Core Elective

InvestigatingProblem SolvingDr Yeap Ban HarMarshall Cavendish InstituteSingapore

banhar@sg.marshallcavendish.com

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.