Help Your Child in Problem-Solving

Heuristics

Dr Yeap Ban Harbanhar.yeap@pathlight.org.sgMarshall Cavendish Institute

Singapore

www.banhar.com

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

Heuristics are rule of thumb that students can use to handle a problem when the solution is not obvious.

The problems used in the presentation are from PSLE Examination Questions Years 2006 – 2010 Mathematics published by Educational Publishing House Pte Ltd.

PSLE 2006 – 2010 Page 13 Question 45

Photo Credit: Primary 2 students at Woodlands Primary School using manipulatives to do multiplication and division.

PSLE 2006 – 2010 Page 13 Question 46

1.2 m x 42 = 50.4 m

43 – 6 = 37 There were 36 spacing

50.4 m ÷ 36 = 1.4 m

The new spacing was 1.4 m.

PSLE 2006 – 2010 Page 19 Question 58

Guess when each tried taking 11

33 Last girl had 11 sweets 41 Last girl had 8 sweets 49 Last girl had 5 sweets 57 Last girl had 2 sweets

PSLE 2006 – 2010 Page 19 Question 58

List 1 List 2

11 + 622 + 633 + 644 + 655 + 666 + 6

16 + 2524 + 2532 + 2540 + 2548 + 2556 + 25

PSLE 2006 – 2010 Page 19 Question 58

List 1 List 2

11 + 622 + 633 + 644 + 655 + 666 + 677 + 688 + 699 + 6

16 + 2524 + 2532 + 2540 + 2548 + 2556 + 2564 + 2572 + 2580 + 25

PSLE 2006 – 2010 Page 19 Question 58

3 x ? = 2 + 25

? = 9

There were 10 girls.

There were 9 x 11 + 6 = 8 x 10 + 25 = 105 sweets altogether.

PSLE 2006 – 2010 Page 19 Question 58

11m + 6 = 8(m + 1) + 25

Alternate Method8n + 25 = 11(n – 1) + 6

There were 10 girls. m = 9

n = 10

women

men 30

There were 4 x 30 = 120 men and women at first.

Photo Credit: Primary 2 students at Woodlands Primary School using the interactive board to learn independently and collaboratively.

Method 2Selecting 4 persons from a group of 5 is the same as to leave out one person from a group of 5.

There are 5 ways to leave out 1 person from a group of 5.Hence there are 5 ways to select 4 prefects from a group of 5 students.

Method 1Azlan, Bala, Chris, DarrenAzlan, Bala, Chris, EnlingAzlan, Bala, Darren, EnlingAzlan, Chris, Darren, EnlingBala, Chris, Darren, Enling,

38 + 57 = 95 2 fifths 38 peaches2 fifths 38 peaches1 fifth 19 peaches

3 fifths 3 x 19 pears = 57 pears

1 fourth = 3/12

1 third = 4/12

remainder= 5/12

5/12 95 fruits

1/12 19 fruits

There were 12 x 19 fruits or 228 fruits.