Calculator Precalculus

Geometry. Geometry. Geometry. It's almost like I don't teach another class. BUT. I totally teach precalculus, and it's fun to get back to it after a 2 year break.

We're currently learning how to solve "simple" trig equations on the calculator. I make the students purchase a scientific calculator, so that they have one at home and so that when we have "graphing" tests, they can still use this calculator.

Here's what we're currently working on, and I just have to say, still LOVE the answer banks. [note: added later .... eek! error in answer bank on front side. "5.6034" should be "3.8214"]






I'm also going to start the 100% or 0% quizzes soon. I want them to have quick and accurate access in their heads to the sine, cosine, and tangent of all the special angles given in radians (including on the axes). I give them a 10 question (14?) quiz and I take it with them the 1st time. I tell them that I'll give them twice as much time as it takes me, and they have to get 100% or it's a 0%. They can take it as many times as they want throughout the 6 weeks. This forces them to have a super fast grasp of it.

"Funny"

As my husband and I were pulling out of the "membership only big store" parking lot, we passed a Wendy's. There was an advertisement for job openings, both cashier and manager. The manager's position said, "make up to $55,000 per year".

Then I had to pause. That's more than I make after 14+ years of teaching as a Texas teacher. Eeesh!

Pizza & Circles

We were at one of those membership-huge-quantities types of stores today, and I saw this. I made my husband go back and film it with his cell phone (as I don't have one). Bla bla bla, dark ages, bla bla bla. Anyway, Geometry! Circles! Engineering! Pizza! Woot! (* this seems to work with Internet Explorer, but not with Mozilla hmmmmmm)

Truth Tables

We're well into our journey of logic in geometry, and we just started truth tables. In the past, I walked them through the 5 basics (conjunction, disjunction, conditional, biconditional, and double negation). We make up funny statements and see how things work. Then IN THE PAST I have immediately stepped into building a large truth table such as: (p or q) --> (~p and q) or some such thing. Shockingly, it was too fast of a leap into the deep end.

I had tried various things such as cutting out each column on pretty paper and moving things around, or working examples with them, or whatever. Not completely successfully. And then this year, I think I got it (after my 10th or 11th year teaching the topic!).

This year, right at the end of class for the basics, I set up a 3 column truth table, where I gave them weird columns for the 1st 2, and I gave them various "T"s and "F"s for the first 2 columns. Then I had them think about what the new action was on the 3rd column.

Example (of 3 column headers):
1st column: (p -->q)
2nd column: ~r and w
3rd column: (p-->q) OR (~r and w)

At first they were all, "what?", but I kept silent and eventually would dole out little clues if they were stuck (like boxing in one color the 1st column header and that same thing in same color in the 3rd column). They FINALLY got, "oh! you're just "ORing" 2 things. Voila! They went to the appropriate basic table and filled in appropriately.

Here's a piece of their homework for that night:



Then, when I started class the next day, we did a "fill in 2 columns" one, and they were okay. THEN I just started truth tables, and it seemed more successful than before. Woot!

Project Results....

Here is the back of the project sheet I mentioned last post. I don't COMPLETELY feel comfortable posting it .... I'm hazy on these copyright laws .... so I'm just showing it to you. AND here are four examples of what my students came up with. They continue to inspire me with their creativity.

Personal Ad Project-ette

It was a day of service last Friday, and I was going to be out with my high schoolers, and leave my little 8th grade geometers stranded, gasping for geometry air. Baby project to the rescue.

A while ago I saw this section in Weight Watchers Magazine where they introduce a new vegetable or fruit or some other healthy food and make it look like a personal ad. Something to the effect of "Hello, My Name is Squash" .... "on weeknights you can find me..." ... "things you may not know about me....", etc. I copied this page on the back of the following sheet:



I didn't get all of them back yet, but holy cow some were funny. One was, "ANGLEina Jolie" whose parents were rays and who had "25 degrees" ranging from accounting to psychology. I'll post some when I get them all back. But those students make me giggle.

Conversation Snippets...

Geometry Class:


Conversation One:
Class: "Are you going to let us have a formula sheet on the test?"
Me: with shocked awe, "No."
Class: Stunned silence as they think I'm kidding.
Me: "Seriously? Three formulas. I know you can handle it."

Conversation Two:
Student: "Are you going to let us use calculators on the test?"
Me: Started a long-winded response on why I'd be doing them a disservice if I let them use a calculator on THIS test .....
Me: glance at the vacant look that is starting to pass over the student's face.
Me: "Do you want the long answer or the short answer?"
Student: "Short answer."
Me: "No."
Student: "Okay."


Conversation Three:
(me walking past a student who I see (or think I see....) stuck on a problem I know is hard from the packet they're working on.
Me: starting in and continuing on being very helpful with hints on how to get started.
Student: politely doing what I ask.
Me: pause.
Student: I wasn't even on that problem.
Me: ..... "did you even call me over, or did I just start helping you?"
Student: "I didn't call you over."
Me: walk on by......


