Tuesday, January 31, 2012

Clock Update

I saw this idea somewhere a while ago, and due to the number of questions I keep getting, I thought I'd have this clock enhancement. I don't say anything, it's just there for them to process. Woot! Future time tellers of America.

Saturday, January 28, 2012

Special Quadrilaterals

We've just finished our unit on special quadrilaterals, and before our test, I thought I would try to drill home the value of marking up your figure with pertinent information to help you solve problems. I also made them cover up their previous attempts with jokes about their wandering eye that may do them harm. I decided to do it in a "race" type format.

I wanted the kids to compete against themselves and make progress between attempts, so I said that they would be timing themselves and grading themselves and being consistent with how they marked mistakes.

I put an online timer on my computer and the document camera (this one was nice). I just set the start time for 0 and end time for 2 minutes just in case.

At each attempt, in one color, the student was to mark up the figure with useful/correct markings that represented the figure. I reminded them to QUIETLY lay down their pencils at the end (by being goofy and demonstrating the jerky contestant who makes tons of noise at the end). Then when everyone was done (all eyes up), we graded in a different color. We did 3 attempts for each shape, and I kept asking for hand raised if they made improvement. I said they could do the 4th attempt on the night before the test.

Helpful? Don't know, but it was a chance to drive home the importance of marking and knowing the properties.

Here's the document:

Thursday, January 26, 2012

Thinking, Contributing, and Confidence...

It finally hit me the other day, the students in my "regular" geometry class were so gun shy of answering questions. You know. I'd say something like, "and what kind of quadrilateral is this forced to be if it has ____ properties?".


Then someone bravely says, "rhombus." Then downcast eyes. Then, "oh I don't know, forget it." More downcast eyes with the body language of, "move on lady, nothing to see here." Even though it turns out the answer was right.

So after it happened again in my next "regular" class. I stopped the lesson and said the following:

You know if I could grade you all on your participation in your learning, it would go something like this.

* 3 points if you answer my question, and it's right. Because you're thinking and active in your learning.
* 2 points if you answer my question, and it's wrong. Because you're still in the game and willing to process your information and try.
* 1 point if you are paying attention and answering in your head but for whatever reason, you don't speak.
* 0 points if you just sit passively and think, oh, someone else will figure it out.
* -1 point if you sit there and think, hmmmm what's for lunch.

Then I mentioned the, "you can't just passively sit there and learn math" spiel. Then I went back to the lesson.

Hmmmm. Then there was lots of participation. And I would interject with, "3 points" .... "2 points" ... etc. ... hopefully it lasts.

Wednesday, January 25, 2012

Statistics vs Calculus

It's choice sheet time, and our current crop of precalculus students (and algebra 2 students for that matter) are asking questions:

* What IS calculus?
* What IS statistics?
* Which one should I take?
* Can I take both eventually?

We've been having conversations on the fly, but I thought it would be good to get it all down on paper and send out a mass school e-mail. This way the students have a more informed way of making a decision as opposed to, "so and so said THIS one was easier .... or THIS one was the one to take .... or my friends are taking this one...".

Here's the document:

Sunday, January 22, 2012


I just got back from the Houston Regional T3 workshop and learned yet more things I can do with the TI-nspire.

* I now know how to use the student software to be useful to me
* I know how to link between calculator and computer/calculator to transfer things
* I know how to upload pictures onto the calculator and then use it for math, say on a graph page or a geometry page
* I know how to easily do piecewise function graphing

I'm very excited to use these activities for upcoming lessons.

AND. Something someone said sparked another idea. I'm wondering if there are any precalculus teachers out there with about 22 students that are willing to collaborate with my 22 students. I don't have a firm idea of the final product, but my thinking is along the lines of: we would somehow match up our "remote" pairs of students, and then they would have to work together to create something - blog, song, newsletter, podcast, other .... that has to do with precalculus - either teaching something as a review, finding a new thing that is associated with precalculus, coming up with a memory tool for a concept we've learned .... I want to leave it open enough, so that they can be creative and most likely think of something we don't envision. I do want to have more firm rules and periodic due dates along the way. I'm thinking of a project/activity that we give them about 3 or so weeks for. In this way, our students can find a new "math buddy" in another state, and they can learn skills of working with a total stranger to complete a task (good future working-life skill).

