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Problem-Solving Heuristics in Mathematics
Dr Yeap Ban HarMarshall Cavendish Institute
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
Red Swastika School Workshop for Parents
Attached School University of Tsukuba
Attached School University of Tsukuba
Attached School University of Tsukuba