1. Linear Growing Patterns and Relations: A Sneak Preview Grade 7 - 9 Wendy Telford Grade 7 - 9 Wendy Telford

2. Today’s Agenda / Another Lesson Plan Template / What are Big Ideas & Why Focus on Them? / Making Sense of the Curriculum Documents / Big Ideas for Patterning and Algebra / Sample Questions and Stumbling Blocks / What the Research Tells Us / Modeling Classroom Activities and Questions / Testing Out Technology / Another Lesson Plan Template / What are Big Ideas & Why Focus on Them? / Making Sense of the Curriculum Documents / Big Ideas for Patterning and Algebra / Sample Questions and Stumbling Blocks / What the Research Tells Us / Modeling Classroom Activities and Questions / Testing Out Technology

3. Another Lesson Plan Template / Used in Mathematics Coaching / Includes Expectations, Big Ideas, Lesson Goals, and Student Misconceptions / Follows the TIPS Match Template (Minds On, Action, Consolidate / Debrief) / Incorporates Questioning and Other Strategies / Encourages Focused Reflection / Planning / Used in Mathematics Coaching / Includes Expectations, Big Ideas, Lesson Goals, and Student Misconceptions / Follows the TIPS Match Template (Minds On, Action, Consolidate / Debrief) / Incorporates Questioning and Other Strategies / Encourages Focused Reflection / Planning

4. What Are Big Ideas? / Sometimes called “Enduring Understandings”, “Key Concepts” or “Key Ideas” / Often present across the grades, but with a shift in focus / Sometimes called “Enduring Understandings”, “Key Concepts” or “Key Ideas” / Often present across the grades, but with a shift in focus

5. What Are Big Ideas? For example, Number Operations goes from simple addition, to adding fractions, to adding like terms, to adding rational expressions as you move up through the grades. For example, Number Operations goes from simple addition, to adding fractions, to adding like terms, to adding rational expressions as you move up through the grades.

6. Why Focus On Big Ideas? / Big Ideas enable students to make connections between new concepts and ideas previously learned, and these connections help students internalize their learning. / Big Ideas help the teacher prioritize / organize specific expectations and choose lessons, activities, and questions with intention. / Big Ideas enable students to make connections between new concepts and ideas previously learned, and these connections help students internalize their learning. / Big Ideas help the teacher prioritize / organize specific expectations and choose lessons, activities, and questions with intention.

7. Looking at the Curriculum Documents

8. Part of the Planning Cycle Expectations Big Ideas Questions & Activities

9. Big Ideas of Patterning and Algebra (*written in Student Language by Dr. Marion Small)

10. Big Idea # 1 Patterns always repeat and you have to know how they repeat to extend them.

11. Big Idea # 2 You often use patterns to learn ideas about number, geometry, measurement, and data.

12. Big Idea # 3 Algebraic reasoning is a way to understand mathematical relationships that apply to a large group of situations.

13. Big Idea # 4 Different representations of relationships or patterns show different things about the relationship, and the representation that is most useful depends on the situation.

14. Big Idea # 5 Comparing mathematical relationships or patterns helps you see that groups of relationships can behave in very similar ways.

15. Big Idea # 6 Sometimes knowing a few things about a pattern or relationship allows you to predict other things about that pattern or relationship.

16. Comparing Big Ideas and Expectations Do these Big Ideas Capture our Curriculum Expectations? Check off the Expectations that are captured by each Big Idea. Do these Big Ideas Capture our Curriculum Expectations? Check off the Expectations that are captured by each Big Idea.

17. Finding / Creating Questions to Elicit Our Big Ideas Choose two questions you like from the examples provided. Match each of your questions with a big idea. Discuss your choices with a partner. Choose two questions you like from the examples provided. Match each of your questions with a big idea. Discuss your choices with a partner.

18. Part of the Planning Cycle Expectations Big Ideas Questions & Activities

19. Sample Questions Check: Where does your question fit within our Big Ideas? Solve your problem with your group. Identify and record potential student stumbling blocks underneath your solution. Check: Where does your question fit within our Big Ideas? Solve your problem with your group. Identify and record potential student stumbling blocks underneath your solution.

20. The Power of Concrete Models / Research suggests that students will grasp graphical and algebraic representations of relations better if they start by building relationships using concrete models.

21. Break!

22. Modeling Classroom Activities: Minds On / Guess My Rule (also called The Robot Challenge)

23. Minds On Questions / Why did you choose those input values? / Describe the strategy you used to find the pattern. / What do you think will happen if this pattern continues? / What information did you need to write a pattern rule? / How could you check if your pattern rule is correct for the given terms? / How could you use your pattern rule to predict the output value when your input value is 100? / Why did you choose those input values? / Describe the strategy you used to find the pattern. / What do you think will happen if this pattern continues? / What information did you need to write a pattern rule? / How could you check if your pattern rule is correct for the given terms? / How could you use your pattern rule to predict the output value when your input value is 100?

