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# Pearl City Hawaii 9 August 2011

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

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### Pearl City Hawaii 9 August 2011

1. 1. Professional Development for <br />Singapore Math (Upper Grades)<br />Day 2 Session 1<br />Open Lesson<br />Visualization & Generalization<br />
2. 2. Emphasis on Visualization & Generalization<br />Draw a polygon with a total of 4 dots on the sides.<br />Other than visualization, the ability to see patterns and to make generalization is another core intellectual competency.<br />
3. 3. Nanakuli Elementary School, Hawaii<br />
4. 4.
5. 5. Nanakuli Elementary School, Hawaii<br />
6. 6. Nanakuli Elementary School, Hawaii<br />
7. 7. Nanakuli Elementary School, Hawaii<br />
8. 8. Professional Development for <br />Singapore Math (Upper Grades)<br />Day 2 Session 2<br />Focus on<br />Visualization<br />
9. 9. Focus on Thinking: Visualization<br />The area of the trapezoid.<br />In Singapore Math, visualization is one of the core thinking skills.<br />
10. 10. Focus on Thinking: Visualization<br />
11. 11.
12. 12. Focus on Thinking: Visualization<br />110g<br />In Singapore Math, bar model method is a key strategy and it emphasizes visualization.<br />
13. 13. Focus on Thinking: Visualization<br />110g<br />290g<br />In Singapore Math, bar model method is a key strategy and it emphasizes visualization.<br />
14. 14. Focus on Thinking: Visualization<br />110g<br />290g<br />In Singapore Math, bar model method is a key strategy and it emphasizes visualization.<br />
15. 15. Focus on Thinking: Visualization<br />110g<br />?<br />?<br />In Singapore Math, bar model method is a key strategy and it emphasizes visualization.<br />290g<br />
16. 16. Focus on Thinking: Visualization<br />290 g – 110 g = 180 g<br />180 g ÷ 2 = 90 g<br />3 x 90 g = 270 g<br />Bella puts 270 g of sugar on the dish.<br />110g<br />?<br />?<br />In Singapore Math, bar model method is a key strategy and it emphasizes visualization.<br />290g<br />
17. 17. Professional Development for <br />Singapore Math (Upper Grades)<br />Day 2 Session 3<br />Focus on<br />Generalization<br />
18. 18. Focus on Thinking: Generalization<br />2<br />3<br />4<br />5<br />6<br />1<br />10<br />9<br />8<br />7<br />11<br />12<br />13<br />14<br />15<br />16<br />20<br />19<br />18<br />17<br />21<br />22<br />23<br />24<br />25<br />26<br />30<br />29<br />28<br />27<br />31<br />32<br />33<br />34<br />35<br />36<br />In Singapore Math, patterning and generalization is an core intellectual competency.<br />
19. 19. Focus on Thinking: Generalization<br />2<br />3<br />4<br />5<br />1<br />8<br />7<br />6<br />9<br />10<br />11<br />12<br />13<br />16<br />15<br />14<br />17<br />18<br />19<br />20<br />21<br />24<br />23<br />22<br />25<br />26<br />27<br />28<br />29<br />In Singapore Math, patterning and generalization is an core intellectual competency.<br />
20. 20.
21. 21.
22. 22. 6 is shared equally between 2.<br />6 ÷ 2 = 3<br />In 6, how many 2s are there?<br />6 ÷ 2 = 3<br />
23. 23.
24. 24. 1÷12=2<br /> <br />2÷12=2  2<br /> <br />3÷12=3  2<br /> <br />4÷12=4  2<br /> <br />𝑛÷12=𝑛  2<br /> <br />
25. 25. 1÷34=113<br /> <br />2÷34=2  113<br /> <br />3÷34=3  113<br /> <br />
26. 26. Skemp<br />Understanding in mathematics <br /><ul><li> relational</li></ul> (conceptual) <br /><ul><li> instrumental </li></ul> (procedural)<br /><ul><li> conventional </li></ul>Teaching for conceptual understanding is given emphasis in Singapore Math.<br />Primary Mathematics Standards Edition Grade 6<br />Primary Mathematics Standards Edition Grade 6<br />
27. 27. Primary Mathematics Standards Edition Grade 6<br />
28. 28. Professional Development for <br />Singapore Math (Upper Grades)<br />Day 2 Session 4<br />Focus on<br />Number Sense<br />
29. 29.
30. 30. There were several ways the value of m was established<br /><ul><li>First, last and middle of the numbers used
31. 31. If there are more odd numbers in the list then m are odd</li></ul>Contributions from course participants<br />
32. 32. The value of s was established in different ways<br /><ul><li>First + last + middle of the numbers used to get the middle s
33. 33. Three times the middle number to get the middle s
34. 34. The middle three consecutive numbers which is essentially the same as three times the middle number to get the middle s
35. 35. The first + second + last of the numbers used to get the smallest s</li></ul>For 72, 73, 74, 75 and 76, we can use the values of s for 2, 3, 4, 5, 6 – just add 210.<br />Contributions from course participants<br />