Transcript Problem solving - PLU | Pacific Lutheran University

Problem solving
Math 123
Why problem solving?
Why problem solving?
• Essential for mathematics
• According to NCTM, one of the processes
through which mathematics should be
taught
• Fun way to begin semester.
Polya’s four steps
1.Understand the problem
2.Devise a plan
3.Carry out the plan
4.Look back
Polya’s ten commandments for
teachers
1. Be interested in your subject.
2. Know your subject.
3. Try to read the faces of your students; try to see their
expectations and difficulties; put yourself in their place.
4. Realize that the best way to learn anything is to discover it
by yourself.
5. Give your students not only information, but also knowhow, mental attitudes, the habit of methodical work.
6. Let them learn guessing.
7. Let them learn proving.
8. Look out for such features of the problem at hand as may
be useful in solving the problem to come -- try to disclose
general pattern that lies behind the present concrete
situation.
9. Do not give away your whole secret at once -- let the
students guess before you tell it -- let them find out by
themselves as much as is feasible.
10. Suggest, do not force information down their throats.
NCTM Standards
• http://standards.nctm.org/
Washington State Standards
• http://www.k12.wa.us/CurriculumInstruct/
Mathematics/default.aspx
Group work
• Problems 34, 35 from Section 1.1
Strategies
• Note that almost all the problems in the
presentation are solved in the textbook.
Strategy: Look for a pattern or Make
a diagram
• Find the sum of all whole numbers
between 1 and 100.
Strategy: Examine a related problem
• Find the sum of all even numbers
between 1 and 100.
Strategy: Examine a simpler case
• Find the sum of interior angles of a
pentagon.
Strategy: make a table
• Molly and Karly started a new job the same
day. After they start work, Molly is to visit
the home office every 15 days and Karly is
to visit the home office every 18 days. How
many days will it be before they visit the
home office on the same day?
Strategy: Guess and check
• A farmer has sheep and chicken running in
the yard. She can count 32 heads and 100
legs. How many sheep and how many
chicken are there?
Other strategies
• Identify a subgoal
• Work backward
• Use indirect reasoning
• Use direct reasoning
• Use a variable
• Look for a pattern
…and others…
Handshake problem
• Which strategies did we use?
Handshake problem
• Draw a picture
• Look for patterns
• Solve a simpler problem
Important!
• Make sure to read this chapter because it
solves sample problems for each strategy
and teaches you how to recognize which
strategy to use.
• Note that you will hardly ever be using one
strategy in isolation. It is not as important to
recognize strategies as it is to solve
problems. This comes with practice.