Geo - Ch 1 Problem Solving Quest

George Polya presented a four step process for problem solving which is still used extensively today. Which of the following is NOT a step in his basic process?

• Devise a plan.

• Understand the problem.

• Carry out your plan.

• Draw picture.

• Look back to analyze your solution.

The Guess and Test problem-solving strategy can be useful when

• there are only a few possible solutions to a problem.

• the problem suggests an equation.

• you are trying to develop a formula.

• you need to find the measures of the angles in a triangle.

• there is an unknown quantity related to known quantities

You may wish to use the “Solve a Simpler Problem” strategy if:

• a. The problem involves very large or very small numbers.

• b. There are a large number of cases.

• c. A direct solution is too complex.

• d. Both (a) and (b) are correct.

• e. Both (a) and (c) are correct.

When using the Guess and Test Problem Solving Strategy you will probably be most successful if you

• a. simply try possibilities at random.

• b. use a means of organizing your guesses.

• c. try to learn from each of the trials.

• d. apply both parts (a) and (c).

• e. apply both parts (b) and (c).

If a problem asks “how many cubes are in the nth figure,” an approach to solving the problem might be:

• Guess and Test.

• Draw a Picture.

• Make a Table.

• Look for a Pattern.

• Use a Variable.

If a problem asks you to “Find a formula . . . “ you might begin by

• drawing a sketch of the problem situation.

• understanding the terms used in the problem.

• looking for relationships between known quantities and the unknown quantity.

• making a tables of values, using n as the unknown quantity.

• trying any one of the above.

If you are given a sequence of numbers and asked to predict the next number in the sequence, a problem solving strategy you might reasonably try is

• Look for a Pattern.

• Draw a Picture.

• Guess and Test.

• Trial and Error.

• None of these is a particularly good strategy.

If a problem begins with “There are 200 people at a dance . . .”, an approach to solving the problem may be

• Draw a Picture.

• Guess and Test.

• Solve a Simpler Problem.

• Deductive reasoning.

• None of these is a good approach.

When we look at specific examples, observe a pattern, and draw a general conclusion, we are using

• the Draw a Picture problem-solving strategy.

• Deductive reasoning.

• the Use a Variable problem-solving strategy.

• The Guess and Test problem-solving strategy.

• Inductive reasoning.

Deductive reasoning requires us to

• accept some initial conditions as true.

• make a table.

• look for a pattern.

• solve a simpler problem.

• draw a picture.