Chapter 1 Mathematical Reasoning Section 1.5 Problem Solving

In the early childhood curriculum problem solving continues to play a bigger role than in the past. The NCTM standards has put increased importance on problem solving. There are many different ways to solve problems. The type and frequency of problems you solve helps determine how good you become at it. Unfortunately there is no one way that will always work no matter what problem you are trying to solve. In fact we will see later that good problem solvers will employ a wide range of methods and be flexible in choosing the methods they use. There are a set of guidelines (or best practices) when it comes to problem solving. In 1945 a man by the name George Polya wrote a book How To Solve It where he described steps to follow to become a more successful problem solver. Polya gives the following 4 steps to problem solving: Understand the problem Devise a plan Carry out the plan Look back

1. Understand the problem It is critical to comprehend what is being asked in the problem. Here are some things that you want to keep in mind to help you. Read or listen to the problem carefully. (Maybe more than once.) Do you understand all the terms or words? What is being asked for? Is there too much or too little information? 2. Devise a plan You will need to determine what approach you will take to solve this problem. Think about the nature of the problem and what methods work. In mathematics this can be many different approaches: Algebra Formulas Guess and check Inductive Reasoning (Examples) Draw a picture or graph Work backward

3. Carry out the plan Follow the plan as carefully as possible trying to avoid mistakes. In many cases the plan is a good approach it is just the implementation is poor. 4. Look back Consider what resulted from following the plan keeping some of the following questions in mind. Did you find a solution? Is the solution what the question was asking for? Can your answer be checked? If so is it right? Will your method work for a similar problem? Lets see if we can apply this to some of the following problems.

Problem 1 Fill in each of the five circles to the right with the numbers 1,2,3,4,5 using each number only once so that the numbers going across and the numbers going up and down add up to the same numbers Problem 2 A class needs to raise $800 to take a field trip. A local business has donated $250 toward the trip. The class has 22 children in it, 10 of them are boys and 12 of them are girls. How much will each child need to pay in order for the class to go on the field trip? Problem 3 What is the area of the blue shaded figure to the right?