EXPLORING ALGEBRA AND THE OPERATIONSSession 1 - Noticing

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

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?

Connecting Arithmetic to Algebra

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 ConjecturesWe 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”?

Noticing

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.

Homework

Grade 3 Addition and Subtraction