Prisms & Polyhedrons

We started out unit on polyhedrons this week, and are learning first about volumes and surface areas of prisms. I know they've worked out volume and surface area with a vengeance in middle school, but I know they didn't do the "hard" problems. With all this in mind, I started with the information that is shown in "Discovering Geometry" about how the lattices of different substances that are made up of the same elements (carbon) can have way different properties (diamonds vs. graphite), and can behave counter intuitively (water expands when frozen and other things don't).

Then, instead of giving them definition upon definition to copy down (edge, vertex, lateral face...), I handed them 2 blue sheets, and we had a race of cutting out the squares (otherwise, la la la, I'll take my own sweet time to trim VERY neatly and NEVER get done). Then they had to match the cards. I didn't answer any questions (what's oblique mean?), and just said that they should use process of elimination. And, "why are there more than one hexagonal prism cards?" .... you'll figure it out. Here are the sheets. (note: for some reason, the "preview" on box.net comes out all wonky formatted, but it downloads nicely. I'm not sure why that happens.)





At the end, I gave them a key and let them keep these to put in a plastic baggy. I plan to do the same with pyramids, cones, cylinders, on different color paper. I also made sure we had a discussion about correctly describing right and oblique prisms.

Ways of Asking For Things

A student came in after school concerned about her algebra 1 grade. This 6 weeks, she was absent for maybe 2 days in one stretch, and then she basically never got back up to speed turning her in stuff (in any of her classes). Then, thank goodness for good parenting, she's now concerned about her grade because her birthday is coming up soon, and if her grades are stinky, well mom won't be too much in the birthday mood.

So I love how she tried to turn in some late work. First of all, she turned it in during class a while ago claiming it was absent work - about 3 week old work, so I gave it back to her and said it was too late (as is our school policy) (thank you sane administrators). Then she tried to turn in stuff after school today. Hmmmm, one had 2 problems out of 8 done, and another had 6 out of 8 done. She tried to do the "air quotes" thing with me claiming that she'd tried to turn them in earlier, but I wouldn't accept them so they were "air quotes" too late "air quotes".

Now I just have to laugh. I asked her why she hadn't done the work. "Well I didn't get it, so I thought I'd just turn it in for some credit (2 of 8 problems)". Then I asked why she hadn't come for tutoring. "Well .... excuse, excuse, excuse". Then I quickly disabused her of her air quotes and said, "hopefully you'll be in school for another 7 years (she's a freshman), and you'll have many teachers. Most likely when you're asking them for a favor, it probably won't do too well if you just come with an attitude, and ESPECIALLY if it looks like you're not even interested in learning the material. A better thing would be to say, 'well, it may be too late to turn this in, but can I still have help on knowing how it's done, and I can practice'".

So somehow, magically she could stay for tutoring on the spot, and we worked through some of the problems. She was a quick learner and showed improvement. Her funny statement then was, "why do I get it when I'm working here with you (she's NEVER been to tutoring), and I can't get it at home?". I asked if she was distracted at home when she was doing her homework. BINGO. "Well, I guess so, but don't tell my mom." We discussed that math was hard, and you had to think about things as you were doing them, and not just half pay attention to your homework.

Maybe she's seen a wee bit of light? Or .... most likely, this is the upswing of the see-saw that is a teenager's personality .... and her birthday incentive will be gone soon. ... I'll take what I can get.

Spring Break Almost Over

I remember how in the past someone had mentioned to me, "Students like routine. They want to have a sense of comfort of what to expect and such." I don't remember the context of the conversation, but I was thinking about it over break. I apparently like routine, too.

Break's all well and good - I slept about 8 or 9 hours every night, delicious; I got to go to bookstores during the day and browse and come upon great new books to read (hello, "Little Bee"). I went rollerblading 3 times in the afternoons (goodbye fish-white pallor ... almost), etc. But. I miss my routines. I missed my 2 favorite yoga classes for various reasons; tap dance class follows the school schedule, so it was canceled. I didn't run at 5am MWF, well, because, who in their right mind would get up at 5am if they didn't have to, I miss my Thursday morning treat of having breakfast out at a 24-hour diner before school and reading the paper and doing the puzzles. I miss the free exercise of being on the go all day and not having easy access to my refrigerator (hello tighter pants).

Waa waa waa. All that is to say, that though I won't like the stress, I'll be happy to go back on Monday and get back to my well-tuned-and-familiar routine. Then pretty soon I can start my finger countdown of weeks until summer .... and then I have to find other ways to resist the fridge and the sitting all day.

