1. Welcome to …

2. TODAY’S AGENDA SMP’s – Examples
A Pizza Problem (Re-engaging our norms)
BREAK
Understanding Division in the CCSSM
LUNCH
Thinking more about Division
Extending Children’s Thinking
Fractions Walk-Across
SMP Reflections
PASS OUT NOTE PADS and explain that these pads are to jot down pedagogical and mathematical connections they make…then later they will be given time to reflect on their own connections.

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.
Gabriel – Have teachers look at their SMP pages we passed previously and state an exemplar of evidence from a student enacting the SMP.
Be thinking about examples you can write about students

4. A Pizza Problem
Eight adults and three children are splitting an extra-large pizza. The three children all get the same amount as one another. The adults also eat the same amount as one another but each adult eats twice as much as one of the children. How much of the pizza does one adult eat?
Day 1 handouts page 2
Ask teachers to share solutions and discuss ideas
Note: Part of the task here often becomes in engaging students in thinking about representing the answer. Some students will come up an answers like, 2 pieces, or 8 pieces, based on the way they split the picture. The problem allows us to discuss how bringing in the total is necessary since the number of pieces does not describe how large each piece might be.
Ask teachers to think about the following question” What do the solutions to this problem have to do with multiplicative and divisional understandings?”

5. Revisiting Our Norms
Look over the “Revisiting Our Norms” handout discuss these 3 questions as a group: Do these still make sense for us? Any additions? Any deletions?
Gabriel: Give the teachers a copy of the “Revisting our Norms” handout.

6. 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.
Gabriel - Make any agreed upon revisions to the norms

7. 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

8. 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

9. Break Time 1

10. Fractions – Division Connections
Use the snap cubes to represent 3
Observe how teachers represent, pull out examples of partitioning methods.
Ask, which one is the correct way to divide and why?

11. Fractions – Division Connections
Group Size Unknown (Fair Share/Partitioning)
The pet kennel has five puppies and 40 treats. How many treats would each puppy get if they were to each get the same amount?
Kendra paid 42 cents for seven apples. What was the cost for each apple?
Have the teachers answer these mentally then devise a statement as to “why” these problem types might be called “Group Size Unknown”
In these question types the whole is known and must be partitioned into a known number of groups, to find the “size of each group”.
Ask teachers to write down the division problem represented by each problem

12. Fractions – Division Connections
Number of Groups Unknown (Grouping/Measurement)
Kendrae has 42 apples. He put them into bags containing three apples each. How many bags did he use?
Blanca walked 24 miles at a rate of 3 miles per hour. How many hours did this take Blanca?
Have the teachers answer these mentally then devise a statement as to “why” these problem types might be called “Number of Groups Unknown”
In these question types the whole is known and must be measured off into groups of a known size to find the “number of groups”.
Ask teachers to write down the division problem represented by each problem

13. Fractions – Division Connections
Group Size Unknown (Fair Share or Partitive)
Number of Groups Unknown (Grouping or Measurement)
Day 1 handout pages 4
The ideas in this introduction to division will be thought about again throughout the two weeks in various other mathematical capacities.
To the presenter: At the moment, the connections between division and fractions have yet to be ferreted out, but this will be developed more on subsequent days.

14. Fractions – Division Connections
Hand Out
Five friends go on a hike together. One of the friends brought along 30 strawberries. How many strawberries would each person get if they shared them equally?
A class of 36 students travels together on a school fieldtrip. The teacher wishes to divide the students into tour groups of 9 students. If each group needs one student leader, how many student leaders will there be for the tour?
Pass out page 4 of handout and ask if directions 1-3 are clear?
Have teacher’s present their ideas and discuss solutions, problem types, and children’s thinking
Pass out pages 5 and work through
Pass out page 6 – read and discuss

15. Fractions – Division in the Common Core
Consider: “Suppose four conference speakers are giving a presentation that is 3 hours long; how much time will each person have to present if they share the presentation time equally?”
Day 1 handout page 7

16. Fractions – Division in the Common Core1

17. Lunch

18. 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.

19. 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

20. 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

21. Understanding Division
Handout Page 9
Let’s take a step back and explore the standard algorithm and think about what is happening:

22. Understanding Division
Handout page 10

23. Understanding Division
Handout page 11

24. 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

25. Break Time 1

26. Task
“There are 6 candy bars for 8 children to share. If each child got the same amount, how much would each child get?”
Solve the task individually. After you solve it one way, try to solve it using another method.
Handout Page 13
Sherry Lane

27. Extending Children’s Mathematics: Fractions and Decimals
Read pages xvii – xxiv (stop at “Looking Ahead: What you Can Expect from This Book”)
Answer the discussion questions individually.
Share your answers with a partner

28. Susan Empson Video

29. Young Mathematicans at Work
Read pages 21 – 35
Read assigned passage
Form groups of Each person shares their reading with the group.
Whole group discussion

30. Walk-Across Groups Group 1 Group 2 Group 3 Rebecca Nottke
Heidi Rosekelly
Lisa Simon
Megan Burch
Sarah Cassel
Char Claus
Becki Webster
Andrea Berlin
Tammy Didion
Erin Coles
Dana Pitcher
Lorna Robbins
Janelle White
Mary Towns
Thomas Borton
Group 4
Group 5
Group 6
Jami White
Terren Paine
Holly Blanton
Deb Coffey
Robin Meyers
Cindy Souter
Linda Poggiali
Sarah Roth
Jackie Betzel-Conrad
Kathy Fulkerson
Sharon Ruggles
Hilaria Walton
Kendra Schweck
Mary Doerner
Jacqueline McClune
Pass out the K-5 CCSSM Content Standards.

31. Develop a Walk-Across for Fractions K-5
Assignment: What is a “Walk Across for Fractions?” It’s a focused look at mathematical connections in the CCSSM:
1) You will demonstrate what connections you can see in the standards across the domains and grade levels.
2) You will explain how a standard connects with prior and/or subsequent standards regarding students’ development of fractional understanding?
They will need to really consider the meaning of the Common Core content standards and concisely develop ways of showing what we want students to know and do and how that connects to prior and subsequent content.

32. Develop a Walk-Across for Fractions K-5
FIRST: To begin, you should give attention to each standard, regardless of domain, and consider whether or not it pertains to ones understanding of fractions. You should only include standards that DO pertain to either development of pre-fraction ideas or directly to fractions themselves. You may find many standards not in the fraction specific CCSSM domain that also act to build fraction sense.
SECOND: Once you find connections among standards, articulate an explanation of how they are connected. Do some standards prepare students for future standards? How so? Show what students would be doing and thinking in one standard and explain how that doing and thinking prepares them to do and think about future mathematics. When explaining connections among standards use the names (for example 3.G.2).
THIRD: There is a large creative element to this task. You may display and explain the connections in any creative media you choose. It can be as formal as a word document, excel sheet, or power point. Or as informal as a large scale painting, video, or drawings. The only delimiters that must be satisfied are 1) and 2) above. That will most likely require text or comments in some form or another.
Handout Page 14

33. Time of Reflection
Take a few moments to reflect on SMP’s connected to the content tasks we did today. -- Name of the task and related SMP’s -- Evidence for the chosen SMP’s -- Jot down how you contributed to our shared community of professionals and what mathematical and/or pedagogical knowledge you are taking away from today.
Handout Page 15

34. Stay Safe Please help us put the room in proper order.
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