Problem-Solving Heuristics in Mathematics

Dr Yeap Ban HarMarshall Cavendish Institute

Singaporebanhar.yeap@pathlight.org.sg

www.banhar.comPhoto Credit: Students solving a mathematics problem using draw-a-diagram heuristic at Da Qiao Primary School.

““Mathematics is Mathematics is an excellent vehicle an excellent vehicle

for the development and improvement of a for the development and improvement of a person’s intellectual competence ...”person’s intellectual competence ...”

Singapore Ministry of Education 2006Singapore Ministry of Education 2006

Source: Mathematics Syllabus Primary Source: Mathematics Syllabus Primary

Singapore Ministry of Education 2006Singapore Ministry of Education 2006

Heuristic: Model MethodHeuristic: 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 – 2010Source: Primary School Leaving Examination 2006 – 2010

The Bar Model MethodThe 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 – 2010Source: 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, LondonKing Solomon Academy, London

This refers to the two numbers

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 InstituteNational Singapore Math Summer InstituteDenver, USADenver, 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.

3Example 4

34Example 5

4Example 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

5Example 6

Did you get 3 as the final

answer?

88 – 34 = 5454 – 34 = 20 34 – 20 = 14

14

2 units = 143 units = 14 ÷ 2 x 3 = 21

21 girls wore goggles on that day.

Method 1 Guess and Check / Make a Table

Number of Children

3 $22 + $6 = $28 $24 + $25 = $49

4

….

Method 2 Using Number Sentences

$25 + $2 = $27$27 : $3 = 9There were 10 children.

Total amount = $8 x 10 + $25 = $105So each child received $105 : 10 = $10.50

Method 1 Guess and Check / Make a Table

30 – 3 = 275 x 27 = 135135 : 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

Attached School University of Tsukuba

Attached School University of Tsukuba