Differentiation Chapter 2

A key point of chapter 2 of the differentiation book I'm reading is that you can differentiate in one of 3 areas:
* content
* process
* product

Her examples are not from math classes (wait! there's one at the end of the chapter), so I have to brainstorm about how to differentiate content. Let's say I'm teaching solving inequalities in 2 variables. Maybe a content differentiation would be to have separate groups of kids: one with basic line inequalities (y=mx+b set-up), one with point-slope inequalities, and one with standard, point-slope, and basic all mixed. Or maybe a group with line equations given where there is some thinking involved to graph the line (the y-intercept is not an integer, or the "easy" point is off the grid I've given them). So then my thinking goes to: when do I separate them into groups? At the outset? After my initial spiel? After a day together? How do I gather them back at the end of class and make sure they learned? Do they have an opportunity to advance to another level if they mastered the basic ones? Is there enough time, or will we move on to the next topic?

Continuing on with the same example for process differentiation: this would be how they're originally learning the information (among other things). Maybe they could listen to me speak, or separate off and learn from the book, or maybe I have a sheet pre-typed out that goes through the process and prompts them to learn the concept.

For the product differentiation: hmmm, this always smacks of "project" to me, and I know it shouldn't. If I get away from a paper and pencil test, how will I allot the time to assess them orally or in other ways? How will I stop from giving them hints either with my body language or with actual words? How do I know they really know the material?

She does discuss starting your differentiating small and adding to your bag of tricks each year.

The Book...

Ode to Freshman Test Takers

Nine Questions. Blank blank blank blank, scribble times four, blank. Partial credit does not compute.

Let me practice writing my name. All over the paper. Curly, squirrely, poorly Q's. First and last name. Oops, ran out of time to complete many problems.

Week-long note on the board: TEST! solving by elimination, solving systems of inequalities, graphing inequalities in two variables. This was not code for DON'T STUDY.

Earnest note at the bottom of a half blank test, "do not understand this part. will come in for tutoring on Friday."

Many practice problems involved integers. Or. GASP. Minor fractions. One Half. GASP GASP. Negative one half.

Thus, my befuddlement at your "23/67" for an answer. And your gumption at following through and plugging in to get y - 2 and 17/93. Yay. Boo. Joy and Sorrow.

Checking Your Answer. Outrageous. Don't Fall For It. She's Tricking You Into Doing Needless Work. Mwa ha ha, Teacher Lady. I will NOT be fooled!

Blank Math Joke Sheet

I started thinking that is would be convenient to have some blank "joke sheets" ready to make a quick practice assignments for various math skills. I took my last geometry sheet and reworked it so that it's ready for a quick altering. In this one, I guess I'd have to find 12 problems that each have 2 parts, or I ask 2 different things, since there's an a and a b component. I guess I could easily rework it to make 24 problems, but I would have to reformat it. Let's see if it works.

Here's the downloadable version. And here's what it looks like:

Grading Projects

Some things I've come away with on my geometry project:

* Even if you don't get around to grading them immediately (say in a week or so), glance through them all and count them. If any students haven't turned the project in, notify them and their parents. I had one child inSIST she turned it in 1 day late in my mailbox - swearing up and down to her parents. I never saw the project. Luckily, the parents were supportive, and the child is turning it in WAY late, but turning it in .... well I say that, it's supposed to be tomorrow. We'll see.

* I like the "wow factor" component. I purposely left it vague, and just said, "wow me", and not everyone, but MANY students went beyond what I would have imagined.

* Put EVERY child's poster up if you're going to hang them .... and don't put them up in waves, do it all at once, or you'll hear about it.

* Don't assume they know how to draw "tilted rectangles" on a coordinate plane. Some just eyeballed the 90 degree angle, and didn't use slopes to force the 90 degrees.

Other than that .... spring break after tomorrow. Woo HOOOOOO. Sleep at last and movies and books and more sleep. I've also assigned a "castle project" to my IED (engineering class), and I have to build my castle on the Inventor program over break since I told them I'd do the project with them. ... Just got home from "Alice in Wonderland". Phenomenal. The creativity of people is very inspiring. It makes me want to go meditate and ponder on doing all sorts of fantastic things. The sky is apparently not the limit.

System of Inequalities

We just finished our unit on inequalities, and my students have a test next class. I'm thinking of putting the following question on it to gauge their understanding of what the solution graph really indicates. (sorry can't figure out a nice way to embed the document directly onto this page ... does anyone have a tried and true method?)

