Exploring Algebra and the Operations

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# Exploring Algebra and the Operations - PowerPoint PPT Presentation

Exploring Algebra and the Operations. Session 1 - Noticing. Four Corners. Corner 2: I know what this means, and I kinda like this stuff. Corner 1: “Whatchoo talkin’ ‘bout Willis?”. Representational &amp; Numerical Proof. Corner 3:

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### Exploring Algebra and the Operations

Session 1 - Noticing

Four Corners

Corner 2:

I know what this means, and I kinda like this stuff.

Corner 1:

“Whatchoo talkin’ ‘bout Willis?”

Representational & Numerical Proof

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.

Four Corners

“ At ease” I know how to do this but it is not my choice kind of like changing a tire

“Nervous”; we could skip this part

What feelings are associated with these terms?

“Steady”; I will make mistakes and stumble through but I am okay with that

“Confident” ask me anything…I got this

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
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?
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.

Agree or Disagree?

Students always notice regularity without a teacher intervening.

Agree or Disagree?

Exploring the conjectures of students can confuse other student and lead them down a road to misconceptions.

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

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?

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

Noticing

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

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