Problem solving Math 123

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 know- how, 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

Washington State Standards Mathematics/default.aspxhttp:// 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.