Download - Exploring Algebra and the Operations
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