national singapore math summer institute denver 2011
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Core Elective
InvestigatingProblem SolvingDr Yeap Ban HarMarshall Cavendish InstituteSingapore
www.marshallcavendish.com/education/mci
Sculpture: Riverside MerchantsSingapore River
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Source: Mathematics Syllabus Primary
Singapore Ministry of Education 2006
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St Edward School, Florida
Princess Elizabeth Primary School, Singapore
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Archipelschool De Tweemaster – Kameleon, The Netherlands
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King Solomon Academy, London
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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
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National Singapore Math Summer InstituteDenver, USA
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2
8
2
8
3x = 8 + 2
x = 10 ÷ 3
10
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National Singapore Math Summer InstituteDenver, USA
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National Singapore Math Summer InstituteDenver, USA
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27 x 5 = 150 – 15 = 135
135 ÷ 3 = 40 + 5 = 45
Each shelf had 45 books at first.
National Singapore Math Summer InstituteDenver, USA
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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
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Draw a polygon with 4 dots on the sides and find its area.
National Singapore Math Summer InstituteDenver, USA
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Number of Dots Area
National Singapore Math Summer InstituteDenver, USA
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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 InstituteDenver, USA
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Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots
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Archipelschool De Tweemaster – Kameleon, The Netherlands
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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 on the perimeter. Find an expression for its area.