Math – Applications for Living XIII

We are at the end of the semester, so today is “final exam day” in our quantitative reasoning course.  Here are two problems from the final — both fairly complex, though students are doing okay with them.

First problem:

A family is filling a child’s “swimming pool” – a round pool that is 6 feet in diameter (3 feet radius). They will fill the pool to a depth of 2 feet, and will be using a garden hose to fill the pool We know that there are about 7.5 gallons of water in 1 cubic foot, and the hose will deliver about 10 gallons per minute. How long will it take to fill the pool, starting from empty, to the desired volume of water?

The formulas for volume are provided.  Students need to find the volume of the pool, and then use the units to correctly convert cubic feet to minutes 

This is similar to an earlier problem shared here.

The other problem is shorter, but more complicated in reasoning:

For a new play area, a school is using 200 meters of fencing. Find the area of a square enclosure, and of a circular enclosure, using this amount of fencing.

Again, formulas are provided.  Students need to find the side of a square with perimeter 200m … then the area; the circle is more challenging … students need to find the radius given the circumference, then find the area.  I have used this problem (with different quantities of ‘fencing’) for a while, and have been pleased with the reasoning students are showing.

 Join Dev Math Revival on Facebook:

3 Comments

• 

  By Linda, May 3, 2012 @ 11:30 pm

  I’m still perplexed by the need for algebra and higher math. What I see from people who tout it is basically that it’s the basis for engineers and computer programers, etc.

  I can also see the reason for saying that it increases logical thinking, but I’m an English teacher and basically I teach logical thinking in discussing how to prove your interpretation of a story/novel/poem/etc. using information from the text.

  So for the two examples above, in real life I wouldn’t use either of them. I would just put the hose in the pool and wait until it filled. Usually the kids will be hanging around, squirting each other, so the time to fill it couldn’t be predicted.

  As for the other, I’d let the contractor do it.

  I don’t want to say there aren’t applications for math in my life (I calculate tips, compare prices using volumes, figure the taxes on my salary after a raise, etc.) but I see those as basic math, not algebra.

  So why did I learn algebra? Why am I going to take it again so I can add it to the courses I can tutor in?

  This may not be the place to ask this question, but it’s burning at me. Can you help?

• 

  By Jack Rotman, May 4, 2012 @ 8:00 am

  Linda:
  I really appreciate you posting this question.
  First, I totally agree with you about logic … math does not have a monopoly on improving logic; in some ways, because of the emphasis math classes put on correct answers and procedures, we discourage logical thinking (“do not worry about understanding why we do this … just do it, so your answer is right”).

  About the examples … this is a tension in my class, as well. For almost any problem we do — some students will say “I know that I will never need this!” The every-day use for both problems is not the answer so much as it is being able to estimate (mathematically) what would happen — will it take 20 minutes or an hour to fill that pool? is a square or circle better for this project?

  Perhaps we can think about ‘algebra’ this way: Algebra provides grammar and syntax to make statements about the world. These statements, in turn, can be paraphrased to be a narrative (numeric and graphical representations); we can also make argumentative statements by using the symbolic form combined with properties of expressions and equations. Much of this work is centered on applying basic algebraic concepts such as rate of change, additive versus multiplicative change, inputs, outputs, appropriate values for an input (called domain), and properties of one & zero.

  As for why a given person has to learn algebra, there are two honest answers: The first (most common historically) is that it was decided that this would be a good experience for them to have; in practice, this is sometimes experienced as ‘math is screening out students’. The second (which we are trying to expand) is that the algebra will help (really help, not just ‘logic’) students in other courses and also in dealing with quantities outside of college; this second reason is based on the type of thinking is the preceding paragraph.

  Hope this helps … at least a little, tiny bit!
  Jack

• 

  By David Thomas, May 10, 2012 @ 7:51 am

  Linda’s question burns not only at her, it burns at many algebra students. The “because I said so” type answer doesn’t cut it for today’s students who are raised from very early on to question everything and to especially question authority.

  My opinion is math is like a toolbox. In life we often find ourselves needing to do something requiring a tool and the know-how to use it. The more tools we have in the box, and the more we know how to use them, the more prepared we are to do the tasks that present themselves to us. We may not be able to predict what those will be, but buddy, when the situation comes up and we have the right tool and the knowledge to go with it, we are cruisin’. If algebra is one of our favorite tools in the box, we are not forced to depend on the contractor’s calculations and assume they are correct.

  The algebra tool has applications beyond engineering and computer science. It is used by environmentalists, economists, statisticians, doctors, and all the social sciences when performing, reporting, and understanding the particular discipline’s research. To me those are among the reasons to require the study of algebra.

Other Links to this Post

RSS feed for comments on this post. TrackBack URI

Leave a comment

You must be logged in to post a comment.