Conversation Four:
(after I explained to my "on level" class how a particular 4 problems on their packet were challenging, so I'd like them to try them, but I don't want them to get stuck on them and then not move on to other problems)
Student: (pushing through and probing on how to be successful on this particular problem) .... "I want to be that student this year that pushes herself to try hard things past my comfort level and go above and beyond."
Me: bursting with pride for her and a big smile and congratulations to her for having that life attitude.

Self-Award-Winning Crank

Oy! Who let ME out of the loony bin? As the week went by I got more and more crotchety and ornery and just generally not fun to be around (if you were a teenager who happened not to behave in a manner I found perfect). I think all the moons aligned and teenagers had to nerve to act like teenagers and as a perfect person who always behaves perfectly, I couldn't abide by the nonperfectness of the young humans around me.

Thank goodness the weekend has rolled around, and I can hole up in my home and reflect on what my options are for buying some patience next week. Maybe there'll be a two for one sale. Maybe I'll get some sleep and store up some patience. Maybe to kidlets will forgive me for snarling at them.

In other news, four school weeks have rolled by, and, no joke, we've already had days off for college field trips, time off to give school tours to visitors, early dismissal for volleyball tournaments, shortened schedules for student council speeches, (upcoming) day off for doing service and for bonding retreats, (upcoming) partial day off for college representative tour. Nope. Nobody here is stressed with the dwindling days to teach.

In funnier news, I heard a joke on Prairie Home Companion today that provided MUCH-needed laughter:
A couple was out celebrating their 25th wedding anniversary, and the wife punches the husband in the shoulder and says, "that's for 25 years of so-so sex."
The husband thinks a bit and punches his wife in the shoulder and says, "that's for knowing the difference."

Geometry Diagrams

Last week after we learned more ways to notate a diagram to represent various things (midpoint, bisecting, ...), I handed out the following activity in class.http://www.blogger.com/img/blank.gif



I walked around a bit until I saw that a couple of problems were done and searched for a mixture of 3 to 4 papers that had mistakes of varying sorts and possibly some correct answers. Then I made sure to thank the students in advance for providing us with a learning opportunity and discussed how you can learn way more from searching for errors than from getting something right the first time.

I put problem #1 on the document camera and made sure that each student's name was not evident, then I asked the class to discuss with each other what were the correct things on the diagram shown and what were things that could be improved or corrected. I tried to use positive language and kept promoting it as a learning opportunity for ALL involved (which, obviously I think it is, but teens being teens....).

We went through a frew #1's, then did the same with #2. Then after I passed back the papers, I repeated the process with a few problems at a time as the need arose.

We especially had good conversations about #4 vs. #8. In number 8 many students wanted to make "T" be 2 different points. In #4, some students thought that if the angles had the same angle measure, then they were "the same angle".

Week Three

I'm sleepy/tired, but I'm having fun with my students. Highlights of this week:

* one of my 8th graders today was staying for geometry tutoring, and apparently her bra was too tight (ask me how I know). She talked at length about it, but each time she said bra, her voice went down to a whisper.

* one of my 11th graders mentioned that she gives hugs more frequently when she's stressed. I've been getting a ton of hugs lately. Especially since I have her for 2 classes and an advisory.

* my students are LOVING the soldering in the Digital Electronics class. We're each of us feeling like "all that" since we're doing something that seemed unmanageable.

* I'm taking the online computer science course with one of my students. Her current grade is higher than mine (don't ask). She's giving me "fun" grief about it. Game on! is what I say.

* I came up with a good activity that was useful and effective in geometry on the fly today (maybe more later). Good feeling.

* Our school is right by a place that has coffee and cookies, and all the math teachers have last block off. Today we mosied down for a short 15 minute break and yapped and caffeinated before we got back to it.

* I dived into introducing the TI-nspire calculator to my precalculus class (I used the "Scavenger Hunt" activity). The kids thought the calculator was the coolest thing.

Bzzzzzzzzzzzy

Have 2 weeks flown by already? I'm a slave to my agenda and am constantly updating and recreating and SOMEtimes crossing off items on my to-do list. It's all still start of the year EXTRA stuff that has to be done and takes time and "gets in the way of" actual planning of what I need to teach.

I did something crazy. A student wanted to take an online computer science/programming course, and our AP asked me if I thought the student could handle it. Hah! This kid can totally do it, so I said yes, she is self-motivated and can handle the course load. Then the AP asked if I would help the student if she needed it. While my mind was processing the answer, "yes", my mind also thought that even though I took/passed the teacher certification test to teach programming, I haven't actually PROGRAMMED in ages (let alone JAVA programming), and then my mind ran through various scenarios of the student asking me for help and me just sitting there with a stunned look on my face not being helpful at all. So. While these horror pictures were running through my head, my mouth decided that the best solution would be to utter the words, "why don't I take the online course with her?"

Flash forward to this weekend where the bulk of my time has been to do our first real reading and doing assignment. It's a semester-long course given through University of Missouri, and it's an AP CS course like in high school. The instructor has it all neatly and well laid out online. There are weekly assignments and midterm/final tests and forums we need to participate in. But ..... bzzzzzzzzzzzzy.

The positive side is that by January, when choice sheets come around for next year, I'll be in a much better position to show what a programming class would look like.

