Core Elective<br />Investigating<br />Problem Solving<br />DrYeap Ban Har<br />Marshall Cavendish Institute<br />Singapore...
 <br />Source: Mathematics Syllabus Primary <br />Singapore Ministry of Education 2006<br />
St Edward School, Florida<br />Princess Elizabeth Primary School, Singapore<br />
Archipelschool De Tweemaster – Kameleon, <br />The Netherlands<br />
King Solomon Academy, London<br />
First Number<br />88<br />Second<br />Number<br />11 units = 88<br />01 units = 08<br />First Number = 6 x 8 = 48 <br />Se...
National Singapore Math Summer Institute<br />Denver, USA<br />
2<br />2<br />3x = 8 + 2<br />8<br />8<br />x = 10 ÷ 3<br />10<br />
National Singapore Math Summer Institute<br />Denver, USA<br />
National Singapore Math Summer Institute<br />Denver, USA<br />
27 x 5 = 150 – 15 = 135<br />135 ÷ 3 = 40 + 5 = 45 <br />Each shelf had 45 books at first.<br />National Singapore Math Su...
Other methods offered by participants<br />Algebraic Method<br />30x = 27(x + 5)<br />Hence 30x = 27x + 27 x 5<br />30x – ...
Draw a polygon with 4 dots on the sides and find its area.<br />National Singapore Math Summer Institute<br />Denver, USA<...
Area<br />Number of Dots<br />National Singapore Math Summer Institute<br />Denver, USA<br />
There was a hypothesis by a participant that the area is also related to dots shown by arrows – dots that are “untouched” ...
Applying this hypothesis, the square has  4 “untouched” dots and the rhombus has 8 “untouched” dots<br />National Singapor...
Archipelschool De Tweemaster – Kameleon, <br />The Netherlands<br />
High School Attached to Tsukuba University, Japan<br />Draw a polygon with no dots inside it. Investigate.<br />A polygon ...
Upcoming SlideShare
Loading in …5
×

National Singapore Math Summer Institute Denver 2011

1,627 views

Published on

Published in: Education, Business, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,627
On SlideShare
0
From Embeds
0
Number of Embeds
760
Actions
Shares
0
Downloads
29
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

National Singapore Math Summer Institute Denver 2011

  1. 1. Core Elective<br />Investigating<br />Problem Solving<br />DrYeap Ban Har<br />Marshall Cavendish Institute<br />Singapore<br />banhar@sg.marshallcavendish.com<br />Sculpture: Riverside Merchants<br />Singapore River<br />www.marshallcavendish.com/education/mci<br />
  2. 2.  <br />Source: Mathematics Syllabus Primary <br />Singapore Ministry of Education 2006<br />
  3. 3. St Edward School, Florida<br />Princess Elizabeth Primary School, Singapore<br />
  4. 4. Archipelschool De Tweemaster – Kameleon, <br />The Netherlands<br />
  5. 5. King Solomon Academy, London<br />
  6. 6. First Number<br />88<br />Second<br />Number<br />11 units = 88<br />01 units = 08<br />First Number = 6 x 8 = 48 <br />Second Number = 5 x 8 = 40<br />The numbers are 40 and 48.<br />
  7. 7. National Singapore Math Summer Institute<br />Denver, USA<br />
  8. 8. 2<br />2<br />3x = 8 + 2<br />8<br />8<br />x = 10 ÷ 3<br />10<br />
  9. 9. National Singapore Math Summer Institute<br />Denver, USA<br />
  10. 10.
  11. 11.
  12. 12. National Singapore Math Summer Institute<br />Denver, USA<br />
  13. 13. 27 x 5 = 150 – 15 = 135<br />135 ÷ 3 = 40 + 5 = 45 <br />Each shelf had 45 books at first.<br />National Singapore Math Summer Institute<br />Denver, USA<br />
  14. 14. Other methods offered by participants<br />Algebraic Method<br />30x = 27(x + 5)<br />Hence 30x = 27x + 27 x 5<br />30x – 27x = 135<br />3x = 135<br />x = 45 where x is the number of books on each shelf at first<br />Model Method<br />The bar model may look rather cumbersome with one bar of 30 units and an equal bar of 27 longer units.<br />5<br />
  15. 15. Draw a polygon with 4 dots on the sides and find its area.<br />National Singapore Math Summer Institute<br />Denver, USA<br />
  16. 16. Area<br />Number of Dots<br />National Singapore Math Summer Institute<br />Denver, USA<br />
  17. 17. There was a hypothesis by a participant that the area is also related to dots shown by arrows – dots that are “untouched” by the polygon when the smallest possible rectangle is drawn around the polygon. Can you figure this one out?<br />National Singapore Math Summer Institute<br />Denver, USA<br />
  18. 18. Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots<br />National Singapore Math Summer Institute<br />Denver, USA<br />
  19. 19. Archipelschool De Tweemaster – Kameleon, <br />The Netherlands<br />
  20. 20. High School Attached to Tsukuba University, Japan<br />Draw a polygon with no dots inside it. Investigate.<br />A polygon has 4 dots on the perimeter. Find an expression for its area.<br />www.marshallcavendish.com/education/mci<br />

×