National Singapore Math Summer Institute Denver 2011

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

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

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.

National Singapore Math Summer Institute
Denver, USA

2
2
3x = 8 + 2
8
8
x = 10 ÷ 3
10

Denver, USA

27 x 5 = 150 – 15 = 135
135 ÷ 3 = 40 + 5 = 45
Each shelf had 45 books at first.
Denver, USA

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

Draw a polygon with 4 dots on the sides and find its area.
Denver, USA

Area
Number of Dots
Denver, USA

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?
Denver, USA

Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots
Denver, USA

Archipelschool De Tweemaster – Kameleon,
The Netherlands

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

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National Singapore Math Summer Institute Denver 2011

by Jimmy Keng on Jul 27, 2011

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National Singapore Math Summer Institute Denver 2011 — Presentation Transcript