Differentiating Instruction u sing the Common Core State Standards

1. Differentiating Instruction using the Common Core State Standards NCDPI Curriculum and Instruction Division 2014 Spring RESA

2. Introductions cc: Microsoft.com

3. Norms A thoughtful and honest conversation amongst those of us who are engaged in our learning community today…

4. Session Outcomes • What is content differentiation? • What is process differentiation? • What is product differentiation? • What do these differentiations “look” like and how do we incorporate them into our practice? • What types of differentiation lead to increased entry points for ALL students? How do we achieve this? • What types of differentiation challenge students to go beyond lesson targets? How do we achieve this?

5. Let’s Do SomeMath!

6. Always – Sometimes – Never

7. Always – Sometimes – Never (x+2)(x-2)=x2+4

8. “Sorting Equations and Identities” In your groups, take turns to place a card in a column and justify your answer to your partner. If you think the equation is ‘sometimes true’, find values of x for which it is true and values of x for which it is not true. If you think the equation is ‘always true’ or ‘never true’, explain how we can be sure that this is the case. Another member of the group should then either explain that reasoning again in his or her own words, or challenge the reasons you gave. When everyone in the group agrees, glue the card onto the poster. Write the reason for your choice next to the card.

9. “Table Talk” • What about Sorting Equations and Identities would you identify as process differentiation? • What about Sorting Equations and Identities would you identify as product differentiation? • What strategies, and how, from Sorting Equations could transcend to other lessons? Be specific and share ideas.

10. The Shell Centerhttp://map.mathshell.org/

11. Just a Minute • In the next four slides you’re going to see different “types” of addressing instruction. • You will see each slide for “just a minute.” • Record your thoughts about this question:What does this imply about the importance of differentiation in CCSS? Which type(s)?

12. Variety of Prior Knowledge Planned time Student A Student B Student C Student D Student E Needed time CCSS Target Level Lesson START Level

13. I - We - You CCSS Target Level Lesson START Level Student A Student B Student C Student D Student E

14. “ANSWER-GETTING” Lesson START Level Student A Student B Student C Student D Student E CCSS Target

15. You – We – I Day 1 Attainment Day 2 Target Lesson START Level Student A Student B Student C Student D Student E

16. What does this imply about the importance of differentiation in CCSS? Which type(s)?

17. “ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.” David Hutchens “Outlearning the Wolves”

18. “Orchestrating Classroom Discussion” • Read “Orchestrating Classroom Discussions” • While reading, use index cards to record reflections and “takeaways” for each of the instructional practices featured. • Use More Than One (1) Card per Practice if Needed

19. Block Party Protocol Chalk Talk • Block Party: Find one or two other people to share two (2) ideas and/or reflections you had or have after reading “Orchestrating Classroom Discussions”? • Chalk Talk: Following each block party you will write “take away” ideas on the posters around the room

20. “Anticipation” Activity Use the following prompts below to develop the “Anticipation” segment for Sidewalk Patterns. The teacher must: • do the problem in as many ways as possible. • collaborate with other colleagues to • anticipate the different strategies and solutions that students may come up with. • determine how to respond to what students produce. • identify strategies that will be most useful in addressing the mathematics to be learned

21. Monitoring • Monitor students’ actual responses during independent work. • Circulate while students work together to solve the problem, carefully watching and listening. • Record their interpretations, strategies, and points of confusion. • Ask questions to get students thinking “on track” or to advance their understanding Selecting • Select student responses to feature during discussion. • Choose particular groups to present because of the mathematics available in their responses, or students based on individual needs.

22. Sequencing • Sequence the student responses that will be featured during the discussion • Purposefully ordering presentations, building a mathematically coherent story line, so as to make the mathematics accessible to all students Connecting • Make sure the mathematical concepts that are the focus of the lesson are clear and accessible. • Connect student responses and lead them to connections during the discussion by asking purposeful questions. • Encourage students to make and share mathematical connections between different student responses.

