exploring algebra and the operations
DESCRIPTION
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: - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/1.jpg)
EXPLORING ALGEBRA AND THE OPERATIONSSession 1 - Noticing
![Page 2: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/2.jpg)
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
![Page 3: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/3.jpg)
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?
![Page 4: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/4.jpg)
Connecting Arithmetic to Algebra
![Page 5: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/5.jpg)
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
![Page 6: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/6.jpg)
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?
![Page 7: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/7.jpg)
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.
![Page 8: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/8.jpg)
Agree or Disagree?
Students always notice regularity without a teacher
intervening.
![Page 9: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/9.jpg)
Agree or Disagree?
Exploring the conjectures of students can confuse other
student and lead them down a road to misconceptions.
![Page 10: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/10.jpg)
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
![Page 11: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/11.jpg)
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?
![Page 12: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/12.jpg)
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
![Page 13: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/13.jpg)
Noticing
What would a teacher need to have in her tool belt to be
able to “notice”?
![Page 14: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/14.jpg)
Noticing
![Page 15: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/15.jpg)
Preparing to Notice
• Go Collecting• Close to 100• Travel Riddles
![Page 16: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/16.jpg)
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.
![Page 17: Exploring Algebra and the Operations](https://reader035.vdocument.in/reader035/viewer/2022062501/56816112550346895dd06dcd/html5/thumbnails/17.jpg)
Homework
Grade 3 Addition and Subtraction