Problem Solving

This week in class we have been going through all different types of problem solving. It's so funny because as the problems were presented in class, I found myself thinking the problems were harder than they actually were. This is a common misconception with kids as well when they are presented with a word problem of this sort. Going back to the basics of math concepts can be harder than you think after learning more complex concepts in the more recent years. If you get down to it and break the problem apart step by step, they are not very difficult and hopefully won't scare kids away as much. 

Here are some step by step helpful tips to keep you going if you get stuck in the middle of a word problem! 

http://www.livingpolesapartbipolar.com/2012/07/08/effective-problem-solving-bipolar-patients/

The problem I would like to share is posted below.

In a stock car race, the first five finishers in some order were a Ford, a Pontiac, a Chevy, a Buick, and  a Dodge. What order did the 5 cars finish? Here are a few hints to help you solve the problem.

Ford finishes 7 seconds before Chevy

Pontiac finished 6 seconds after the Buick

Dodge finished 8 seconds after the Buick

The Chevy finishes 2 seconds before the Pontiac

When I first read this problem I began to think in through in my head and try to randomly place the cars in the right order. I realized this was not a very accurate method, so I decided that I needed to draw a picture instead. There is nothing wrong with drawing a picture! In school I was always more of a visual and hands on learner, so these word problems always scared me away and I felt like drawing a picture was silly or meant I was stupid. Most kids will be able to understand what the words mean when a picture is drawn on paper and they will probably end up grasping the concept more fully rather than trying to process words and numbers on a paper. Other kids may need something in their hands to put the cars in order. It would also be a great idea to use toy cars for the kids to be able to manipulate the cars in the right order to reach all different types of learners.

I used the clues to decide what I should do first. I decided to make a number line to start out. I am in love with the idea of using a number line whenever possible! 

• First, I put a bunch of hash marks on the line representing 1 second per hash mark.  The first clue said Ford finished 7 seconds before the Chevy. I put Ford down first and then counted 7 seconds backwards on the number line and wrote down Chevy. 
• The next clue mentioned the Pontiac and the Buick. So far there was nothing written down referring to those two models of cars so I went on to the next clue. 
• The next clue said Dodge finished 8 seconds after the Buick. Again, there was no reference to the Ford or Chevy that were already on the number line so I skipped to the last clue. 
• The last clue stated that the Chevy finishes 2 seconds before the Pontiac. Because the Chevy was already on the number line, I counted back 2 seconds from the Chevy and wrote down Pontiac. Now that Pontiac was on the number line I was able to continue with the previous two clues. 
• The previous clue said that the Pontiac finished 6 seconds after the Buick. This gave me the reference point of the Pontiac. I counted 6 seconds ahead of the Pontiac and wrote down the Buick. 
• That left only one more clue which stated that the Dodge finished 8 seconds after the Buick. Now that the Buick was on the number line I counted 8 seconds backwards and wrote down the Dodge. 

My final answer is this: 

Even though some of the clues were not helpful right away, I kept going through the problem and came to them at the end to be able to complete the problem. It's important not to let confusion or getting stuck in the middle of a word problem discourage you from moving forward and identifying another aspect of the problem that could be solved first. Drawing pictures can make the problem so much more fun and not as painful to get through.

 Happy Problem Solving!