Saturday, November 02, 2013

Related Rates and Crowd Sourcing

Year Six of teaching this pickle of a topic in Calculus. I keep changing it up hoping I'll happen upon the magic elixir that will allow students to eagerly gobble up the problems and spit out the correct answers with joy and understanding oozing out of their pores.

* Finding problems that aren't the Wisconsin of all Cheese Balls.
* Reading and interpreting the problem.
* Being able to translate known information and subtly given information into Math Speak.
* Finding the right equation that links all the variables together.
* Navigating the Dangerous Path of Implicit Differentiation.
* Plugging back in at JUST the right time.
* Finishing things up with a tidy bow.

I have a good feeling about this year! And yes, I say and mean that every year, so I am allowing my bubble to remain floating blissfully in the air yet again.

First of all, cheesy problems: ladders sliding down walls, circles mysteriously expanding and contracting, lots of liquids being poured into and leaked out of cylinders/cones/prisms, cars passing in the night at some perpendicular intersection.

I started off this year's spiel with just a blathering of why this topic is important:

BP oil spill, how fast is it spreading? How will they know how much resources to devote to the problem?

The rain recently in Austin, TX, people's houses were ruined, water was rising at various rates, what could that mean for drainage capabilities and emergency personnel?

Fires in Bastrop, containment, speed of spreading vs speed of dousing ....

The amusement park problem on some previous AP exam about rates of people in park and number of employees needed ...

But then alas, we had to start on the cheeseball problems. But I prefaced it with, "no one really cares about a balloon being expanded or contracted, but as with all math modeling, we may have to start with a simplified version of reality just so we can gain understanding and maybe add difficulty and more accuracy later. Think about some real life things that could be modeled by a malleable sphere."

That was about as far as I got on that THEN. Wait for it .....

Also, I spent a class period JUST setting up problems with the students, and their homework was to differentiate and solve. I found Bowman's set up with the table for variables very nice and tidy and useful. I'm a convert. In the past, I just set the students on their merry ways to attempting each problem on their own. This year I was uber bossy and said I wanted things set up in a specific way - enter the drawing and table and something new I added: a highlighted box or equation that I labeled SUBTLE information. There are some things that are not specifically mentioned in the problem, but you can figure needed information out like a detective. I wanted the students to be on the lookout for such things and to know that they exist.

I think this is the NEW component I'm adding to the homework next time. They will get the goofy circle/square/car problems, but with EACH problem or maybe just one, they have to do extra. This is where my crowd surfing comes in. I want them to think of a NEW specific real life situation that (say) could be modeled by this simplified version or expanded upon, and discuss what rates are needed and why anyone would care.

I'm looking forward to seeing their responses.


  1. I hate the ladder problems too - it's not going to slide down at a constant rate! So I skip 'em.

    And I've always skipped the ones with zero context.

    But I have a fondness for coffee pots with conical filters above them, and clock hands and baseball players running. Maybe college students are more forgiving?

    I'll look over your stuff carefully. I have to grade the test that includes related rates today or tomorrow. If they do badly, maybe I can give them some tips from your stuff, so they can learn it, retake their related rates mini-test, and excel!

  2. Anonymous7:01 PM

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  3. Hi Sue. Oh my kids DO the problems, but I guess I personally want to see some more relevant ones. It's still fun to teach, though, and I'm hoping for more success this year.

  4. Funny, but I always loved teaching that topic. It was fun getting the kids to come up with equations and then solve them. Oh, some were really bad, but I loved the thought process and the fact that there was no one size fit all solution.

  5. PO! It IS fun to actually see the calculus in context. ... And I am sorry about your dad. Hope you are surrounded by love.

  6. Hi! My name is Jamie Baxter, and I am a student in EDM310 at the University of South Alabama. I am going to school to become a teacher.

    After reading your post, I can see the issues you have when teaching the concepts of related rates and crowd sourcing.

    I love the idea you have that the students have to do extra by thinking of a real life situation that could be modeled by the simplified version on one of the homework problems. This will get the students thinking outside the box of just solving the problem, and they will understand it more.

    I am taking note of this for when I become a teacher. This is a great idea!

  7. I will be back to this market to try the mooshie burger and I will be back for the Ciabatta too!! I am becoming a mushroom lover, yay! candidate sourcing