Did you know that there is an actual Pearson book for AP CS classes? I respect the Pearson books in general because they don't seem as "babyish" as the Holt book I have for Geometry. The one seems great so far.

Am a a juvenile in thinking upon seeing "Cara Cocking"'s name that she totally must have taken a lot of ribbing in school (or her husband did if that's the case).

Mobiles and Matching

I was SO excited for the 1st weekend to come after school started, so that I could catch up on sleep. Didn't happen. Apparently, my body now thinks it's a great idea to try existing on 6 hours per night or so. BUT this is only in the school year. Go figure. AND I have jury duty on Monday. What's up with that?

Anyway, I had some great projects come back from our summer packet for geometry kids. The kids are so creative. Here are some:











I also did this activity just yesterday with my geometry kids. I like the fact that it's not necessarily a direct match up, so they have to think.

Funny 1st Day Story

We had an all-school assembly before classes started on the first day of school yesterday. Tons of hugs were given and received between returning students and teachers. Before I continue, in my defense, I just want to say at the outset that I got my fair share of hugs. I'm just saying.

At one point, I see one of my former students (I've had her for 3 classes so far, and another this year), starts running towards me with her arms outstretched and a big smile on her face. So, I smile back and open my arms ..... just as she runs past me to greet another teacher.

As she passes me and sees me waiting, she hesitates slightly ONLY slightly as if to say, "oh, awkward", and then continues to go for the OTHER teacher hug.

First Day Activities

I'm happy with the outcome of my geometry and precalculus day 1 activities. Now we'll see how they pan out. Now to plan/map out the REST of the year.

Geometry:





Precalculus:

Outlook

We "finished" our first "fake week back" at school. And by finished I mean that I'm going in today to continue to get ready for the students' first day on Monday. Things are mostly done, but I still have to make copies and finalize my decision on the first day activity for 2 classes.

I THOUGHT I had a general plan of what to do, but then my friend/dept. chair throws THIS book at me. Oy! There are some great things in there, and once I finally adjust the idea of my geometry day plan and my precal plan, I'll share.

Which brings up another thing that was happening as I planned. I don't know if it's past experience or other reasons for the hesitation, but I printed things out: syllabus, autobiography, seating chart plan, etc. and then I hesitated on making my final copies and getting it done. I guess I've done that enough and made tons of copies, and then realized that it wasn't JUST right or JUST what I wanted. Or maybe I just like the thrill of the last minute. Hmmmm. Anyway, it worked out well this time, because, YES I had to alter the syllabus, YES I had to alter the seating chart (yay! largest class currently is 26 and not 30), YES I totally am revamping my 1st day activity.

Which finally brings me to another funny saying I've seen lately: I have CDO. It's like OCD, but with the letters in alphabetical order - like they're supposed to be.

Last Friday Before the "Fake" 1st Week of School

To relieve my bum's fascination with sitting and surfing on the computer all the time (it's really talented), I went in to school every day this week for a wee bit and unpacked and decided on desk structure (30 kids! Woot!) and stuff. You can see I'm still not done, but I've made headway, and my butt thanks me for actually walking around. You're welcome, bane of my rear.

Here are the unpacked boxes SO FAR:


Here is what I'm trying out. Two students per table. Long rows. No extra room. Oh! and look! More schtuff to put away:


I'm trying to be more organized this year. I tried to put myself on a pen diet last year. NO MORE PEN BUYING. Apparently, my fascination with the show, "Hoarders", .... hmmmm, a little sensitive?


What's this? More hoarding tendencies? And I didn't even buy any pens or stickies this year. Yet.

Funny...

This made me giggle. I don't know if it makes me feel super old or super young or what. I'm FaceBook "friends" with several former students. Most of the time it's okay, but sometimes I have to hide all the posts from a particular ex-student because I don't want to know how much they drank or did other things. That's about 1% of them. The rest are just fun to see grow up and explore and get jobs and live.

Anyway, this student graduated HS about 2007, so maybe he's graduated from college right now and roughly 22 years old. His post was:

Is it just me or is the crap that kids are watching now a days really really suck?? I mean what happened to the good stuff??

Hah! "Kids these days"! Does he feel like an old man?

Update ...

I couldn't let it go, and it kept bothering me for a variety of reasons. So I just sent the following e-mail to the person mentioned in my last post.

DD,

I was just going to let this go, but it's been really bothering me since last Saturday night at the banquet when you made your extremely offensive remark against a person that happens not to be white.

One, I'm saddened that you think it's okay to blurt such stuff out in public (let alone think it), and two, I'm insulted that you think I must be of a like mind. I'm not, and I don't want you to harbor the impression in the future that I think like you apparently do.

***

At least I feel better about taking some action.

Okay, back to math ..... I've heard through the grapevine I may have a class of 30 students. Oooh! Now I know (sadly) that this may seem like a nonevent to others, but in a classroom where I'm to use those long tables as "desks" as opposed to actual desks, it's a tight squeeze. It's going to be a cozy year.

