1 Math CAMPPP 2012 Breakout 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 2

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. 3

Session Agenda Listening : Why? How? Who? Learning Activity - fraction concepts and the area model - fractions and algebraic reasoning 4

Classroom Vignettes 5 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? 6

Math Talk Learning Community Read the Research Synopsis –High light key ideas –Review the Action Trajectory 7

Wonder What is the role of Listening in a Learning Community ? 8

Interpretive Listening Create a Frayer Model for Interpretive Listening. 9 Interpretive Listening DefinitionCharacteristics ExamplesNon-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 10

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 operator ex. is 2 plus, it is also 2.5 ex. is 3 divided by 5, it is also 3 times, it has a value of 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  +  7x+3x 12

Reasoning about relationships… 13 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 14 six groups of two and two thirds…

Distributive Intuition 15 6 groups of 2 6 groups of 2/3 12 4

Introduction to Area Model From Counting Groups / Arrays To Measurement Dimensions / Area = 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 17

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 18

Learning Activity Work through the questions as a group Practice Listening and Questioning to understand and build on each other’s thinking –Students: Listening / questioning to learn –Teachers: Listening/questioning to understand and push thinking Record your thinking on chart paper 19

Student Instructions 1. Represent 144 using the base 10 blocks. Show several different arrangements. Write equivalent expressions that reflect these arrangements. 2. Now suppose the big square represents 1. What do your arrangements illustrate? 3. Now suppose the big square represents x 2. What do your arrangements represent? 20

Consolidate Teacher consolidation or Gallery Walk 21

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? 22