222 LOVING PROBLEM SOLVING Problem solving is an

222

LOVING PROBLEM SOLVING

Problem solving is an activity performed routinely by scientists and engineers. Problem solving can be seen as a process: IOT I 1 -10 POLY ENGINEERING

Another view of the problem solving process: IOT I 1 -10 POLY ENGINEERING

… from a 1947 arithmetic book … IOT I 1 -10 POLY ENGINEERING

Sometimes we have a humorous opinion of problem solving …. . IOT I 1 -10 POLY ENGINEERING

PROBLEM #1 : A man has a chicken, a fox, and some chicken feed. He wants to take all of them across a river, but his boat isn’t large enough. He can transport himself and only one other item during each crossing of the river. He can’t leave the chicken alone with the fox for the fox will eat the chicken. He can’t leave the chicken alone with the chicken feed for the chicken will eat the feed. How can the man get all three things to the other side of the river? Write down your answer. IOT I 1 -10 POLY ENGINEERING

PROBLEM #1 DIAGRAM SOLUTION: 1. Chicken crosses the river. 2. Boat returns to the other side. 3. Chicken feed crosses the river. 4. Chicken and boat returns to the other side. 5. Fox crosses the river. 6. Boat returns to the other side. 7. Chicken crosses the river. IOT I 1 -10 POLY ENGINEERING

PROBLEM #2 : A man lived one-fourth of his life as a boy in Baltimore, one-fifth of his life as a young man in Youngstown, one-third of his life as a man in Manitoba, and the last thirteen years of his life in Thurmont. How old was the man when he died? Write down your answer. IOT I 1 -10 POLY ENGINEERING

PROBLEM #2 ALGEBRAIC SOLUTION: Define the unknowns: X = man’s total age. X/4 = years as a boy X/5 = years as a youth X/3 = years as a man Write an equation: X = X/4 + X/5 + X/3 + 13 Solve the equation: 60 X = 15 X + 12 X + 20 X + 780 60 X = 47 X + 780 13 X = 780 X = 60 years IOT I 1 -10 POLY ENGINEERING

PROBLEM #3 : Given a stack of individual blocks as shown. How many more blocks are needed to fill the empty spaces and form a large cube? Write down your answer. IOT I 1 -10 POLY ENGINEERING

PROBLEM #3 MODEL SOLUTION: 9 blocks on level four 8 blocks on level three 6 blocks on level two 23 blocks were missing IOT I 1 -10 POLY ENGINEERING

PROBLEM #4 : HOMEWORK Given a stack of individual blocks as shown. If all of the visible blocks were to disappear suddenly, how many blocks would remain? Write down your answer. IOT I 1 -10 POLY ENGINEERING

PROBLEM #5 : HOMEWORK Draw the following figure in one continuous action without lifting your pencil off the paper and without crossing any lines. You may begin at any point. IOT I 1 -10 POLY ENGINEERING

September 20, 2010 HOMEWORK: (Problem Solving) 1. Complete any problems from today’s lesson that you didn’t already finish. 2. Answer problems # 4 - 5 on the printed sheet. IOT I 1 -10 POLY ENGINEERING