Anatomy of a Racist Encounter

You attend a 3-day, 10th annual event because of your husband. You see people you only see once a year, and some people that you see throughout the year. You have nice conversations about a variety of things with a variety of people. You talk with a 78 year old man, CI, about many things, and a couple of times he makes slightly in-poor-taste remarks about people of different ethnicities. You scrunch up your face to show distaste, and he backtracks and conversation goes on. You think to yourself, well, he's of a "generation".

You are at a final-evening banquet sitting with 3 people you see once a year, one of whom you've had good conversations with for 2 days, let's call him DD. The conversation turns to politics - local Texas small town mostly. There are big drought issues and land issues and two of the locals don't agree with how the city has decided to deal with things, and they start in with, "once you become a politician, it seems you become an expert in everything you know nothing about."

Then the 3rd person, DD, interjects an awful racist remark, "oh, like that ____ ____ ____ ____ over in the White House." The other two don't allude to DD's statement and just keep talking. You're stunned into shocked silence and not quick on your feet and still processing the fact that this person has literally let his racism hang out in public airing just like that. The conversation has continued. You're still stunned and really uncomfortable and want to say something, but don't know how or what or with what tone. You're angry with him, and you're angry with yourself for staying quiet. Isn't that the same as pretending what he said was okay? Doesn't that give him another vote of confidence that other people think like he does? You excuse yourself and don't return to the table. The evening ends.

And here's the thing. Now you have one more chink in your armor of trusting that people that you meet and that seem nice really ARE nice. That most everyone you meet that SEEMS human judges others on their character first/mostly and not on their race/sexual orientation/wage-earning. And you wonder when it will come out when meeting new people or talking with people you've known for a while. And what about the other 2 people at the table? Did they think the same way as DD because they didn't say anything? Do I have to wonder about them? Or were they flabbergasted like I was and are wondering the same about me?

And mostly you're still upset with yourself for letting it slide at the time and not knowing the right thing to say and the right tone, so that the person knows that he's offensive, and it is not okay and beneath his humanity. You don't think you can change his views, but you think that you should speak up. You keep thinking about it. You hope you come up with a phrase or two that will be on the tip of your tongue next time. But hopefully there won't be a next time.

Fun and Apparently Free

One of my goals ("someday") is to be fluent enough in at least 2 languages (ideally tons, but I could start with two). To that end, I dabble here and there and practice. I downloaded (when they were still free AGES ago) the "Learning Spanish Like Crazy" and "Learning Italian Like Crazy" CDs and listen to them in my car. I like both, and I'm pleased with the Spanish one because it's Latin American Spanish which is more relevant for me.

Apparently, some of my students think I know 5 or 6 languages (or maybe they're just humoring me) because sometimes I'll count in Japanese or say a word in German or such just to break things up. If they ask, I tell them how many I've "learned" in the past (in order: English, Farsi, German, Russian, Spanish, French, Japanese, Italian), and I also tell them how many I'm fluent in now (1). Go English!

Let's not fool anyone here. Maybe there's some segment of my brain that remembers these things, but those foreign words/phrases are not making that trip to my mouth. Anyway, as I was surfing the web today and went to the BBC site, I found THIS! Holy cow. There are videos and little dialogs and tests and all sorts of fun things.

I browsed through the French test, and got one wrong, and they linked me to these possible sites. I liked the Ma France one. Oh oh! more things to distract me from doing work.

Utopia....

You know how certain segments of society are all, "oh no, I need to lose weight. I need to get fit. I need to look more attractive. I feel bad about myself because I'm not thin/pretty/hot/young like people I see on TV/ads/movies." (no names mentioned)

We need a society where the stress is more, "oh no, I need to be more ethical. I need to be a nicer person. I need to do more good for the world. I feel bad about myself because I'm not nice/ethical/good-natured."

Or reverse, instead of, "I'm hot spit because I'm attractive." This needs to be more, "I feel GREAT about me because I'm basically a good person."

Where's THAT parallel universe?

Nervous.....

In the course of making and filling out my school calendar for next year and planning for various classes, I came across these 3 scary months on some official calendars:

March:


April:


May:


Notice the 5 bazillion weeks of state testing. Now of course our state is in the process of switching over from one test to the other, but that just means that we'll have to administer both for the next few years.

I also counted up the actual teaching days I get, and tried to discount for these weeks and finals weeks and other weeks that seem to fall away, and I REALLY hope I'm wrong, but I counted about 140 or so actual days of teaching.

Must go cry now.

"Working"....

Okay, so I'm SLOWLY working through my to do list:



But this is HEAVILY sprinkled with the fun things I've done.

My coffee cup from a paint-your-own pottery place. LOVE the 20 oz. cups:


My agenda book for next year. I found a ton of pictures and sayings and taped them on the covers. Now I just have to make all the calendars for the back section, and I'll be ready to roll.

FRONT:




BACK:


This agenda book idea worked really well last year, and then towards the end of the year, I looked at another person's book, and she had a running numbered list of things she had to accomplish then crossed out(instead of just higglety pigglety around all pages). I started doing that, and loved it.

TI-nspire Start Up Worksheet

I've just created a "getting to know you" sheet for my students for the TI-nspire. Again, we'll just be using it for in-class explorations, and I don't expect students to rush out to buy them.

