Problem solving techniques

[Mr. Whiting]

PROBLEM-SOLVING STRATEGIES

http://library.thinkquest.org/25459/learning/problem/#strategy

1. Make a table

2. Make an organised list

3. Look for a pattern

4. Guess and check

5. Draw a picture or graph

6. Work backwards

7. Solve a simpler problem

The list of problem-solving strategies above is by no means exhaustive. You may like to read up on some other strategies such as

(i) Reading and restating problem.

(ii) Brainstorming

(iii) Looking in another way

(iv) Making a model

(v) Identifying cases

Note: Different strategies can be used to solve the same problem.

Back to top

 

 

 

 

PROBLEM EXTENSION

Goals for Extension

1) Lead pupils to generalisation

2) Introduce or integrate other branches of mathematics

3) Provide opportunities for divergent thinking and making value judgements

 

Principles for Extending a Set of Problems

At a party I attended recently, I noticed that every person shook hands with each other person exactly one time. There were 12 people at the party. How many handshakes were there?

Principle for Problem Variation	New Problem
A. Change the problem context/ setting (e.g., party to a Ping-Pong tournament).	A. Twelve students in Ms.Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each students would play one game against each other students. How many games were played?
B. Change the numbers (e.g., 12 becomes 20 or n).	B. At a party I attended recently, I noticed that every,person shook hands with each other person exactly one time. There were 20 people at the party. How many handshakes were there? That if there were n people at the party?
C. Change the number of conditions(e.g., instead of the single condition that "every person shook hands with each other person exactly one time," we add the condition "Tim shook hands with everyone twice."	C. At a party I attended recently I noticed that every person but the host,Tim, shook hands with each other person exactly one time. Tim shook hands with everyone twice (once when they arrived, once when they left). There were 12 people at the party. How many handshakes were there?
D. Reverse given and wanted information (e.g., in the basic problem you are given the number of people at the party and you want to find how many handshakes there are; the reverse is true in the new problem).	D. At a party I attended recently I noticed that every person shook hands with each other person exactly one time. If I told you there were 66 handshakes, could you tell me how many people were at the party?
E. Change some combination of E. context, numbers' conditions, and given/wanted information (e.g., in problem E both the context and the numbers have been changed). Note: There are 11 combinations possible!	E. All 20 students in Ms. Palmer's fifth-grade class decided to have a Ping-Pong tournament. They decided that each student would play one game against each other student. How many games were played?

Back to top

 

 

 

 

REFERENCES

1. CHARLES, R. I. AND MASON, R. P. AND NOFSINGER, J. M.AND WHITE, C. A.
Problem-Solving Experiences In Mathematics. Addison-Wesley Publishing Company; 1985.

2. DOLAN, D. T. AND WILLIAMSON, J.
Teaching Problem-Solving Strategies. Addison-Wesley Publishing Company; 1983.

3.MEYER, CAROL AND SALLEE, TOM.
Make It Simpler. Addison Wesley Publishing Company; 1983.

4. POLYA G.
How To Solve It. Princeton University Press; 1973.5.

CAROLE GREENES, JOHN GREGORY AND DALE SEYMOUR.
Successful problem Solving Techniques. Creative Publications, Inc.

Back to top

 

http://math.about.com/cs/testprep/a/ps.htm?rd=1

http://store.atozteacherstuff.com/download-now/red0008.html

http://www2.yk.psu.edu/learncenter/acskills/mathprob.html

http://library.thinkquest.org/25459/learning/problem/#strategy