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

2. 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

3. 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

4. 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

5. 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

6. 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

7. Mathematical Processes7

8. 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

9. 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

10. The Important Book
by Margaret Wise Brown 10

11. 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

12. 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

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