A really nice person sent me a "Scavenger Hunt", and I used that as my inspiration. Of course now that I go through my e-mail to thank her in "person", I can't find the message, so a PUBLIC THANKS to you.

My next goals are to create a teacher sheet for the other math teachers at my school to show them where the resources are, and IF I HAVE TIME (and it seems to be quickly dwindling), I want to create actual activity sheets.

You can find this sheet here. If the graphics mess up, then I'm guessing you know how to adjust them. Preview:

Summer Math Packet Update...

Back in mid June before I went to my workshop I sent out 2 sets of e-mail for summer math work - one to my rising precalculus students, and one to my rising geometry students. I'm still working out how I'll grade these or assess these, since this was a last minute decision, and basically given out via e-mail without any warning to the students to watch for e-mail (long story).

I'm not sure of the fairness in holding them accountable for this work since some may not even get it. What I'm leaning towards is for THIS SUMMER (as opposed to next because I'm sure this will now be a given) is to either give them extra points on the homework portion of their semester grade, or to create an extra quiz grade and assess it that way, and for the students that did not do it, they do not get the quiz opportunity.

Here's my precalculus e-mail:

You can finally breathe a sigh of relief, your summer math work has arrived. You're going to be learning a ton of cool things in precalculus next year, and there are a few things I want you to refresh your memory on: function notation, right triangle trigonometry, and special right triangles.

You're welcome to do these things in any order and at any time over the summer, but I highly recommend spreading the wealth out and not cramming it into one or two sessions. I also recommend maybe ALSO looking at the information and doing the practice once every few weeks, so it has time to soak in and get trapped in your brain cells.

Here are some suggested sites for each of the three topics. Note that they may not be the best for how you learn, so you're welcome to Google search on any of the purple topics on your own. You know if you're successful if you can complete all of the "goals" with great accuracy. By mid July, I will send you some online quizzes for each of these topics. Your job is to take the quizzes and score 80% or better. You can take various versions of the quiz as many times as you like.

Please send me e-mail once you've received this e-mail, and you can e-mail me any time during the summer.

function notation video:
http://www.youtube.com/watch?v=Kj3Aqov52TY
http://www.youtube.com/watch?v=FoDHSqQZuiw&feature=related
GOALS:
1. be able to evaluate functions presented in function notation for numerical inputs (i.e. find g(7) if g(x) = 5x^3 - 9x + 1)
2. be able to evaluate functions presented in function notation for any expression input (i.e. find h(x^2+1) if h(x) = 4x - 3x^2)
3. be able to find the input that satisfies the output (i.e. find x such that f(x) = 10 if f(x) = 2x^3 - 6)

sine cosine tangent:
http://www.mathsisfun.com/sine-cosine-tangent.html
http://www.mathwarehouse.com/trigonometry/sine-cosine-tangent.html
http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_trigsincostan.xml
http://www.youtube.com/watch?v=_S35Ht4imhs
GOALS:
1. given any right triangle and a designated acute angle in that triangle, you can set up equations for sine, cosine, and tangent
2. you can pronounce "sin" accurately
3. on any right triangle with angle information given and one side length given, you can use trig to find the remaining 2 side lengths
4. on any right triangle with side lengths given, you can find the remaining angles of the triangle

special right triangles:
http://www.cliffsnotes.com/study_guide/Special-Right-Triangles.topicArticleId-18851,articleId-18821.html
www.mente.elac.org/presentations/spec_tri.pps
http://www.youtube.com/watch?v=nVTtSE5nv7c
GOALS:
1. you can recognize 30-60-90 triangles and 45-45-90 triangles
2. you can quickly place the ratios of sides around either
3. you can find all exact side lengths of a special right triangle given any side

For geometry I decided to make it two-fold: actual math practice, and a project.

Here's the e-mail:

Hello Mathies,

Here is your summer geometry work with instructions included in the document. I'd recommend downloading the attachment instead of just viewing so that the formatting doesn't go all crazy on you. Have fun, and look for another e-mail from me some time in July (as mentioned in the attachment).

Please send me e-mail if you have any questions.

Big Hugs and Big Math,

Ms. D

(here's part of the attachment):

Hello Future Geometry Kidlets,

There are 2 parts to your summer math work (you’re welcome).


PART 1:
Choose one of the following projects to complete. These are due the first day of class, and we’ll share out. I will do the project also and share my results.


PROJECT 1:
1. Go to this link: http://www.district87.org/staff/powelln/Geometry/Projects/GoldenRatio/GRProject.htm
2. Click on various parts to see what’s what.
3. If you didn’t already, click on the “learn about pantographs” link under the “CONSTRUCTIONS” part of that page (http://www.ies.co.jp/math/java/geo/panta/panta.html). Play around with the applet on the bottom.
4. Make your own real life pantograph. Figure out how much larger you make your drawing (give me a ratio and explain how you found it). You can be creative with the objects you use. You don’t have to spend a ton (any?) money. Extra points if you can do this for free.


