2. Identification of developmental differences

3. Increase or Decrease the:

4. Abstraction

5. Extent of Support

6. Sophistication

7. Complexity of goals, resources, activities & products

9. First cast of the dice … 3 1 + 2 = 3 1 x 2 = 2

10. Second cast of the dice … 3 + 12 15 3 + 4 = 7 3 x 4 = 12

11. Third cast of the dice … 15 + 6 21 5 + 1 = 6 5 x 1 = 5

12. Fourth cast of the dice … 21 + 18 39 21 + 9 30 3 + 6 = 9 3 x 6 = 18

13. Modifications for Advanced Students Play to 100 Disallow paper for calculations or remembering numbers Use powers Use subtraction Allow negative numbers What about fractions?

14. Tiered Lesson: Using Powers Option 81 34 = 3 x 3 x 3 x 3 = 81 43 = 4 x 4 x 4 = 64

15. Tiered Lesson:Exploring Options 2+ 6 = 8 62 = 36 2 x 6 = 12 2 - 6 = -4 26 = 64 6 - 2 = 4

16. What about using … 64 … a multi-sided die 36 … or two

17. 12 We could really shake things up… … try three dice and use the distributive law! 12 + (3 x 18) = 12 + 54 = 66 (12 + 18) x 3 = 30 x 3 = 90 Did you get closer to 100?

18. Standards What Students will Be Able to Do CONTENT Unit Concepts and Generalizations What Students will Understand What Students will Know

19. The Horse Before the Cart Product Content Process

20. Flexible Grouping Materials PROCESS Pace of Instruction Think- Pair-Share Graphic Organizers Simulations Learning Contracts Tiered Assignments

21. Debate Puppet show Essay Detailed Illustration Letter PRODUCT Model Graph Timeline Survey Venn Diagram Video Film or Documentary Demonstration Display

24. Abstractness

25. Open-endednessTomlinson, C. (1995). The Differentiated Classroom. Alexandria, VA: ASCD.