Problem Solving

Polya's Problem-solving principle

Concepts

Understand the problem!

Make sure the first thing you do is, truly understand what the problem is asking you and what it is you are supposed to do!

Devise a Plan

Think of different ways of how you could solve the problem

Carry out the plan

Try the plan you have decided to use and if that plan does not seem to work, try something else!

Look back

Go over what you have done and recall how you got there so you will be ready for the next time, a similar problem occurs!

Problem solving strategy of "guess and check."

Example

Problem solving strategy of "make an orderly list"

Example

Problem solving strategy of "draw a diagram"

Example

Work Backward- this means to start at the end of the problem, with the result you are looking for.

Example

By applying the working backwards strategy, students find the solution to a problem by starting with the answer and using inverse operations to undo the steps stated in the problem.

e.g., a + b = c : c - a = b

A problem may tell you what happened at the end of a series of steps and ask you to find what happened at the beginning. To solve the problem, work backward step by step to the beginning.

Example

Brady was trying to decide when to get up in the morning. He needs 45 minutes to get ready for school. It takes him 25 minutes to drive to school. He wanted to get to school 20 minutes early to use the library. If school starts at 7:30, what time should he get up?

The problem gives you the amounts of time it will take to complete three tasks (45 minutes, 25 minutes, 20 minutes). It also tells you the time the last task must end (7:30). To solve the problem, work backward to the beginning.

Task Amount of Time Conclusion

1 Brady went to the library for 20 minutes. Then it was 7:30. He went to the library 20 minutes before 7:30, at 7:10.

2 He drove for 25 minutes. Then it was 7:10. He got in his car 25 minutes before 7:10, at 6:45.

3 He needed 45 minutes to get ready for school. Then it was 6:45. He began getting ready 45 minutes before 6:45, at 6:00.

Brady should get up by 6:00.

Remember:

The answer is found by starting with the end result and working back to the beginning.

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Topic Index | Grade 4 Math | Elementary Test Prep | StudyZone

Created by Carol A. Carroll

Updated by Nicole Freebern

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Eliminate the possibilities

Example

Pingeonhole principle-

Example

Pascal's triangle:

Pas·cal's tri·an·gle

nounMATHEMATICS

a triangular array of numbers in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row above (the apex, 1, being at the top). Found at: https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=define%20pascal's%20triangle

A counter example- this is an example that proves your statement false. Very helpful when deciding if what your plan is, is valid or not.

Conclusion- is when you have found a true statement, in regards to the problem you are working on.

Fibonacci sequence- this sequence starts with the two number ones, and then you add consecutive terms to get to the next one.

Use a variable- trying using a symbol, letter for a variable to use to represent and discover a number that is the answer to the problem you are solving.

Example

Algebraic Expressions- an expression using numbers, variables and symbols.

Examples

Algebraic reasoning- while using algebraic reasoning, you have several steps to follow: introduce variables, form and solve equations, interpret solution to solve the problem.