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Math CAMPPP 2012Breakout Session 4A

Gr. 9-12

Session Goals

Participants will have the opportunity to explore, practice, and discuss:

• Listening and questioning strategies• The role of teachers and students in a learning

community• The connection between number sense,

fractions and algebra• How the area model supports math reasoning

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Group Norms

• All ideas will be listened to carefully and responded to respectfully.

• Everyone will have a voice.• All questions and comments will be presented

with the intent to move the collective forward.• Clarifying questions are welcome.• Everyone will engage fully in the moment.

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Session Agenda

Listening : Why? How? Who?

Learning Activity

- fraction concepts and the area model

- fractions and algebraic reasoning

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Classroom Vignettes

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• Watch this video

Jerry Sienfeld teaches History

• And this

Grade 8 : The Pythagorean relationship

What do you Notice?

What are the key differences between the two “classes”

What is the role of the teacher?

What is the role of the students?

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Math Talk Learning Community

Read the Research Synopsis

– High light key ideas

– Review the Action Trajectory

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Wonder

• What is the role of Listening in a Learning Community ?

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Interpretive Listening

Create a Frayer Model for Interpretive Listening.

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Interpretive Listening

Definition Characteristics

Examples Non-Examples

Learning Activity: Goals

1. To understand how work with fractions supports relational thinking and algebraic reasoning.

2. To explore the area model to represent part to whole relationships and fraction operations

3. To practice interpretive listening and responding as students and teachers

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Conceptual Understanding Matters

• “Fractions offer students the opportunity to grapple with fundamental mathematical relationships that constitute the core of Algebra”

• Tight integration of number and operatorex. is 2 plus , it is also 2.5

ex. is 3 divided by 5, it is also 3 times , it has a value of 0.6

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5

3

5

1

2

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2

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Extending Children's Mathematics Fractions and Decimals: Innovations in Cognitively Guided Instruction

By Susan B. Empson and Linda Levi

Reasoning about the unit….

Seven “units” plus 4 “units” gives 11 “units”

Grade 2 Grade 7 Grade 9

70 + 40 + 7x+3x

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37

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Reasoning about relationships…

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Extending Children's Mathematics Fractions and Decimals: Innovations in Cognitively Guided Instruction

By Susan B. Empson and Linda Levi

Reasoning about Multiplication

• Think of “groups of” and repeated addition

Ex. Multiply

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3226

six groups of two and two thirds…

Distributive Intuition

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3226

6 groups of 2

6 groups of 2/3

12 4

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Introduction to Area Model

• From Counting

Groups / Arrays

• To Measurement

Dimensions / Area

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4 + 4 + 4 = 12

3 x 4 = 12

Choose your Teacher!• Pick one person from your group to act as the

“teacher” for the next activity

• Teachers go away to “prep” the activity

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Question Stems for Students

• As a group, come up with a set of question “stems” that you will use as students during the learning activity

• Write your stems on a tent card at you table for quick reference

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Learning Activity

• Work through the questions as a group• Practice Listening and Questioning to build

on each other’s thinking• Students:• Teachers:

• Record your thinking on chart paper

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Consolidate

• Teacher consolidation or Gallery Walk

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Exit Card• Teachers: What did you notice about

listening / questioning while you were playing the role of the teacher?

• Students: What was your experience with listening / questioning while you were learning?

• Both: Do you have any Lingering Wonderings?

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