Frogs, frogs, frogs

Sometimes, I over think math problems.  And sometimes, over thinking the problems doesn't help me out! My math class just took our first math exam and I didn't do as well as I had hoped.  My goal was an A, but I got a B (I know, a B is still a good grade but I was still bummed).  As I looked through my test, I noticed that there were silly mistakes.  For example, I got confused with a question and thought it was asking about the odds with cards rather than the odds with dice (my numbers were completely off).  There was one particular problem that I missed, and I had hoped that the question wouldn't be on the test (with my luck, it was).  For some reason, I could not figure out how to interpret the question.  I was over thinking the problem.

I looked through my online homework questions (the question was taken from the online homework) to see if I could find the solution and hopefully come to understand it.  As I looked at the examples, I figured out that it was a very simple question!  

Here is the problem that I struggled with...

An estimate in the frog population in a certain pond was found by catching 25 frogs,

marking them, and returning them to the pond.  The next day, 60 were caught, of 

which 14 had been marked the previous day.  Estimate the frog population of the pond.    

My initial thought is to put these numbers into a proportion.  But in what order?  And then after we make the proportion, how do we figure out the entire frog population of the pond?

In my homework, there was an example of a proportion to a similar question.  Instead of frogs, it was trout. By looking at this example, it really helped me understand this question and how to set up the proportion.

So in order to start the question about the frogs, we have to set "X" equal to the estimated number of frogs in the pond.

Let X = the estimated number of frogs in the pond

Then we have to set up a proportion, similar to the picture above.

             

After this step, we need to cross multiply.  We will have an equation, and all we need to do is solve for "X".

Since we cannot have .14 of a frog, we need to round off the answer.  The estimated number of frogs in the pond is 107.

This question may seem very easy to some people.  But we all have those instances when we are over thinking on a math problem and can't seem to figure it out.  It is those particular times when we can learn the most, if we can break down the question and work it out.

Source for the test question:

Klassen, Rosanna. Math test. Mathematics for Elementary Education Teachers II. Mesa Community College, Mesa, AZ.

Source for the homework problem:

Libeskind, Shlomo, and Johnny W. Lott. "Chapter 9 Probability." A Problem Solving Approach to Math for Elementary School Teachers. By Rick Billstein. 10th ed. N.p.: Pearson Education, n.d. 515-87. Web.