1. Welcome to Day Two

2. Agenda 5 Practices for Mathematical Discourse
Division – More ideas about engaging students in noticing the difference between “number of groups unknown” and “group size unknown”.
Special Divisions
Lessons and Reflection

3. The Standards for Mathematical Practice Student Reasoning and Sense Making about Mathematics
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Sherry – Have teachers look at their SMP pages we passed previously and state an exemplar of evidence from a student enacting the SMP. Ex. 1 is of SMP 2 – the student is contextualizing a mathematics problem to help solve it.
Ex. 2 is of SMP 8 – where the students looked for and expressed regularity in repeated reasoning.
Sherry – Tell the teacher to be thinking about examples you can write about students; Explain to Teachers that we will reflect for ourselves about the tasks we do and the connections and evidence of SMP’s, at the end each grant day.

4. Bring your ideas…
As a group of professionals we have made a commitment to helping children attain success in life and a voice in the world.
Many times the best part of these kinds of professional development is simply the chance to share ideas, raise questions, and work with other practitioners to improve our own understandings and practice.
Please bring your stories of children’s learning with you.

5. Our Socio-mathematical Norms
Listen intently when someone else is talking avoiding distractions
Persevere in problem solving; mathematical and pedagogical
Solve the problem in more than one way
Make your connections explicit - Presentation Ready
Contribute by being active and offering ideas and making sense
Limit cell phone and technology use to the breaks and lunch unless its part of the task.
Be mindful not to steal someone else’s “ice cream”
Respect others ideas and perspectives while offering nurturing challenges to ideas that do not make sense to you or create dissonance.
Limit non-mathematical and non-pedagogical discussions
Gabriel - Make any agreed upon revisions to the norms

6. Presentation Norms
Presenters should find a way to show mathematical thinking, not just say it
Presenters should indicate the end of their explanation by stating something like “Are there any questions, discussion, or comments?”
Others should listen and make sense of presenters’ ideas.
Give feedback to presenters, extend their ideas, connect with other ideas, and ask questions to clarify understandings
Gabriel - Make any agreed upon revisions to the norms

7. BREAK

8. Understanding Division
Anything Strange about this picture?
Mathematical Language - Quotient, Dividend, Divisor
Horizontal bar in a fraction 1/3 is called the “Vinculum”
The traditional division symbol 25 “divided by” 5 is called an “Obelus”.
Teacher Hats Off - I want you to step out of your mindset of teacher for a series of connected mathematics tasks. Let’s just make sense of these ideas together.

9. Understanding Division
Division: Learning through play
Handout Page 8
Play the leftover game. Short version with blue cards, snap cubes, and dice.
Start with 19 cubes- roll and divide. Put out that number of cards...etc
Then, play leftover game with divisor and factors.
After this exploration ask what way of thinking about division did this task focus on? ---Group Size Unknown

10. Can Pre-School Children think about Division?
Considering Division
Can Pre-School Children think about Division?
The case for “Number of Groups Unknown”
Recent research about spaces for number development
Share Breanna’s pre-school class story

11. Sharing and Discussing Ideas
When engaging students in thinking about ideas for themselves what are the necessary parameters that allow for authentic mathematical “sense-making”?
Other questions or thoughts from you?

12. Understanding Division
Division: Exploring with Snap-Cubes
Explain how young children can explore mathematical ideas involved with dividing through snap cubes
Can 12 be divided into groups of 2…by 3? What other numbers can twelve be divided by?
After this exploration ask what way of thinking about division did this task focus on? ---Number of Groups Unknown
Tell Breanna’s pre-school story about finding the connection between division and multiplicative factors

13. LUNCH

14. Understanding Division
Use four 4’s and any mathematical operation to find a result of 1 in as many ways as is possible.
Which team can come up with the most ways?

15. Understanding Division
Can we divide by any number?
Hand OUT Page 12
0/6; 6/0; 0/0 Use your understanding of the division types to make sense of the solutions to these divisions

16. BREAK

17. Math Content for our Classrooms
Each day we will spend time with grade level teams making lesson plans.
Each of us will make one plan that is part of a unit of plans the grade level team is working on.
Each plan must have the following:
Connected mathematics content focus from Ohio’s Mathematics Learning Standards
A focus SMP
Designed to Orchestrate Productive Mathematics Discussions (The 5 Practices)
Handout Page 15

18. Math Content for our Classrooms
Three checks must be made for the completion of lesson plans:
Check 1) Consult with Sandy and/or Mary about the mathematics content of the lesson and explain to her its mathematical appropriateness. When the lesson is complete Sandy, our resident mathematician, will sign off on its content (SMC’s).
Check 2) Consult with Sherry about the design of the lesson to promote mathematical discourse (5 Practices). Sherry must sign off on the lessons discourse elements.
Check 3) Consult with Dr. Matney about the design of the lesson having a focus Standard for Mathematical Practice. Dr. Matney must sign off on the lessons mathematics proficiency elements (SMP’s)
?Questions about COMP Lesson Plans?
Handout Page 15

19. On a sticky note tell us one thing you learned today.
Time of Reflection
On a sticky note tell us one thing you learned today.
Tell us one think you liked or one thing you are still struggling with.
Handout Page 15

20. Stay Safe Please help us put the room in proper order.
Please leave your name tents for next time.