended (0)


  • Using Extroverts Transcript

    Chuck Pack: If you're looking for a strategy in how to engage students in Mathematical Practice.

    Chuck Pack [in

    Using Extroverts Transcript

    Chuck Pack: If you're looking for a strategy in how to engage students in Mathematical Practice.

    Chuck Pack [in classroom]: What is our lesson today?

    Student: How tall is our flagpole?

    Chuck Pack: Using an extrovert is a good technique for doing that.

    Chuck Pack: It's always good to have students come to the board. High School students, I know, are hesitant, often to jump up and say, "I want to come and draw in front of my peers." If you identify a student in your classroom who's an extrovert, who's used to being on stage, loves to be in front of students - that will be helpful to you. And, Cooper is certainly that young man in our classroom. He was happy to stand up in front of the others and draw. And he's also one who is not gonna be crushed by some peer criticism and having others judge his reasoning. It's one of our mathematical practices. Critiquing your own reasoning and the reasoning of others. You can do that with the students and your introverts that are sitting --- that do not want to --- are very shy, do not want to be exposed, can watch other students engage in that behavior.

    Chuck Pack [in classroom]: Thank you, Cooper.

    Chuck Pack: And your introverts, you can work on your practice with them in more of a close setting. A 1 on 1 or more of a small group. And allow them to show their reasoning and practice their skills. This is a good strategy. Using an extrovert -- using extroverts and knowing --- having knowledge of who your students are.


School Details

Tahlequah High School
591 Pendleton Street
Tahlequah OK 74464
Population: 1183

Data Provided By:



Chuck Pack



All Grades / All Subjects / Tch Tools

Lesson Idea

Grades 9-12, All Subjects, Class Culture

Lesson Idea

Grades 9-12, ELA, Class Culture

Teaching Practice

All Grades / All Students / Class Culture