LATER: Thanks to a wonderful commenter, I learned a new skill of "screen shots" (after I asked him how to do it ... and then thought of "Google University"):

Special Triangles

We are just finishing up trigonometry and special triangles in geometry and moving on to areas, but as with all skills, they need to revisit the topic a few times. Here's a sheet I made up that I'll be giving my students next week.

EDITED LATER TO ADD: Well, after I made the sheet, I thought about how much I like the puzzle sheets with answer banks, so I improved it to make the following puzzle geometry sheet.

Quadrilateral Project

Holy Cow, my kids are awesome. Out of about 23 students in geometry class, 8 turned in amazing projects, and the rest (barring 2 late assignments) did great stuff (but not with the "wow!" factor of the first 8). Here are 6.

Here's "super man". You can put it in front of your chest and strut your stuff.


Here's a purse. All the math equations and essentials are on strips of paper inside.


Here's a camera, taking a picture of the world.


Turtle Soup. The "recipe" is awesome.


Surfer Dude (had an incident with a shark).

Monster in the closet.

Differentiation Chapter 1

Maybe this will motivate me to actually get through the differentiation book. There are 18 chapters, and I like her writing style and attitude. Invariably, though, for me, with all good ideas I read about, I'm all "Great Idea!" and then it's a crap shoot as to whether I implement it. So maybe if I talk/blog it out, it'll have a better chance of going into action.

The first chapter can be summarized as "there were no good old days of teaching". Way back in the late 1800's only a teeny percentage of boys went to and completed high school. And it seems the debate was always on about the purpose of high school and what should be taught and such. Here's a site with one synopsis.

So what does this have to do with differentiation? I guess in the early days only a select type of kid went to high school and only a few graduated. Now we're trying to get everyone to be successful, so that means we have all levels of kids in our classroom, not just the select few. And not everyone learns the same way.

She has one statistic that by 1990 only 38% of the nation had graduated from high school. Wow. Page 11 of this document breaks down graduation rates by state in 1990 and 2000. Too many percentages in the 60's and 70's. So I guess if kids weren't cutting it in school or the school wasn't serving them, then off they went. These days, I'm guessing most schools would not make "adequate yearly progress" if these were the numbers, and the school would be a potential candidate for closing.

So, this sort of makes the case for differentiating for students who need more/different ways of learning instead of just listening and notes. It's not making a case for the "fast learners" and how to differentiate for them. We have to keep both in mind.

Algebra Epiphany

I'm apparently a slow learner. I just realized the other day that I'm treating my algebra 1 preAP students like "gifted" kids, or "true preAP" students. I show them 1-3 examples (they work at least 2 of them by themselves in class) of a particular topic, and then invariably the bell rings MUCH too soon, and I send them off with homework. I also provide them with my school website in which I've linked various videos and sites that help for that topic.

I give about 10 problems of a type, and then the next class starts and we move on to a new topic after we've gone over homework. About 25% of the class (very rough estimate) is fine with this and can self assess and readjust their thinking and learn from their mistakes. BLACH! That means I'm not serving 75% of my students. They need MANY more examples, they need more hand-holding, they need more time in class to process new information.

Then there's always the war raging on in my head: Ackh! I'm going too slow, we won't learn everything we need to know for algebra. Eek! I'm molly-coddling them too much, when will they learn to stand on their own. Oof! what about the kids that get it, what will they do when we're practicing more in class when they already GET it. Yeesh! This is a preAP class, step up to the plate, kiddies.

Yes ... the "D" word ... differentiation. I had started to read a good book about it a while ago, and then as always seems to happen, other things got in the way, and I only finished 3 of 18 chapters. Then just the other day, I started reading it again. I'm on chapter 3. MUST. READ. BOOK. Must reflect on another way to do things.

Textbook Skills

I had a major scare yesterday after school during tutoring. My kids had a test the following day, and the homework I assigned was 1/2 odd problems (answers in the back) and 1/2 even on all the skills they needed for their test. One of the students was working an odd numbered problem, and then asked me if it was right. I told her to check the answer in the back. This was a total revelation to her. She didn't know the odd numbered answers existed, and after I told her, she couldn't track them down.

Then another student asked me how to do another problem. I asked her what the directions were and had her read them to me. Then I asked her to flip to the start of this particular section of problems. She didn't know what to do. We figured that out. Then I asked her to find an example they work through that is similar to that problem. We struggled to do that, too.

So, their homework tonight is a Textbook Scavenger Hunt (we use the Holt book).

New Math Game Addiction

So what do you do on your weekend when you are procrastinating doing your work? Well, you play this, which I found out about from her, (who is also the source of other game addictions).

