Last year in calculus on day one, my students explored local linearity on the calculator. The NEW fancy schmancy TI-nspire calculators that THAT class had experience with. This year's group is used to TI-84's, so they need some prep work. But since I wanted to start with Calculus and not Calculator-us, I'm switching
what we're doing:
As I'm taking care of administrative things, they will be working on this. They know nothing about derivatives and integrals and calculus. I will not help them.
I want them to see the difference in difficulty from the left pictures and the right ones. I want them to see the possibilities that exist. I want them to struggle with strategies. I want them to remember some geometry. I want them to think about reading graphs. I want them to be intrigued.
Afterward, we will discuss the "words" that define calculus: a study of rates of change, instantaneous values, ...
Lovely start! If I can find the time to post, I should describe my first week of calculus. It's been fun (for me, anyway).
ReplyDeleteI love this! Thank you so much for sharing! :)
ReplyDeleteThanks, "guys"! I can't wait to see what comes up on Monday and how they handle it.
ReplyDeleteGood luck today! They'll see both differential and integral calc on the first day!
ReplyDeleteAlso, can you direct me to a how-to to make the images pop out when clicked on? Can it work for PDF files as well?
~Mr. C
Hi Mr. C. I really don't know the specifics of the image popping. It's just a feature of blogger.com.
ReplyDeleteIs that what you use, or is this for a different context, or am zi misunderstanding your question?
That's what I was asking. I use weebly, and I'm not quite sure how to make it work.
ReplyDeleteDid the students have good ideas about figuring out that shape's volume?
~Mr. C
Mr. C. I looked on Weebly, and the "put a picture here" button had a "pop out option". It didn't make it any larger, so I don't know how it would work for PDF pictures.
ReplyDeleteThere was interesting discussion about the shape's volume. Some just did a rectangle around it and got a max. Some did big and little rectangle and got a range. One student got the closest, and she made DISCS and summed them up :).
That's awesome! Not only did they get approximations, you got to talk about how good those approximations are with upper and lower bounds!
ReplyDeleteThanks for the help. I actually got something close enough to work. You can check it out
http://internallytangent.weebly.com/1/post/2013/08/broadway.html
Cool! Thanks.
ReplyDeleteDo you ever go over the solutions or at least give the answers?
ReplyDeleteHi Jenn. For this assignment, we have a discussion at the end of the first day about what they did. I also mention that with knowledge of the functions that make up the curves we can find the EXACT values using calculus and that's part of what this year is about. As for other homework throughout the year, I hand out a detailed key (one per 2 people) every class for them to go over. Then I post the keys online.
DeleteShireen, Thanks for getting back to me so quickly! I am always looking for something interesting to do on the first day of Calc that wouldn't get too involved. We only have 47 minute classes on the first day. Do you then do some review or do you just jump in and start with limits or derivatives? BTW: I'm a crocheter too. I got lucky this summer and made about 8 new hats and finished a cowl that I began a year ago! Hard to find the time during the school year. I teach AP Calc AB and AP Stats. whew! Thanks for the great blog and resources. :)
DeleteHi Jenn. We don't do any review, and we do jump right in. I get nervous about the time available to get everything in, and I feel 2 things about a review: one, is that they'll forget it when we actually get to it, and two, they'll be lulled into a false sense of ease of calculus because they've seen stuff before. Don't know if this is true, but those are my thoughts.
ReplyDeleteGo you on the finished projects. Super impressive on 9 items. I flaked out this summer and hope I get my oomph back one day. I have too much yarn just sitting around waiting to be made into something.
Have a great year, and I am off to Canada for a week-long in-law trip today.
LOVE this!!!! I've been searching for a way to get students to "see" what calculus is all about. This is perfect!
ReplyDeleteThanks for your kind comments. Hope you and your class benefit from using this.
DeleteThat's what I was asking. I use weebly, and I'm not quite sure how to make it work.
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ReplyDelete