1. Differentiating Instruction ● Go to: http://goo.gl/BvCzSw and complete form (Enter Session Code on board)http://goo.gl/BvCzSw ● On the post-it notes, please write questions you may have now, if any, about differentiating instruction in a math classroom.

2. Session Desired Outcome: Teachers will become familiar with differentiated instruction as modeled in a math demonstration lesson on the fundamental counting principle.

3. Outcome Demo Lesson

4. Bell Work Find the prime factorizations of: A. 20 B. 30 C. 36 D. 98

5. Fundamental Counting Principle Study Questions First & Last Name Math 1 Essential Question:

6. Fundamental Counting Principle Study Questions First & Last Name Math 1 Essential Question: How many factors does have? Vocabulary: Factors Prime numbers Prime factors Prime factorization Fundamental Counting Principle (FCP)

7. Fundamental Counting Principle Study Questions First & Last Name Math 1 Essential Question: How many factors does have?

8. Fundamental Counting Principle Study Questions First & Last Name Math 1 Essential Question: How many factors does have? Vocabulary: Factors Prime numbers Prime factors Prime factorization Fundamental Counting Principle (FCP)

9. Quickwrite: Without doing any calculations, describe why 2 12 is much larger than 12 2.

10. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The factors of ____ are _________. Thumbs up if you agree with what I say.

11. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The factors of 10 are 1, 2, 5 & 10. Repeat together when I hold my arms out.

12. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The prime factors of ____ are _________. Thumbs up if you agree with what I say.

13. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The prime factors of 10 are 2 & 5. Repeat together when I hold my arms out.

14. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The prime factors of ____ are _________. Thumbs up if you agree with what I say.

15. Fundamental Counting Principle Study Questions Practice/Reinforce Sentence Frames The prime factors of 30 are 2, 3 & 5. Repeat together when I hold my arms out.

16. Fundamental Counting Principle Study Questions List the factors of 20. 1, 2, 4, 5, 10, 20 20 has 6 factors.

17. Fundamental Counting Principle Study Questions What are the prime factors of 20? 2 & 5 20 has two prime factors.

18. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

19. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

20. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

21. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

22. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

23. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 =

24. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 = Think about how many ways 2 can be used. Show on your fingers how many ways 2 can be used.,, can all be used to create factors of 20.

25. Fundamental Counting Principle Study Questions How many ways can 2 and 5 be used to create the factors of 20? 1 = 2 = 4 = 5 = 10 = 20 = Think about how many ways 5 can be used. Show on your fingers how many ways 5 can be used., can both be used to create factors of 20.

26. Fundamental Counting Principle Study Questions,, can all be used to create factors of 20., can both be used to create factors of 20. There are three ways to use 2 and two ways to use 5.

27. Fundamental Counting Principle Study Questions ____________ x ____________ = ___________ Ways to use 2 Ways to use 5 Factors of 20

28. Fundamental Counting Principle Study Questions ____3_______ x ____________ = ___________ Ways to use 2 Ways to use 5 Factors of 20

29. Fundamental Counting Principle Study Questions ____3_______ x _____2______ = ___________ Ways to use 2 Ways to use 5 Factors of 20

30. Fundamental Counting Principle Study Questions ____3_______ x _____2______ = ____6______ Ways to use 2 Ways to use 5 Factors of 20

31. Fundamental Counting Principle Study Questions

32. Fundamental Counting Principle Study Questions How many kinds of pizzas can be created with: 3 meats – pepperoni, seafood, ground beef (or none) 2 veggies – mushrooms, olives (or no veggies) 1 cheese – cheese (or no cheese) No doubling up (and no meat, no veggies, and no cheese counts as a choice). __4___ x ____3______ x ___2___ = __24____ Meats Veggies Cheese Pizzas

33. Study Questions How many kinds of pizzas can be created with: 3 meats – pepperoni, seafood, ground beef (or none) 2 veggies – mushrooms, olives (or no veggies) 1 cheese – cheese (or no cheese) No doubling up (and no meat, no veggies, and no cheese counts as a choice). __4___ x ____3______ x ___2___ = __24____ Meats Veggies Cheese Pizzas Work with a partner to construct a visual in your notes that would represent this problem. Fundamental Counting Principle

34. Study Questions Return to the Essential Question. How many factors does have? A.30 B.315 C.480 D.630 Fundamental Counting Principle

35. Study Questions Dyads create/exchange example problems. Verify solution with table group. These ideas are critical to enabling “Public Key Encryption.” Without the understanding of very large prime numbers and the Fundamental Counting Principle, you would not be able to use the ATM or make purchases online. Fundamental Counting Principle

36. 1.Respond to the essential questions. 2.List five key phrases or words from your notes. 3.Use your five key phrases or words to write three to five complete sentences summarizing your notes and answering the essential questions. GIST Summary

37. Study Questions Can “cover” standards-based content while ensuring that students are active and engaged Fundamental Counting Principle

38. Study Questions Ticket out the door: Write your answer on a sticky note—do not put your name on it. How many factors does 2 4 3 2 5 3 have? On your way to break, put your note on the Parking Lot/Community Forum. Fundamental Counting Principle

39. Reflection Question: How does the prior activity provide access for AEL (Academic English Learners), Special Education and GATE students?

40. ELD Identifiers: ● Emerging: AELs need substantial support ● Expanding: AELs need moderate support ● Bridging: AELs need light support

41. ELD Standards Part 1: Interacting in a meaningful way ● A: Collaboration ○ 1 - Exchanging information and ideas: Contribute to class, group, and partner discussions, including sustained dialogue, by following turn‐taking rules, asking relevant questions, affirming others, and adding relevant information. ● C: Productive ○ 9 - Presenting: Plan and deliver brief oral presentations on a variety of topics and content areas (e.g., retelling a story, explaining a science process, etc.). ○ 12 - Selecting language resources: Use a growing number of general academic and domain‐specific words in order to add detail, create an effect (e.g., using the word suddenly to signal a change), or create shades of meaning (e.g., scurry versus dash) while speaking and writing. Link to full document: Grades 6-8, Grades 9-12Grades 6-8Grades 9-12

42. Universal Design for Learning (UDL) Principles: Video on UDL (4 minutes) Video on UDL (4 minutes) 1.Provide Multiple Means of Representations - The what of teaching and learning, content 2.Provide Multiple Means of Action and Expression - The how of teaching and learning, process 3.Provide Multiple Means of Engagement - The why of teaching and learning, product

43. GATE (link to Ca Math Framework on GATE, start at bottom of page 1)link to Ca Math Framework on GATE ● Depth ● Pacing ● Complexity ● Novelty

44. RUSD Lesson Template (see page 2)Lesson Template ● Sample Lesson: 8th Grade, Unit 1: Representing and Combining TransformationsRepresenting and Combining Transformations

45. Pick a topic/lesson and expand to include strategies

46. Closing: ● Post parking lot questions that we have not answered (YET) during this session.

47. Resources: ● UDL Presentation UDL Presentation