Linear Growing Patterns & RelationsSession 1Summer Institutes

August 25, 2009

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!

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!

4

Meet and GreetShare 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.

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.

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.

7

Mathematical Processes

8

Matching ActivityIdentify the Big Idea that most closely fits each question. (BLM PL 1.1)

Be ready to defend the highlighted questions.

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 BigIdea 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 …”

10

The Important Bookby Margaret Wise Brown

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

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

13

The Important BookThe important things about Linear Patterns & Relations I learned today are …

•

•

•