national singapore math summer institute denver 2011
TRANSCRIPT
Core Elective
InvestigatingProblem SolvingDr Yeap Ban HarMarshall Cavendish InstituteSingapore
www.marshallcavendish.com/education/mci
Sculpture: Riverside MerchantsSingapore River
Source: Mathematics Syllabus Primary Singapore Ministry of Education 2006
St Edward School, Florida
Princess Elizabeth Primary School, Singapore
Archipelschool De Tweemaster – Kameleon, The Netherlands
King Solomon Academy, London
88
11 units = 8801 units = 08
First Number = 6 x 8 = 48 Second Number = 5 x 8 = 40
The numbers are 40 and 48.
First Number
SecondNumber
National Singapore Math Summer InstituteDenver, USA
2
8
2
8
3x = 8 + 2
x = 10 3
10
National Singapore Math Summer InstituteDenver, USA
National Singapore Math Summer InstituteDenver, USA
27 x 5 = 150 – 15 = 135
135 ÷ 3 = 40 + 5 = 45
Each shelf had 45 books at first.
National Singapore Math Summer InstituteDenver, USA
Other methods offered by participants
Algebraic Method30x = 27(x + 5)Hence 30x = 27x + 27 x 530x – 27x = 1353x = 135x = 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
Draw a polygon with 4 dots onthe sides and find its area.
National Singapore Math Summer InstituteDenver, USA
Number of Dots Area
National Singapore Math Summer InstituteDenver, USA
There was a hypothesis by a participant thatthe area is also related to dots shown byarrows – dots that are “untouched” by thepolygon when the smallest possible rectangleis drawn around the polygon. Can you figurethis one out?
National Singapore Math Summer InstituteDenver, USA
Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots
National Singapore Math Summer InstituteDenver, USA
Archipelschool De Tweemaster – Kameleon, The Netherlands
www.marshallcavendish.com/education/mci
High School Attached to Tsukuba University, Japan
Draw a polygon with no dots inside it. Investigate.
A polygon has 4 dots onthe perimeter. Find anexpression for its area.