Geometry Polygon Project

Inspired my Mrs. H and by the cool graph separation of a grid from Mr. K, I designed this geometry project for my kids after we've covered all things polygon. I'm going to pass it out next week and see what I get back.

A Valentine for "sticky notes"

I love the versatility and color choice and usefulness of sticky notes. Especially for returned homeworks.

Line Project Finale

Well, all, okay most of the projects have been turned in, and now comes my grading fiesta (ay yi yi yi) which I solemnly do swear NOT to put off until forever and a day (p.s. I dread grading projects). I love the creativity of the students, and was impressed with some of the facts they found that they thought interesting. Here are a few of them (with no mention yet of whether they are accurate or not).









Things I've learned and would change for next time:
Be more specific about what you want on the poster (data, what work, the sentence of the prediction, the fact that the prediction has to be from using the line equation and not just the slope).
Be SUPER HAND-HOLDY on the step by step procedure of finding the equation of the line of best fit.
Grin and take Deep Breaths because even though some projects are not exactly what you were expecting, everyone still learned something about how lines are used in "life".

Lines Project Continued

My students are still working on their Line Project, and I'm glad I assigned it because various things have come up that I think are good learning experiences for them and for me. I had separated their completion of the project into 3 successive class periods, and for the 1st one they had to turn in a set of data points and a computer-generated scatter plot to show the linear correlation. Well!

Most kids were fine, but others had a variety of issues:
* "The spreadsheet won't make a scatter plot of my data!" (the student was entering data of height vs. weight, and the heights were typed in as 4ft 5in, 4ft 6in, ...)
* "Here's my data ... SEE! Linear" (the set of points was EXACTLY linear since the student found a site that said that every 1 second ___ kids drop out of school, and the student had used that to create 5 coordinate points)

The 2nd class period, they had to turn in their own hand-created scatter plot and best fit line and equation and idea for a prediction using their line equation. Issues:
* Some kids used rise/run to calculate their slope, but the scale of their graph wasn't in "1's".
* Some prediction ideas were: I predict the cost of a loaf of bread will rise 31 cents every 7 years (they used their slope instead of their equation)
* Some just connected the data points, forgetting the example we worked on in class for best-fit line.

And so on. This seems to have taken them out of their comfort zone of how our math class has been going, so I'm glad they're being "mathematicians in action" and learning extra skills. I'm also glad I broke it up into 3 days of checkpoints since I'm guessing I saved myself (and them) the agony of incorrect or NO final products. While I was walking around critiquing their graphs this past class, I gave them THIS to work on.

On a side note, after my hectic week of various extra tasks added on to the already busy schedule, I went out for drinks with my friend, and we had an interesting discussion about the difference between "unethical" and "immoral". What types of things would fall into each separate category? Would some things be both? What's the distinguishing characteristics of something that is one or the other?

Lines Project

In algebra 1 we've covered most line topics I think are important:
* calculating slope from a graph and from 2 points without a graph
* looking at a graph and finding the line equation in all 3 ways (standard, pt-slope,slope-int)
* being given either 2 points or a point and a slope and calculating any of the 3 equations.
* looking at any of the 3 line equations and graphing
* looking at any of the 3 line equations and finding 5 points on the line (and the intercepts)
* seeing that if you have a graph and it's line equation in any form, that you can plug in any point on the line and it will "work" and plug in any equation not on the line, and it won't work in the equation.
(I've probably missed some, but this is what I remember)

We still have to talk about parallel and perpendicular lines, but soon we'll move on to systems of equations. Before we do that, I thought that this would be the perfect time to assign a line project to my students. In all their later topics and math courses, lines will just be an aside where it's already assumed they have learned about them.

We had a discussion about positive and negative linear correlation and no correlation and correlation that is not linear. We went through the process of creating best fit lines and using that line to make a prediction for another point that is not represented by your data. Then I discussed that in real life, people collect data, and if they all fell on a straight line, the mathematicians/scientists would faint from the rareness of this occurrence, and that usually, if the data seems to be linear, it'll look like our scatter plots that have a linear correlation, and THAT'S how this is used in real life. People make a model and then use that model to make predictions.

Then I assigned this project that I will collect in a succession of 3 class periods. I already have had one student send me her data that was interesting. She found information about teacher pay from the 40's to the 2000's, and you can see that it looks linear until about 1980, and then there's a BIG leap of the points and then it looks linear again. After a back and forth e-mail discussion, she found that some site stated that there was a 400% increase in pay in 1980 .... hmmm, haven't verified that, but I remember some of my older teacher friends mentioning their super low pay in the 70's.

Visual Clues