Problem Solving WEEK 3

Activity 1.2: Ducks & Cows Farmer McDonald raises ducks and cows. The animals have a total of 9 heads and 26 feet. How many ducks and cows does Farmer McDonald have?

How do you solve the problem ? What are the heuristics you use in solving the problem? What are the steps? What are the PS strategies you use? Did it work/didn’t work ? Why? How can you improve your PS heuristics?

EXTENSIONS…What if…. What if … there were: 9 heads and 20 feet; 10 heads and 24 feet; 8 heads and 24 feet; 9 heads and 50 feet; 6 heads and 17 feet; or 10 heads and 18 feet What if Farmer McDonald sees some of each kind of animal and altogether sees 24 feet (not including his own), how many ducks and cows does he see? Show all possible answers.

Towers of Brahma Towers of Brahma is more commonly called 'Towers of Hanoi' and rarely 'The End of the World Puzzle' (the legend explains the second name).  It was invented in 1883 by a French mathematician named Edouard Lucas, based on an ancient Hindu legend.  

Towers of Brahma 1. Only one disk can be moved at a time The legend tells that Brahma placed 64 gold disks on a pillar of Benares Temple stacked in order of size (as shown). The monks there are asked to move the disks from the first pillar to the third pillar with these conditions:- 1. Only one disk can be moved at a time 2. No disk may be placed on a smaller disk at any time. How long does it take to move the disks if the time taken to move one disk is one second?

Strategies used Use objects Identify sub goal/Simplify the problem Experimentation/Simulation Collect data Use a table to record data Identify pattern Look for a relationship Use induction

Experimentation and Simulation Acting out the problem forces an understanding of the nature of the problem. Some manipulative objects can be used to represent things or people Can simulate the action by making drawing or a table

Identify pattern and making table No. of disk No. of steps 1 1 2 3 3 7 4 15 5 31 n Identify pattern 2-1 = 21 - 1 4-1 = 22 - 1 8-1 = 23 -1 16-1 = 24 - 1 32-1= 25 - 1 2n - 1

Discuss… Examples of real-life problems, Application of problem-solving skills in real life, and Creative problem solving in real life.

Tutorial Do Tutorial 1.2