1. E XPLORING A LGEBRA AND THE O PERATIONS Session 1 - Noticing

2. Four Corners Corner 1: “Whatchoo talkin’ ‘bout Willis?” Corner 2: I know what this means, and I kinda like this stuff. Corner 3: I have some idea what this means, but I could not give you an example.. Corner 4: I know what this means, and I have an example. Representational & Numerical Proof

3. Four Corners “ At ease” I know how to do this but it is not my choice kind of like changing a tire “Confident” ask me anything…I got this “Nervous”; we could skip this part “Steady”; I will make mistakes and stumble through but I am okay with that What feelings are associated with these terms?

4. Connecting Arithmetic to Algebra

5. Session Goals To consider using the algebraic reasoning about operations as a vehicle for promoting classroom discourse and reasoning. To engage with SMP # 2 and 7 deeply and develop an understanding of each

6. Reflect How might asking questions that we don’t know the answers to about how the operations work help us to deepen mathematical proficiency? What role do teachers play in getting children to notice regularity? How might exploring generalization and conjectures develop proficiency with content and mathematical practice?

7. Agree or Disagree? Asking questions that we don’t know the answers to about how the operations work will help us to deepen our own mathematical proficiency as well as the proficiency of the students we teach.

8. Agree or Disagree? Students always notice regularity without a teacher intervening.

9. Agree or Disagree? Exploring the conjectures of students can confuse other student and lead them down a road to misconceptions.

10. Math Activity Agree upon a definition of an even & odd number Feel free to revise these definitions to be more precise as we continue to work

11. Math Activity Be sure to create representations as you work. Number sentences must be justified using representations. Can you create representations that would justify any number?

12. Math Activity Recording Conjectures We do not need a slide for this but after they work let’s get a few of the conjectures up on charts for discussion. I will try to have doc cams so that we can view representations

13. Noticing What would a teacher need to have in her tool belt to be able to “notice”?

14. Noticing

15. Preparing to Notice Go Collecting Close to 100 Travel Riddles

16. Homework Your assignment is to visit grade 3 classes and pay attention to what children say. During our next visit we will want to share what we noticed.

17. Homework Grade 3 Addition and Subtraction