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Cypher IV Mathematics Leadership Project Teaching Student-Centered Math Book Study K-3 Group Session 3 Developing Meaning For The Operations & Solving Story Problems

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(Re)Introductions Kim Ramsay (Gr. 2 Teacher, Whitehorse) Cathy Hines (Gr. 3 Teacher, Whitehorse) Kathryn Lewis (K Teacher, Old Crow) Shari Heal (Grade 3 French Immersion Teacher, Whitehorse) Tammy Stoneman (Learning Assistance Teacher, Teslin) Tina Moody Curran (Gr. 1-2 Teacher, Teslin) Bernadette Roy (French Gr. 3 Teacher, Whitehorse) Kathleen Evans (K Teacher, Faro, YT) Jenna Sawkins (Gr. K&1 Teacher, Dease Lake) Nita Connolly (Grades K-2 Teacher, Atlin) Dana Caljouw (K-3 Teacher, Telegraph Creek)

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Group Norms Be Responsible For How & What You Learn Everyone brings prior experience & knowledge. Take ownership of your learning by being on time and staying, doing the reading & reflection to prepare for discussion, and be willing to try out new ideas in your classroom. Encourage Risk-Taking and Accept All Ideas When learning and discussing, everyone needs to feel safe& that ideas will be respected, even if there is disagreement. Discussion of new ideas allows everyone to ? their own beliefs & discover new ways of thinking – an essential focus of this book study.

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Group Norms - contd Be Your Own Watchdog Monitor and manage your participation to prevent contributing too much or too little. Be An Attentive Listener Listen to each other during the discussion. Turn off your and refrain from surfing the net during the sessions.

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Homework Review (Small Group) Based on the homework assigned in the previous session, discuss the following questions in a small group: What have you tried in your classroom as a result of the last session? What role did you play in the teaching and learning of math? What role did the students play in their learning? What discoveries did you and your students make? What misconceptions, if any, surfaced about the topic? How did you redirect the students? What suggestions do you have for others when they try this?

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Objectives Focus on the Big Ideas of operation sense Define addition and subtraction Explore problem structures for addition, subtraction, multiplication, and division Work with models for addition, subtraction, multiplication, and division Discuss important issues related to solving story problems

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Materials Counters (Create counters as you need them on the whiteboard in the breakout room screens.) Square tiles or snap cubes (Create as needed on breakout room screens.) Grid Paper (Will be provided within the breakout rooms.) Evaluation Form (Sent at the beginning of the session.) How Bear Got A Short Tail Materials (Problem Structures) are within the slide show.

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Before Teaching Through Problem Solving Divide into smaller groups for 10 minutes. What does it mean to teach through problem solving as opposed to teaching problem solving? Ideas:

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During - Big Ideas Review the Big Ideas for this chapter (p. 65) on your own for 2 min. Discuss these ideas with a partner in a breakout room for 8 min. by sharing examples from your teaching that illustrate each of these ideas.

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Defining Addition & Subtraction The typical definitions for addition and subtraction describe addition as putting together & subtraction as taking away. These definitions can be misleading. Read the problems in the + and - section on p. 65 and do the first Stop & Reflect box (p. 66). When you are done, read the 2 paragraphs following the Stop and Reflect box. Put your hand up when you are done. Prepare to discuss the following question with the group: How does this info change the way that you think about addition and subtraction?

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Problem Structures for + & - + & - problems can be categorized based on the kinds of relationships involved. The four categories of problems are: Join (Room 1) Separate (Room 2) Part-Part-Whole (Room 3) Compare (Room 4) Task Review the section of the text you chose Define the category Create examples of each type of problem Show how counters could be used to model and solve the problem (use the whiteboard tools) Be prepared to present to the large group in 15 min.

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Problem Structures for x & ÷ x & ÷ problems can also be categorized according to the types of relationships involved. The two most common structures are: Equal-group problems (Rooms 1 & 2) Multiplicative comparison problems (Room 3 & 4) After reviewing the sections of the text on Equal-Group Problems (p. 78) & Comparison Problems (p. 79), get into pairs or 3 to solve the problems in the text as directed in the Stop & Reflect box (p. 79). Create 1 of each type of problem with your partner(s) for 18 min.

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Using Models For x & ÷ An important model for multiplication and division is the array. An array is any arrangement of things in rows and columns, such as a rectangle of square tiles or blocks. In pairs, Represent the factors of 30 using arrays. Record your arrays on graph paper and write the multiplication expression that the array represents beside it. Be prepared to share.

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Using Models For x & ÷ (p. 82) How and why do arrays support students in their understanding of multiplication? How could arrays be used to support students in their understanding of division?

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Solving Story Problems Review, More Thoughts About Children Solving Story Problems (pp ). Why is is important to avoid using key words as a strategy, encourage problem analysis, and require explanations?

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Avoid Key WordsEncourage Problem Analysis Require Explanations

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After What does it mean to think through problem solving as opposed to teaching problem solving? Discuss how learning about the various problem structures in this session will help you to teach through problem solving. Evaluation & Self- Assessment Form Homework Try several story problems with some students. Use problems from the chapter, problems that were created in this session, or your own. Fax student samples to by the Mon. prior to the next session to share with the group. Read Chapter 4

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