23. “Table Talk” • Classroom Discourse • How do lessons that develop “Classroom Discourse” using “The 5 Practices for Orchestrating Math Discussions” by Smith and Stein, differentiate instruction for every learner? Using the CCSSM? • How might these ideas and practices challenge teachers in your district or school? How might you move their thinking forward?

24. “Down at the Dock”(A Game of Chance in Probability Theory) Which team can launch their boats first?

25. “Table Talk” • Games and Stations • How does “Down at the Dock” differentiate instruction for every learner? • How does “Down at the Dock” support the CCSSM?

26. Tiered Task From Proportion to Linear Function • Concrete to Abstract • Middle School Content Fractured Numbers • Inside Mathematics leveled task • Fractions to Math 3 concepts Pick the task more appropriate to your level of instruction to explore. We will jigsaw to report out.

27. Inside Mathematics

28. “From Proportion to Linear Function”(Concrete to Abstract)

29. “Table Talk” • “Tiered” Lessons • What types of differentiation do tiered task offer? (Content, Process, and/or Product) • How do tiered lessons support the development of the CCSS mathematics? • Discuss additional ways lessons can be tiered to meet the needs of every learner and align to the CCSSM?

30. Problem Analysis “The process of examining an existing mathematics problem to find ways to modify and/or extend the problem, creating a richer learning opportunity that reaches learners at all levels” (Katie Garcia and Alicia Davis, Dec 2013/Jan 2014 Mathematics Teacher, p. 349)

31. Problem Analysis • First – An example as students • Second – Look at the work from other regions • Third – Try it out

32. Dunking Booth • Student council is holding a fundraising event. They plan to rent a dunking booth as they are quite sure students will pay to dunk teachers or administrators into a tub of cold water.

33. Create a viable solution to “Dunking Booth”All four representations should be addressed in your solution.

34. In text. . . Dunking Booth The student council at West High School is holding a dunking booth fundraiser as the council is sure that students will pay for an opportunity to dunk a teacher or principal into a tub of cold water. It cost $150 to rent the booth and the council will charge $0.50 for each throw. • How many throws need to be sold to cover the cost of the rental agreement? • How many throws need to be sold to to raise $200? • Predict the number of throws sold if the council raised $350. Show your work. • Write a linear function, p(t), showing the profit for t number of throws.

35. Problem Analysis Teachers • Reach all learners simultaneously • Fit old textbooks to new curriculum standards Students • Experience higher-ordered thinking • Make important mathematical connections

36. High School Content Examples Exponential Growth Quadratic Functions

37. Middle School Content Examples Area and Perimeter of irregular shapes Coordinate Geometry

38. Problem Analysis Activity • Identify a mathematics problem that has potential to develop deep understanding, but barely skims the surface. • Use the problem provided below, or choose one of your own! Example Problem: Find the area of the triangle with vertices at A(-8,-6), B(6,9), C(8, -14)

39. Problem Analysis Activity • Use the guiding questions listed on the activity sheet to modify and/or extend the problem to meet the needs of all learners by; • Scaffolding to assist students at the beginning • Including intermediate steps to bridge thinking to higher-levels • Provide extensions to challenge students to go further. Example Problem: Find the area of the triangle with vertices at A(-8,-6), B(6,9), C(8, -14)

40. “Table Talk” • What thoughts and reflections occurred as you completed this activity. • When and how will you use this activity to implement the CCSSM?

41. Session Outcomes - “Revisited” • What is content differentiation? • What is process differentiation? • What is product differentiation? • What do these differentiations “look” like and how do we incorporate them into our practice? • What types of differentiation lead to increased entry points for ALL students? How do we achieve this? • What types of differentiation challenge students to go beyond lesson targets? How do we achieve this?

42. “Open Online Resources” Illustrative Mathematics http://www.illustrativemathematics.org/ Inside Mathematics http://insidemathematics.org/ Mathematics Assessment Project (MARS) http://map.mathshell.org/materials/ Mathematics Vision Project (MVP) http://www.mathematicsvisionproject.org/ NCTM Illuminations http://illuminations.nctm.org/

43. www.ncdpi.wikispaces.net

44. What Questions Do You Have?

45. NCDPI Mathematics Section

46. Thank You!