PROJECT 2:
1. Go to this link: http://www.district87.org/staff/powelln/stringart/index.html
2. Click on the various links to explore “string art”.
3. Explore this YouTube video: (http://www.youtube.com/watch?v=gPn8obkZyPI) and possibly others shown on that page.
4. Create your own string art. Again, you can be creative with the objects you use. You don’t have to spend a ton (any?) money. Extra points if you can do this for free.


PROJECT 3:
1. Go to this link: http://www.district87.org/staff/powelln/Geometry/Projects/OrigamiMobiles/OrigamiMobiles2007.htm
2. Click on the various links to explore “origami mobiles”.
3. Create your own origami mobile. You must have at least 6 different origami pieces. Your mobile must balance.
4. Again, be creative with the objects you use. You don’t have to buy origami paper. Extra points if you can do this for free with objects found around the house.



PART 2:
Complete the following problems. You must show all your work. I will send an answer key soon for you to check your work. I will also send a few online quizzes some time in July to make sure you understand the concepts. You can take the quizzes as many times as you want, but you must ultimately score at least an 80%.

Now the chickens come home to roost, or the fat hits the frying pan, or whatever.... I'm off to make the quiz assessments on proprofs.com. And I will also do all 3 projects for fun and to see what the various cool math aspects are.

Trips Galore...

I'm finally home after basically 3.5 weeks away: 2 weeks for the Digital Electronics training, and 1.5 weeks for visiting family old and new friends.

POed graciously agreed to meet me while I was in NYC, and we had a walking and talking marathon. She suggested tons of great places to visit: the highline park, riverside park, yotel, gershwin hotel, and YES, the best pizza ever - at Ray's way down south. You know it's a great pizza place when you ask for fresh garlic as a topping, and they pile 2 heaping tablespoons full on top. My husband will be surprised that even I had to scrape some off. I'm very impressed with POed, though, she was not such a sissy and finished all her garlic topping like a champ.

Love her, by the way - she's smart, friendly, caring, and fun to trade war stories with. Here are some pictures from NYC.

Sculpture along Riverside Park:


Another Riverside Park sculpture .... inside was basically living quarters - bed, chair, toilet, ....:


Yotel. This was a robot in the entryway and you could command it to store your baggage in these little drawers. How cool is that?


Highline Park, built along old railroad tracks:


View from Highline Park. There's amphitheater type seating with a Plexiglas window in front where you can watch the street action:


Sculpture from one of the many parks we passed on our trek:

Workshop Thoughts

Okay, it's Wednesday, and Friday is the last day of our 2 week workshop. Here are random teaching thoughts that have floated around in my head while it's being crammed with electronic information:

1. Hey workshop participant, you don't have to voice every thought that passes through your brain. ALL the way through our class from 8am - 5pm.

2. Linking new information to a good story or visual is a great latch. For example, on certain IC chips (details not relevant to the story), there are two inputs that serve a certain purpose. If they're "activated" they basically take over in a certain way. So our cool teacher spun this tale about Zeus and Hades and said that the gods don't "follow the clock", so when they wake up, whatever they want goes, and Zeus is "higher" so things change to 1 whenever he wakes up, and Hades is "lower", so things change to 0 whenever he wakes up. They're gods, and do what they want. When they go back to sleep, the IC chip pattern follows the clock again. So now whenever I come across these certain "pins" in my homework, DING, I think back to Zeus and Hades, and the information of how to proceed is immediately available to my head.

3. Perseverance is key. My table mate and I were pushing through and seeming to struggle with breadboards for the LONGEST time. Note: we finally and successfully completed the assignment, but the thing that sticks in my mind is somewhere after 4 days, one of the teachers said, "well, you know, you can use this OTHER automated breadboard and don't have to continue to fiddle with these ones". What I HEARD was, "hey, dummy, now that you can't handle the hard stuff, here's the baby version that may be more your speed." Well, that put additional light under my butt and I refused and was ultimately successful and proud of myself, versus if I gave up and settled for the easy way out. Also note to self, don't make the same suggestions of any sort to my students. DO mention that overcoming something hard will make you better.

4. pandora.com ROCKS .... especially at 12:30am when you're finishing your homework, and yes, I'm late to the game.

5. I love meeting new people and hearing various cool things about their lives or experiences and occasionally meeting new friends and laughing so hard I have to pee.

Ignorant vs Stupid

And not that you'd call anyone "stupid".

Maybe I haven't mentioned it more than 5 baZILLION times, but I'm SO excited to be at a 2 week training for "Digital Electronics" in the PLTW curriculum. I've been through 3 actual days of class time now (Thursday at 11pm), and it's intense but loads of fun.

Let's just throw around some terms that I've bantered about and slowly become acquainted with in the last few days: ohm, resistor, digital logic board, capacitor, analog, digital, light emitting diode, power source, switch, TTL, Boolean algebra, sequential logic, SOL, AOI, DE, valence shell, soldering, tinning, oscillator circuit, frequency, duty cycle (tee hee), time high, time low (hee and hee), breadboard, .....

If I could go back in time and read those words (say before last Sunday), you'd see this glazed look over my eyes combined with a fight or flight response of, "ackh! others know more than me, and I should know this, and they're saying it's obvious and oh no, let's switch the subject..."

