Red Swastika School

Problem-Solving Heuristics in Mathematics Dr Yeap Ban Har Marshall Cavendish Institute Singapore [email_address] www.banhar.com Photo Credit : Students solving a mathematics problem using draw-a-diagram heuristic at Da Qiao Primary School.

“ Mathematics is an excellent vehicle for the development and improvement of a person’s intellectual competence ...” Singapore Ministry of Education 2006

Source: Mathematics Syllabus Primary Singapore Ministry of Education 2006

Heuristic: Model Method In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket? Source: Primary School Leaving Examination 2006 – 2010

The Bar Model Method In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket? Source: Primary School Leaving Examination 2006 – 2010 15 3 units = 15 1 units = 5 18 units = 18 x 5 = 90 There are 90 fruits in the basket.

King Solomon Academy, London This refers to the two numbers

88 11 units = 88 0 1 unit s = 0 8 First Number = 6 x 8 = 48 Second Number = 5 x 8 = 40 The numbers are 40 and 48. First Number Second Number

National Singapore Math Summer Institute Denver, USA

12.2 can be seen as 12 and 20 hundredths. Students who lack number sense may give the incorrect answer of 3.5 instead of 3.05.

3 Example 4

3 4 Example 5

4 Example 5

3 units = $12 1 unit = $4 8 units = 8 x $4 = $32 Kyla had $32 at first. Alternate Method $12 ÷ 3 x 8 = $32 Model Method 5 Example 6

Did you get 3 as the final answer?

88 – 34 = 54 54 – 34 = 20 34 – 20 = 14 14 2 units = 14 3 units = 14 ÷ 2 x 3 = 21 21 girls wore goggles on that day.

Method 1 Guess and Check / Make a Table Method 2 Using Number Sentences $25 + $2 = $27 $27 : $3 = 9 There were 10 children. Total amount = $8 x 10 + $25 = $105 So each child received $105 : 10 = $10.50 Number of Children 3 $22 + $6 = $28 $24 + $25 = $49 4 … .

Method 1 Guess and Check / Make a Table 30 – 3 = 27 5 x 27 = 135 135 : 3 = 45 There were 45 books on each shelf at first.

Attached School University of Tsukuba

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Attached School University of Tsukuba

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Red Swastika School

by Jimmy Keng on Aug 03, 2011

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