Linear Growing Patterns & Relations Session 1 Summer Institutes August 25, 2009 Welcome and introductions – name, position, board parking lot Wendy Telford

Goals for the 3 days: • Develop an Understanding of Big Ideas from Patterning, Algebraic Reasoning, and Linear Functions Connect the Mathematical Processes to Big Ideas Experience and Practice Differentiated Instruction Discuss Effective Use of Technology / Manipulatives Develop Questions to Evoke and Expose Thinking Build a Math-Talk Learning Community Have Fun! 2

Group Norms All ideas will be listened to carefully and responded to respectfully; Everyone will have a voice; All suggestions will be presented with the intent to move the collective forward; Clarifying questions are welcome; Everyone will engage fully in the moment; Suffering is optional! 3

Meet and Greet Share a strategy you have used or would like to use in the first week of class to help students feel comfortable with sharing and talking about mathematics in your classroom. Share our strategy: using popsicle sticks 4

Big Ideas from Patterning to Algebraic Reasoning Algebraic reasoning is a process of describing and analyzing (e.g., predicting) generalized mathematical relationships and change using words and symbols. Comparing mathematical relationships helps us see that there are classes of relationships and provides insight into each member of the class. Different representations of relationships (e.g. numeric, graphic, geometric, algebraic) highlight different characteristics or behaviours, and can serve different purposes. Limited information about a mathematical relationship can sometimes, but not always, allow us to predict other information about that relationship. 5

Big Ideas for Linear Growing Patterns & Relations  Describing the relationship between two things as a pattern is a foundation to algebraic reasoning.  The mathematical structure of a linear growing pattern can be represented in different ways (e.g., numeric, graphical, geometric, algebraic, verbally). Different representations highlight different characteristics and can serve different purposes.  Linear growing patterns can be distinguished from other patterns by the way they grow.  Two pieces of information about a linear growing pattern can be sufficient information to fully describe the pattern or function. Emerging 1) representing 2) Connecting 3) Selecting tools and computational strategies 6

Mathematical Processes 7

highlighted questions. Matching Activity Identify the Big Idea that most closely fits each question. (BLM PL 1.1) Have Participants match the questions to big ideas individually first. Then have them compare with an elbow partner if time, or just at the table, before moving on the next slide. Be ready to defend the highlighted questions. 8

Connecting Questions to Big Ideas Pick one question you liked (BLM PL 1.1). Which Big Idea does it fit most closely? Go to the corner representing your Big Idea. Identify your question and complete the statement: “I think this question fits most closely with this Big Idea because…” Now determine which expectations (BLM PL 1.2) connect to your Big Idea. Complete the statement: “The connection(s) I see between the overall expectations and this Big Idea is …” 9

The Important Book by Margaret Wise Brown 10

Important Book Make a ‘hot dog’ paper fold Make a ‘hamburger’ paper fold Fold again in this direction Open paper; make ‘hamburger’ fold With folded edge along the top, tear along the vertical crease until the horizontal line Open paper; make hotdog fold; push towards centre to join edges Fold to form a book of 8 pages 11

Label Pages Page 1- Cover: The Important Book Page 2- Big Ideas Page 3- Linear Patterns & Relations Page 4- Planning Page 5- Open Questions Page 6- Parallel Tasks 12

The Important Book The important things about Linear Patterns & Relations I learned today are … • 13