1. Core Elective Investigating Problem Solving DrYeap Ban Har Marshall Cavendish Institute Singapore banhar@sg.marshallcavendish.com Sculpture: Riverside Merchants Singapore River www.marshallcavendish.com/education/mci

2. Source: Mathematics Syllabus Primary Singapore Ministry of Education 2006

3. St Edward School, Florida Princess Elizabeth Primary School, Singapore

4. Archipelschool De Tweemaster – Kameleon, The Netherlands

5. King Solomon Academy, London

6. First Number 88 Second Number 11 units = 88 01 units = 08 First Number = 6 x 8 = 48 Second Number = 5 x 8 = 40 The numbers are 40 and 48.

7. National Singapore Math Summer Institute Denver, USA

8. 2 2 3x = 8 + 2 8 8 x = 10 ÷ 3 10

9. National Singapore Math Summer Institute Denver, USA

12. National Singapore Math Summer Institute Denver, USA

13. 27 x 5 = 150 – 15 = 135 135 ÷ 3 = 40 + 5 = 45 Each shelf had 45 books at first. National Singapore Math Summer Institute Denver, USA

14. Other methods offered by participants Algebraic Method 30x = 27(x + 5) Hence 30x = 27x + 27 x 5 30x – 27x = 135 3x = 135 x = 45 where x is the number of books on each shelf at first Model Method The bar model may look rather cumbersome with one bar of 30 units and an equal bar of 27 longer units. 5

15. Draw a polygon with 4 dots on the sides and find its area. National Singapore Math Summer Institute Denver, USA

16. Area Number of Dots National Singapore Math Summer Institute Denver, USA

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? National Singapore Math Summer Institute Denver, USA

18. Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots National Singapore Math Summer Institute Denver, USA

19. Archipelschool De Tweemaster – Kameleon, The Netherlands

20. High School Attached to Tsukuba University, Japan Draw a polygon with no dots inside it. Investigate. A polygon has 4 dots on the perimeter. Find an expression for its area. www.marshallcavendish.com/education/mci