Now, peshaw! I'm totally going to be throwing those words out at my next math party and be the hit of the evening, right?

But anyway, a typical day so far has been: get up at 4:30am in a panic because I didn't finish the homework from the last class(es). Do as much as I can before I hit the gym at 6am. Shower and have breakfast. Class from 8am - 5ish pm (with lunch). Dinner and unwinding for a couple of hours. Homework until 11:30pm until I crash, and repeat all over again the next day.

Anyway, tonight I had to create a "Voting Machine" logically on paper and in a simulation program before I took it to actual DLB to work. (so if you know what I'm talking about great; if not, you're me 4 days ago). One of the instructors was down in the common room helping us (8pm - 9:30pm). I was apparently doing something TOTALLY ridiculous on the simulation program. Sure, the theory I have down pat; it's logic and math. My paper version was all correct. The electronics .... (wait for it), I'm "ignorant on" at this point. Well, sheesh, that's why I'm here, to learn. I'm not stupid .... (obnoxious and anonymous brag alert) ... I have 4 math/applied math degrees .... (end of alert). But I am IGNORANT about electronics. Please don't treat me as if I'm stupid. Just explain it to me and answer my actual questions so that I can internalize and process the information (shout out to my instructor). ... To give him credit, in the end, I finally understood the issue (I think) .... hint: for a circuit to work that has an LED in it you have to ..... okay, you don't care.

The point is, "note to self", don't treat my students as stupid, and be sensitive about when you may be making them feel stupid when really they're just ignorant on the current topics. AND be very careful to answer the questions they ask, not the ones you think they're asking with all your filters of assumptions on what they get or don't get or can get or can't get.

Okay, what am I doing blogging when I have homework to do .....

Fun Problems

A few days ago, Allison posted a problem you could really sink your teeth into and enjoy the puzzle of it all. It reminded me that it's been a while since I did this sort of brain challenge type problem just for the heck of it. Many years ago, I came across this problem:

Consider a square cake that's frosted on the top and sides. How do you cut it into 5 pieces so that everyone gets the same amount of cake AND the same amount of frosting? You must serve the whole cake. (be able to prove why it works) (added bonus: what if it's a rectangular cake?)

Now as a selfish person, I'm wondering if anyone has links to other cool such problems that make you think and tinker for a longer while than usual. Share! Share!

Fun Crafts

We're soon visiting my husband's brother's wife's sister's two little girls, and I wanted to make some knitted or crocheted toys for them. I didn't have a ton of time, and I like really fast projects, so I altered and eyeballed and shrunk down visually from a doll pattern and came up with these two beauties that are about 3 to 4 inches tall. Woot Woo!

The alien baby dolls. Or maybe they can be the Einstein Dolls and the girls can play pretend relativity theory. I still have bits and pieces of 2 weeks left, so maybe I'll make dogs and leashes and beakers and microscopes and such to go with them.

Education Experts

Did you ever think up this really cool idea for one of your lessons. You were really excited! This was going to be so clear and fun and educational and work perfectly. Of course, you spent time working out the details and thinking through all the THEORETICAL issues that could come up. You launched it.

Most often it didn't work as planned. Various things came up. REALITY set in, and you had to think on your feet. You fixed what you could. If it seemed MORE usable than not, you made notes and adjustments for next time. For me, it usually takes about 3 times through before I work out *most* of the bugs.

But the deal is, it really didn't work as you had planned. But being a teacher, and as important, just being one of you, and knowing you're the expert of your classroom you could adjust quickly and on the fly. And no one has to throw it back in your face and say, "ha! you messed up! double ha!"

But I want to get back to the "didn't work as you had theoretically planned" business. I'm thinking that this is what happened and is happening with all the uppy ups telling us how to teach and what to teach and shoving state assessments down our throats and strategic compensation and whatnot. Because theoretically, that sounds so true and good and seems to make sense: hold people accountable. Hold teachers accountable. Hold students accountable. What could go wrong? People will rise up to the high level of expectation and perform better.

Hah! Reality could go wrong, apparently. Theory is all well and good, but reality is what you have to deal with in the end. And they're such a huge bureaucracy, and they have a "ton more students and classrooms", that how long does it take to adjust their strategy? And how easy/hard is it to admit you've made a mistake when so many people are watching you.

Or maybe I have it all wrong, and "they" are still sitting "up there" saying, "it's all the teachers' faults. If only they'd be better and do what we ask, we'd fix education! A pox on the teachers. Slackers the lot of them. And they get the summers off!"

Stories and Pictures

I'm going to a 2-week Digital Electronics workshop soon, and since I didn't want to show up with no remembrance of anything electricity, I thought I'd better brush up. I didn't want my "brushing" to be too painful, so I found this book to help me, "The Manga Guide to Electricity".

Super cheesy, right? I'm not a "manga" person at all, but I figured it would be a "fun" (?) way to review.

Well, what do you know. It works! I think part of the effectiveness, for me anyway, is that when one of the characters is explaining various aspects of electricity, he links it to a picture and/or something I know. Now later on in the book when that aspect is referred back to, I conjure up that picture in my head and can see the story line and know what he's talking about. I can keep things straight instead of just plowing through various equations and thinking, now what equaled what?

