This three-day professional development organized by Nanakuli Elementary School and Department of Education (State of Hawaii)

1. Professional Development for Singapore Math (Upper Grades) Day 2 Session 1 Open Lesson Visualization & Generalization

2. Emphasis on Visualization & Generalization Draw a polygon with a total of 4 dots on the sides. Other than visualization, the ability to see patterns and to make generalization is another core intellectual competency.

3. Nanakuli Elementary School, Hawaii

5. Nanakuli Elementary School, Hawaii

6. Nanakuli Elementary School, Hawaii

7. Nanakuli Elementary School, Hawaii

8. Professional Development for Singapore Math (Upper Grades) Day 2 Session 2 Focus on Visualization

9. Focus on Thinking: Visualization The area of the trapezoid. In Singapore Math, visualization is one of the core thinking skills.

10. Focus on Thinking: Visualization

12. Focus on Thinking: Visualization 110g In Singapore Math, bar model method is a key strategy and it emphasizes visualization.

13. Focus on Thinking: Visualization 110g 290g In Singapore Math, bar model method is a key strategy and it emphasizes visualization.

14. Focus on Thinking: Visualization 110g 290g In Singapore Math, bar model method is a key strategy and it emphasizes visualization.

15. Focus on Thinking: Visualization 110g ? ? In Singapore Math, bar model method is a key strategy and it emphasizes visualization. 290g

16. Focus on Thinking: Visualization 290 g – 110 g = 180 g 180 g ÷ 2 = 90 g 3 x 90 g = 270 g Bella puts 270 g of sugar on the dish. 110g ? ? In Singapore Math, bar model method is a key strategy and it emphasizes visualization. 290g

17. Professional Development for Singapore Math (Upper Grades) Day 2 Session 3 Focus on Generalization

18. Focus on Thinking: Generalization 2 3 4 5 6 1 10 9 8 7 11 12 13 14 15 16 20 19 18 17 21 22 23 24 25 26 30 29 28 27 31 32 33 34 35 36 In Singapore Math, patterning and generalization is an core intellectual competency.

19. Focus on Thinking: Generalization 2 3 4 5 1 8 7 6 9 10 11 12 13 16 15 14 17 18 19 20 21 24 23 22 25 26 27 28 29 In Singapore Math, patterning and generalization is an core intellectual competency.

22. 6 is shared equally between 2. 6 ÷ 2 = 3 In 6, how many 2s are there? 6 ÷ 2 = 3

24. 1÷12=2 2÷12=2  2 3÷12=3  2 4÷12=4  2 𝑛÷12=𝑛  2

25. 1÷34=113 2÷34=2  113 3÷34=3  113

27. Primary Mathematics Standards Edition Grade 6

28. Professional Development for Singapore Math (Upper Grades) Day 2 Session 4 Focus on Number Sense

31. If there are more odd numbers in the list then m are oddContributions from course participants

33. Three times the middle number to get the middle s

34. The middle three consecutive numbers which is essentially the same as three times the middle number to get the middle s

35. The first + second + last of the numbers used to get the smallest sFor 72, 73, 74, 75 and 76, we can use the values of s for 2, 3, 4, 5, 6 – just add 210. Contributions from course participants