Using Polya's 4 Steps to Problem Solving

Grade Level: 9

Materials: Prices of admissions and food to The Miami Seaquarium, paper, pencil, calculator, overhead projector.

Objectives: Students will be able to solve problems using Polya's 4 steps to problem solving.

Mathematical Concepts: Problem Solving, percents, arithmetic, decimals.

NCTM Standards:
Standard 1: Mathematics as Problem Solving
Standard 2: Mathematics as Communication
Standard 4: Mathematics Connections
Standard 7: Computation and Estimation
Standard 8: Patterns and Functions

Procedure: Introduction:

The class will review the 4 steps to Problem Solving (Polya's).

(1) Understanding the Problem:
Determine what is being asked, what information is known, what information is unnecessary to addressing the problem, and what information is missing or not known.

(2) Devising a Plan:
Find a strategy to help in solving the problem.
Strategies for Problem Solving include the following:

1. Look for a Pattern; 2. Make a Table; 3. Examine a Simpler Case 4. Identify a Subgoal; 5. Examine a Related Problem; 6. Work Backwards; 7. Write an Equation; 8. Draw a diagram; 9. Guess and Check; 10. Use Indirect Reasoning.

(3) Carrying Out the Plan:

Attempt to solve the problem with the chosen strategy. If the strategy does not work, try another strategy.

(4) Looking Back.

Check to see if the answer 'makes sense'. A good way to look back is to use another strategy to see if the same answer results.

(Note: This is not a lesson on Problem Solving Strategies, but rather on using the strategies that would have already been taught).

Development:

1. Students are given a list of prices for admission and lunch for the Miami Seaquarium (see attached).

2. The questions to be answered are written on the chalkboard. For each problem students will write their thought/working for each step of the Problem Solving Strategy. (See attached for problems)

Conclusion:

Students will volunteer to share their steps to solving the problems, and the solutions.

Answers:

1. $322.01; 2. Answers will vary: (i) Hot dog (ii) potato chips, soft drink, candy bar; 3. Hot dog, potato chips, soft drink, candy bar; 4. Answers will vary.

Extension:

Each students will write the number of members in their family, their ages, and the amount it will cost for the family to go to the Seaquarium, again writing each step of the problem solving strategy.

References: Curriculum and Evaluation Standards for School Mathematics (NCTM), Miami Seaquarium Brochure, Louis Musgrove, Tour & Travel Manager, Miami Seaquarium. Polya, How to Solve It.

Contributors: Major: Kimberley Collie
Minor: Carol Marinas, Leatisha Brown, Kari Kupler

Regular Admissions:

Children Under 3 years Free Admission
Children 3 - 9 years $13.95, plus tax
Children years and up $18.95, plus tax
Adults $18.95, plus tax

School Admission:

Pre-K to Grade 6 $4.00, plus tax
Grades 7 - 12 $6.00, plus tax

Lunch:

(Tax included)

Hamburger $ 3.01
Hot Dog $ 2.46
Potato Chips $ .70
Soft Drinks $ 1.09
Candy Bar $ .70

Group Lunch $2.50 (Includes a choice of hamburger, hot dog or pizza, a bag of potato chips and a soft drink)

(Tax is calculated at 6.5%)

Questions:

1. In order to get the group rates on admission and lunch, the trip must be paid for in advance. In a class of twenty-five 9th grade students, only 19 can pay in advance. If all of the students are going to the Seaquarium, how much would the class pay in total for admissions and lunch (the students who are not paying in advance order the same lunches as those paying in advance, half order hot dogs and half order hamburger) for a day at the Seaquarium? Calculate the tax on the total amount for the class.

2. What combinations of lunches can the students who do not pay in advance have, allowing them to pay as much as, but no more than, the students who purchase lunch in advance? (Remember: Water is free!)

3. If you had only $5.00 to spend for lunch, what could you buy to spend as much as possible?

4. What are the advantages and disadvantages of paying for lunch and admission on the day of the trip?