Slide1: Red Swastika School Model Drawing and Heuristics Workshop for Parents 17 July 2004, Saturday 9.30 am AV Theatrette


Slide2: There were 3 men and 3 cannibals at the near-bank of a crocodile-infested river. They planned to cross the river to the far-bank using a small boat which could only carry 2 people. At any time there should not be more cannibals than men, otherwise, the cannibals would eat up the men. How could all 6 people cross the river? TUNING-IN ACTIVITY


Slide3: Problem Solving should be essential part of mathematics activity. Problems should include familiar and unfamiliar problems and those related to everyday life situations. Pupils should be encouraged to use varied strategies to solve problems, to seek alternative solutions to problems and to create, formulate or extend problems. MATHEMATICAL PROBLEM SOLVING (MOE, 2000)


Slide4: Process - the means by which an individual uses previously acquired knowledge, skills and understanding to satisfy the demands of an unfamiliar situation. 2) Individuals must synthesize what he has learnt and apply it to the new and different situations. WHAT IS PROBLEM SOLVING?


Slide5: According to Oxford dictionary, they are referred to as the study of how people used their experience to find answers to questions or to improve performance. WHAT IS HEURISTICS?


Slide6: Algorithms Procedures which if applied correctly guarantee a solution in a finite number of steps. Heuristics (Problem-Solving Strategies) Procedures which, while they have a high degree of success in directing you to a solution (information), do not guarantee success.


Slide7: PROGRAMME Examination Format Introduction to Part-whole Models Guess and Check / Listing Working Backwards Look for a Pattern Logical Reasoning Make a systematic List Act it out


Slide8: PSLE EXAMINATION FORMAT SECTION A: Multiple-Choice Questions 5 Questions  1 mark 10 Questions  2 marks SECTION B: Short-Answer Questions 20 Questions  1 mark


Slide9: SECTION C: LONG-ANSWER/STRUCTURED (55 marks) 15 Questions 2/ 3/ 4/ 5 mark Questions Marks awarded for working shown. PSLE EXAMINATION FORMAT


Slide10: John’s age is 1/3 of Alice’s age. Mr Wu’s age is 3 times Alice’s age. If Mr Wu is 40 years older than John, how old is Alice? Workings: Alice’s age John’s age 8 units  40 years 1 unit  5 years Alice’s age = 5 × 3 = 15 years old 40 years Mr Wu’s age


Slide11: Johnny spent 1/5 of his salary on food, 3/8 of the remainder on clothes, $125 on transport and had $875 left. What fraction of his salary was spent on transport? Workings: Johnny’s salary 8 units  40 years 1 unit  5 years Alice’s age = 5 × 3 = 15 years old Food Remainder


Slide12: Johnny spent 1/5 of his salary on food, 3/8 of the remainder on clothes, $125 on transport and had $875 left. What fraction of his salary was spent on transport? Workings: Johnny’s salary 5 units  $1000 1 unit  $1000 ÷ 5 = $200 Amt of Johnny’s salary = $200 × 10 = $2000 Fraction of his salary spent on transport = 125/2000 = 1/16 Food Remainder Clothes $125 + $875 = $1000


Slide13: A sum of money is divided among William, Xavier and Yvonne in the ratio 4 : 2 : 3. If Xavier and Yvonne get a total of $5175, what is William’s share? Workings: William Xavier 5 units  $5175 1 unit  $5175 ÷ 5 = $1035 William’s share = $1035 × 4 = $4140 Yvonne


Slide14: P3 and P4 pupils participated in a competition in the ratio 2 : 1. All the P3 participants were girls. Among the P4 participants, the ratio of girls to boys is 4 : 3. What fraction of the P4 participants are boys? There are 70 more P3 girls than P4 girls taking part in the competition. How many participants are girls? Workings: 4 units + 3 units  7 units Fraction of the P4 participants are boys = 3/7 Girls Boys


Slide15: P3 and P4 pupils participated in a competition in the ratio 2 : 1. All the P3 participants were girls. Among the P4 participants, the ratio of girls to boys is 4 : 3. What fraction of the P4 participants are boys? There are 70 more P3 girls than P4 girls taking part in the competition. How many participants are girls? Workings: 14 units - 4 units  10 units 10 units  70 1 unit  70 ÷ 10 = 7 Total number of units = 14 + 14 = 18 No of participants are girls = 18 × 7 = 126 P3 P4


Slide16: Danny has a total of 24 two-dollar and five-dollar notes. If he has $69 altogether, how many two-dollar notes does he have? No. of $2 notes Amt of money No. of $5 notes Amt of money Total amt of money 20 19 18 17 $40 $36 $34 $38 4 5 6 7 $35 $30 $25 $69 $66 $63 $60 $20 Answer: He has 17 two-dollar notes.


Slide17: Thomas bought a total of 50 goldfish and angelfish. Each angelfish cost $6. Each goldfish cost $5. If the total cost of the angelfish is $47 more than the goldfish, how many angelfish and goldfish did Thomas buy? No. of angelfish Amount No. of goldfish Amount Difference 25 26 27 $150 $162 $156 25 24 23 $115 $120 $47 $36 $25 $125 Answer: He bough 27 angelfish and 23 goldfish.


Find the area of the right-angled triangle shown below.: Find the area of the right-angled triangle shown below. Given length of hypotenuse, find the area of the right-angled triangle. How do you solve it without using Pythagoras’ theorem? 10 cm


Find the area of the right-angled triangle shown below.: Find the area of the right-angled triangle shown below. 10 cm 10 cm 10 cm 10 cm Area of the right-angled triangle = (10 ×10) ÷ 4 = 25 cm2


Find the value of : + + + + + : Find the value of : + + + + +


Find the value of : + + + + + : Find the value of : + + + + + + = + + + + = + + + + + = + + + + + = =


Slide22: This quiz is supposed to have been written by Einstein. He said that 98% of the people in the world cannot solve the quiz. Could you be among the other 2%? Adapted from http://www.grand-illusions.com


Slide23: There are 5 houses, each is a different colour. In each house lives a person of a different nationality. These 5 owners all drink a certain beverage, smoke a certain brand of cigar and keep a certain pet. No owner has the same pet, smokes the same brand of cigar or drinks the same drink as another owner. 1. The Briton lives in a red house. 2. The Swede keeps dogs as pets. 3. The Dane drinks tea. 4. The green house is on the left of the white house (they are also next door to each other) 5. The green house owner drinks coffee. 6. The person who smokes Pall Mall rears birds. 7. The owner of the yellow house smokes Dunhill. 8. The man living in the house right in the centre drinks milk. 9. The Norwegian lives in the first house. 10. The man who smokes Blend lives next to the one who keeps cats. 11. The man who keeps horses lives next to the man who smokes Dunhill. 12. The owner who smokes Blue Master drinks beer. 13. The German smokes Prince. 14. The Norwegian lives next to the blue house. 15. The man who smokes Blend has a neighbour who drinks water. The question is: WHO KEEPS FISH?