Sunday, February 16, 2014

Accumulation Functions

I didn't like the treatment I gave to Accumulation Functions and the "2nd part" of the Fundamental Theorem of Calculus, so I thought I'd change it up this year.

Me Last Year: Here! Look at some quick calculations of going "forward" and "backward" on derivatives and integrals all mixed up. Boom! Here's the formula and let's apply. Oh, and here are accumulation functions. Area! Let's do it.

Me This Year: Okay, okay, let's spend more than a day point 5 on these things so you really internalize them and can get the nuances in your sleep and go on to fame and fortune accumulating all sorts of calculus knowledge.

(or at least this way of teaching it is a step in that direction).

I am not even mentioning FTC-2 to begin with. I'm going to start with this packet I made up. I have seen similar things on my web search, but I did not come across any that gave the context of the problems. I feel that THAT would have led to the same short memory of the process problems I encountered last year. 

I came up with 3 types of problems. I wanted them to be ones where the kids wouldn't feel like, "well hold on a minute there. Why don't we just measure the volume. This it too made up." Don't know if I nailed it, but I guess we will see when I present it tomorrow.

I think I will have to stop them at several points along the way just to make sure they don't get the wrong answer and then keep going on and cementing that to their brain.

Also, I have some ideas on then how to do the integrals "backwards" from a larger limit number to a smaller limit number. Still working on that. Then I think I can introduce FTC-2 based on all these problems and POOF! Success! Or at least that's how it goes in my mind.

Also, also, just because it's my last chance to brag. Okay, that's not true. I'll totally milk it at school tomorrow. I completed my first marathon today. Woot! 

And "funny" story in the continuing saga of my students feeling I'm 1 foot in the grave at 49. A kid the other day said she thought about me when she was in the store looking at cards. One was, "do you know what we call old people running a marathon? Obstacles."

Hah. Hah.  Of course she reassured me that she wasn't referring to me as "old". D*@# whippersnappers.


  1. Anonymous10:22 PM

    Thank you! I used these problems with my students and so far I think they've got it. Of course it helps that every time they used the phrase "total accumulation" I did a fist bump. Now if we can just keep our total accumulation of snow to a minimum, I can assess how much the understand as individuals.

  2. Sounds like there are TONS of snow days in the northern regions. Yeesh. We had 3 "snow" days, and are feeling behind, so I can't imagine 11 days or more.

  3. Do you happen to have an answer key for this worksheet? I just want to check my answers before using it. Thanks!

    1. Hello. Send me email at, and I can send you the key.

    2. Could I get the key as well? Would like to check my answers before my students do this. Thank you!

  4. This is awesome! I have never felt like my students really grasped accumulation functions, and I think this will be so helpful. Would you mind sending me your solutions, as well? ( I would like to check the wording I have used in some of the explanations. I am working with my students on being precise with their justifications, so I am trying to practice what I preach. Thanks in advance!

  5. Can i get an answer key? I'm a 1st yr calc teacher so this would be really helpful. Thx