24. Modeling Classroom Activities: Action / Secret Pattern Building Challenge secret pattern building challenge With your partner, build the first three positions (1, 2, and 3) for this rule: number of tiles = position number x 2 + 1 secret pattern building challenge With your partner, build the first three positions (1, 2, and 3) for this rule: number of tiles = position number x 2 + 1

25. Connecting Patterns and Graphs / We introduce the “zero” position in the pattern because of the important role it plays when moving to graphical representations.

27. Action Questions / What strategies did you use to determine the pattern rules for each pattern? / Which patterns were the easiest to figure out? Which ones were the hardest? Why? / Are there any similarities or differences in the patterns you saw or the pattern rules? / How can we show that the pattern rule works for the given terms? / Can we be sure our pattern rule is true for all cases? In what cases might your pattern rule not be true? / What would your pattern look like if we graphed the relationship between # of tiles and position number? / What strategies did you use to determine the pattern rules for each pattern? / Which patterns were the easiest to figure out? Which ones were the hardest? Why? / Are there any similarities or differences in the patterns you saw or the pattern rules? / How can we show that the pattern rule works for the given terms? / Can we be sure our pattern rule is true for all cases? In what cases might your pattern rule not be true? / What would your pattern look like if we graphed the relationship between # of tiles and position number?

28. Modeling Classroom Activities: Consolidation Representing the Patterns With Graphs / Graph three rules on the same grid: / Tiles = position number x 3 + 2 / Tiles = position number x 3 + 6 / Tiles = position number x 3 + 9 Representing the Patterns With Graphs / Graph three rules on the same grid: / Tiles = position number x 3 + 2 / Tiles = position number x 3 + 6 / Tiles = position number x 3 + 9

29. Consolidating Questions / What is the same about the pattern rules? What is different? / What is the same about the lines on the graph? What is different? / What effect does the multiplier have on the steepness of the line? / What effect does the constant have on the graph of the line? / How would you describe the relationship between the position number and the number of tiles for each graph? / What is the same about the pattern rules? What is different? / What is the same about the lines on the graph? What is different? / What effect does the multiplier have on the steepness of the line? / What effect does the constant have on the graph of the line? / How would you describe the relationship between the position number and the number of tiles for each graph?

30. Modelling Classroom Activities Use the following ‘games’ to enhance or check understanding: / Pattern Building Competition / Memory Match Game / Cube Game / Sorting Cards Use the following ‘games’ to enhance or check understanding: / Pattern Building Competition / Memory Match Game / Cube Game / Sorting Cards

31. Modeling Classroom Activities Online resources can be used for demonstrations, investigations, practice, self-assessment, and even teacher assessment of student learning Consider what questions, handouts, or consolidating materials you might need to support an online resource. Online resources can be used for demonstrations, investigations, practice, self-assessment, and even teacher assessment of student learning Consider what questions, handouts, or consolidating materials you might need to support an online resource.

32. Modeling Classroom Activities Technology supports available online to enhance or check understanding: / CLIPS (www.edugains.ca)www.edugains.ca / Gizmos (www.explorelearning.com)www.explorelearning.com Technology supports available online to enhance or check understanding: / CLIPS (www.edugains.ca)www.edugains.ca / Gizmos (www.explorelearning.com)www.explorelearning.com

33. LUNCH!

34. Technology: TI-83’s and CBR’s Potential Uses: / As a ‘hook’ to introduce relationships / To apply concepts learned about linear relations to real world settings and data Potential Uses: / As a ‘hook’ to introduce relationships / To apply concepts learned about linear relations to real world settings and data

35. Using Technology Effectively On your flip chart paper, answer the following questions to help ensure your students get the most out of a CBR activity.

36. / When would you use an activity like the one we just did, and why? / “Hook” vs. “Application”: What are the pro’s and con’s? / When would you use an activity like the one we just did, and why? / “Hook” vs. “Application”: What are the pro’s and con’s?

37. / What prior knowledge would you need to activate in your students and how would you get them ready? / What challenges or stumbling blocks might you need to address for your students, and how would you address them? / What prior knowledge would you need to activate in your students and how would you get them ready? / What challenges or stumbling blocks might you need to address for your students, and how would you address them?

38. / What questions might you want to ask before, during, and after the activity? / What is the big idea or key concept you want them to experience? / What questions might you want to ask before, during, and after the activity? / What is the big idea or key concept you want them to experience?

39. / How will you consolidate their learning? / How will you know what the students learned? / How will you consolidate their learning? / How will you know what the students learned?

40. Exit Card The most valuable part of today’s class for me was… Something I’m excited about is… I would like to know more about… The most valuable part of today’s class for me was… Something I’m excited about is… I would like to know more about…

41. Thank you and Good Luck!