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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:

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Presentation Transcript
four corners
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 corners1
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
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
  • 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
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 disagree1
Agree or Disagree?

Students always notice regularity without a teacher intervening.

agree or disagree2
Agree or Disagree?

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

math activity
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 activity1
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 activity2
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


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

preparing to notice
Preparing to Notice
  • Go Collecting
  • Close to 100
  • Travel Riddles

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.