Then I got to thinking, wouldn't it be fun/interesting (possible?) to have a running storyline (or a few) in, say, geometry. Then when you're teaching a new topic, there's pictures the kids can refer back to or some link that connects it to what they know. I guess ideally it shouldn't just be random things because maybe that adds to the memory retrieval problem.

What would it look like? Would they each develop their own story, sort of like that "here's a sentence and let's pass it around and everyone add another sentence and let's create a story" type of deal. Oh, maybe that's it. Every night someone new would be responsible for adding to the story. We could have an online geometry story that would be a work in progress all year. The kids could go back to it whenever they wanted to review.

Logistics: Would each class have their own story? Would we have one total? What if a kid flakes and doesn't do their part, how is that remediated? Blog? GoogleDoc? Other? Homework grade? Extra quiz grade? No grade? How many times a year will a student have to add to the story? Is there a way where they can sign up for a schedule?

It's just crazy enough for me to want to try it next year.

Summer Math Packet

Our math department decided to give summer math work for students, the same way they get summer reading. I'm of mixed minds about this, but I'm doing it anyway. And since I came late to the game (try LAST 3 DAYS OF SCHOOL) (don't ask) (and maybe I would do it in this manner anyway), I'm going to make it more of an online "packet". My idea is to pick some topics I want them to review or refresh their memories on using YouTube or other online links. Then I'll use my proprofs account to quiz them.

I don't know if I'll have them try various quizzes until they reach a certain score or what. I also don't know how they'll be held accountable come school time. I'm batting these ideas around in my head: bonus points, homework passes, quiz the first week or 2 of school, homework grade,...

I will be doing this for rising geometry students and rising precalculus students. I'm also thinking of having various packets sent out and "due" every 2 or 3 weeks, so they don't leave it all to the end .... incentive for them to do it in a timely manner? More "points"?

Precalculus Topics: right triangle trig, special triangles, function notation, ... any other suggestions?

Geometry Topics: solving equations, graphing lines, factoring, working with fractions, ... any other suggestions?

Soooooo, I'd better get my butt in gear and actually send out the "packet" information.

Too Cool Not To Share...

As I was culling through my work e-mail today in my quest of cleaning EVERYTHING up this summer, I came across one from our excellent librarian. She shared this link. Holy Cow! It's mesmerizing, and I want to watch it over and over to see how many patterns emerge. Also, I'm sure there's math that's accessible to high school students as to when they "converge" or "meet up" or how many times they meet up. Or we could all just watch over and over again like little 2-year-olds and their movies.

Kids' Chairs

Here are some pictures of my students' cardboard chairs. They are in various stages of completion and of success. We only had time to finish prototypes, so I don't really know how people actually had time to THEN go make the final version. Maybe they had more students on each team. Maybe they could dedicate more time during the school day to the project. Maybe they were just faster than us. Anyway. Most of them supported weight (as long as you didn't move around too much). They presented their chairs on the day of their finals, and we had interesting discussions as to what worked and what didn't work and WHY and what could be tested to improve the chairs.

I also handed out a questionnaire that I found informative. The prompts were something along the lines of (because of the project):
* what did you learn about yourself?
* what did you learn about engineering?
* what did you learn about chairs?
* what do you like about your chair?
* what could be improved?
* and various questions where they graded themselves on each aspect of the project.

I liked this last section. Instead of letting them choose a 0% - 100% grading scale, I worded it as follows. I think it then was clear for the students to decided on their grade:

Last Day of School

Sort Of. I've become more relaxed about making sure EVERYTHING is done before the last bell on the last day. You know. "The Check Out List". Make sure you: turn in your keys, box everything up, turn in all technology, do a complete inventory of all PLTW items on a new system on the computer, have finals graded and packaged up and stored, ....

Yes, I still do those things, but I'm not too worried about them getting done by ___. Now maybe that makes me the jerk to work with, but here are my thoughts. I know I'm ethical, and I know I need to do those things, and I know I will do them. BUT. I'm not going to kill myself doing them by a certain time frame when more pressing things need to be done: grading the finals thoughtfully, entering the grades and making sure kids get the grades that will serve them best, talking with kids that either will not be back or just I'll miss or they'll miss me over the summer. Also, I don't mind going in partial days for those first 2 weeks of summer, it'll break up my day from my potential slouching on the couch sessions interspersed with trips to the refrigerator.

Today was the last day for kids, but tomorrow the staff has to go in and work and have a year-end review. I can do some packing then and on Friday and next week.

Phew! Over! Done! Sort of. Then as usual, there's the summer plans I have: go to D.E. training for PLTW for 2 weeks (ooh, acronym city), learn TI-Inspire and make worksheets for beginning teacher/student users, make activities for TI-Inspire, learn electronics before above-stated workshop, learn/practice computer programming, relearn and revamp my precalculus curriculum, revamp geometry and potentially teach it to a potentially new geometry teacher, read/have fun/relax/see movies/purge my house of more stuff that's just sitting there/knit-crochet 3 baby gifts ....