*Because they launched into steps 2 and 3 with abundant understanding, those steps typically took experts less time. Experts use each successful problem solving experience as a chance to hone their skills and knowledge.If you’d like to become an expert problem solver, the last step is vital. What extensions or related problems could be solved in a similar way? The non-experts rushed into a plan, carried it out and quit.*

The vertex can “slide” along this parallel without changing the height of the triangle, so all triangles created this way have the same area. This led to the idea of “slide the base” of a trapezoid.

If you create a trapezoid with bases of length 1 and 4 (and height 1), you can slide either base along its parallel line without changing the area.

You find reasonably quickly that area calculations just mean counting up squares and half squares.

You run out of easy figures pretty quickly, maybe after 5 or 6. One problem is that many of the figures are congruent – they are exact copies of each other after a rotation or reflection (or both).

Expert problem solvers spent a large amount of time not just checking their work but reflecting. They had no idea if their solution was correct and typically gave up if their plan failed. Expert problem solvers often find during step 3 that the plan they devised isn’t working.

However, they realize that they are back to step 1 and now understand more about the problem.

The you create a triangle with area 2 (base 2, height 1) and begin adding triangles to its base. Step 4: Refelction When I did this problem, I realized several things.

First, the “slide the vertex” triangle activity is important. Draw a line through the third vertex that’s parallel to the base.

For example, they might simplify the problem purposefully and work on the easier problem for a few minutes.

They might draw diagrams or create an organized list.

## Comments Polya Problem Solving Steps

## Polya’s Problem-Solving Process

Polya’s Problem-Solving Process Problem-solving is the cornerstone of school mathematics. The main reason of learning mathematics is to be able to solve problems. Mathematics is a powerful tool that can be used to solve a vast variety of problems in technol-ogy, science, business and ﬁnance, medecine, and daily life.…

## How to Solve It - Wikipedia

Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya's work. How to Solve it by Computer is a computer science book by R. G. Dromey 29.…

## Polya's Problem Solving Process - YouTube

This video walks you through using Polya's Problem Solving Process to solve a word problem. 4 Steps to Math Problem Solving - Duration. Sabrina Knopf 21,310 views.…

## Polya’s Problem Solving Techniques - edu

Polya’s Problem Solving Techniques In 1945 George Polya published a book How To Solve It, which quickly became his most prized publication. It sold over one million copies and has been translated into 17 languages. In this book he identifies four basic principles of problem solving. Polya’s First Principle Understand the Problem…

## Polya's four-step approach to problem solving

To begin this task, we now discuss a framework for thinking about problem solving Polya’s four-step approach to problem solving. Polya's four-step approach to problem solving 1. Preparation Understand the problem Learn the necessary underlying mathematical concepts Consider the terminology and notation used in the problem 1.…

## Polya's 4-step problem solving process - YouTube

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## Steps to Problem Solving - Scholastic

This content resource describes problem-solving methodology. The resource breaks down problem solving into 4 essential steps, describing each step in detail, based on the problem-solving steps first outlined by George Polya in 1945.…

As mentioned above, I use Polya’s four steps to problem solving to show students how to solve word problems. Just note that your math teacher or math book may word it a little differently, but you will see it all basically means the same thing.…