Welcome to Day 1

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 and successes with you to share with others.

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

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

Agenda Welcome Back Number Talk CMI – Task, Video and Reading Division – What do we know? Lunch Division Tasks Reflection

Notebooks are 2 for $3; what is cost for 6 notebooks? Number Talk Notebooks are 2 for $3; what is cost for 6 notebooks?

Connecting Mathematical Ideas Task Pool Border 1. Determine the number of tiles in the pool border.   2. Devise a method for determining the number of tiles in the border for any size pool.

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Connecting Mathematical Ideas Reading Read “Lesson Background of the Lesson – Cathy’s Perspective” pages 13 – 16 Share significant ideas you noticed with a partner. Whole group discussion

Connecting Mathematical Ideas Video Video Norms & Setup Transcripts Make note of any important “noticings” that were prominent for you. Video Questions Handout

Video Discussion Questions What evidences of student thinking did you observe? What were important points or moments you noticed in the video?

Connecting Mathematical Ideas Read “Lesson Analysis and Reflection” pages 16 – 20 Discuss any points you noticed with small group Discuss whole group

Connecting Mathematical Ideas Read “Case Commentary -- Jo’s Analysis” pages 21 – 23 Discuss significant ideas you noted with small group Discuss whole group

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Fractions/Ratios – Division Connections Use the snap cubes to represent the solution to 15 3 Observe how teachers represent, pull out examples of partitioning methods. Ask, which one is the correct way to divide and why?

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

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

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.

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

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

Fractions – Division in the Common Core   1

Lunch

Connecting Mathematical Ideas Task 2 Pool Problem Extension: Thinking back to the earlier “Pool Border Task”, consider a pool that is rectangular and surrounded by 1 x 1 tiles. How many tiles are needed to surround any size pool? What if you have a pool in the shape of an l x w rectangle and you put a border r unit wide around it, what is the total area? What about an L-shaped pool?  What if the tile surrounds a circular spa pool with diameter d by one-foot tiles. How many tiles are need to surround the spa?

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Connecting Mathematical Ideas Reading Read “Background of the Lesson – Cathy’s Perspective” pages 24 - 28 Share questions or points of interest with a partner. Whole group discussion

Connecting Mathematical Ideas Video Video Norm Reminder & Setup Transcripts Make note of important “noticings” Video questions HandOut

Video Discussion Questions What evidences of student thinking did you observe? What were important points you noticed in the video?

Connecting Mathematical Ideas Read “Lesson Analysis and Reflection” pages 29 - 32 Discuss ideas or occurrences you noticed with a partner Whole group discussion

Connecting Mathematical Ideas Jigsaw Jo’s ”Analysis” pages 33 -39 Read your group assignment Discuss your part with small group Share whole group Review “Teacher Questions” (p. 37) What is the significance/importance of teacher questions? What are important considerations & strategies for questioning?

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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.

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

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

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

Understanding Division Handout page 10

Understanding Division Handout page 11

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

Reflection and Professional Residue What important points and mathematical ideas from our work today are you taking with you? How will these ideas impact your classroom teaching practice?

Reflection and Professional Residue Let’s Discuss and Share out each of our reflections and our most significant professional residue from our time today

Lesson Study Reminders Next meeting date – Saturday, September 24 Expectations Task/Problem Lesson Template Lesson Enactment Lesson Study Dates Tuesday, September 27; Grade 6 (Group 1) Wednesday, September 28; Grade 6 (Group 2) Thursday, September 29; Grade 7 Friday, September 30; Grade 8

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