Any takers? If so, leave a comment, or send me e-mail (math_mambo@yahoo.com), and we can take it from there.

For that matter I have roughly 4 classes of geometry that we can do the same thing with. But in that case, I'd ultimately need about 86 or so total students.

Sunday, January 15, 2012


I've been obsessively using the TI-nspire as a discovery tool in my classes these last 2 weeks. In geometry, we just started parallelograms, and I wanted them to explore the 5 properties of parallelograms, and it worked great.

One extra thing that I'm excited about is that I had them hold up their closed fists, and I asked them to put up a finger for every syllable of "parallelogram". Five! Ohhh! Five properties. So. Every time they discovered a new property on the calculator, I had them run through the list so far and tick off a new finger for the newly discovered property. We did this until we got through all 5 properties. Woot! Memory tool. Hopefully, they'll remember that there are 5 and parallelogram has 5 syllables, and they can recite all the properties:

1. parallel opposite sides
2. congruent opposite sides
3. congruent opposite angles
4. supplementary adjacent angles
5. diagonals bisect each other

Monday, January 09, 2012

Six Word Memoirs

Recently, I was reminded of the "six word memoirs", and I decided to have that as my first day back homework for my precalculus students.

I had them create a small poster with 2 such memoirs, one for their "math life" and one for their "other/real life". Here's the assignment:

Here are some samples. Some were creative, some were eh, some were funny. I told them I'd do it to, so I'm tossing mine in the mix. Each poster has 2 memoirs on it.

Sunday, January 08, 2012

Challenging Precal Problems

A while ago, I gave my precalculus class a "clock faced" problem that was not something they were used to seeing. Some of them rose to the challenge and figured it out. Most started the problem and then petered out. Too many didn't know what to do.

I struggle with how to effectively teach problem solving skills, so here is my latest attempt that will be their homework tomorrow.

Friday, January 06, 2012

Polygon Angles

I've tried various ways over the years of presenting the following 2 facts:
* (n-2)*180 is the sum of the interior angles of a polygon.
* 360 is the sum of the exterior angles of any polygon.

Yes, the students remember ultimately, but as I was looking over my old files this year to do it again, things just didn't sit right ... or I was in the mood for a change ... or I'm a different person now, and I want to approach it differently.

I hit upon the following method, and I think I like it the best (ask me what I think next time). Here are things I like about it: it's not talk, talk, talk. It's not, "let's do it all theoretically and then POOF here's the formula." It's not, "let's all explore a different polygon by drawing and measuring and seeing what happens and there'll be human error, but we'll hand wave that away." It's pretty efficient. It's different from what I usually do, so it'll stick in MY students' minds (hopefully).

I had everyone get a piece of colored paper and fold it in 4ths and cut the 4 separate rectangles. Then on one rectangle, I had them draw a heptagon (we drew a light circle, put 7 dots on it, and connected the dots). We took a colored marker to the border of the heptagon and made sure that some color was on the interior. We drew diagonals from one vertex. We cut out the heptagon. Then we cut the triangles out.

Then I said, so what we want to explore is if I had asked you to measure all the interior angles and add them up what would you get. So now look at what we have done, and see if you can figure out the answer and then ALSO figure out why I asked you to do these particular tasks.

Then I waited and eavesdropped. Then I asked a kid to explain. Then I had them tape this into their composition books to look something like this:

Then (after some other polygon stuff), on another piece of the colored paper, I had them draw an octagon but extend the sides to show the exterior angles. Before I had them do the following thing, I had them take thumb votes on the scenario, "as the number of sides increases, what do you think happens to the sum of the exterior angles as shown: thumbs up for increases, down for decreases, sideways for stays the same, or open palm for it depends on other factors." They thought and voted. Then we did....

Then I had them cut out the interior octagon and leave the border. We reviewed what the sum of the interior angles was (6 * 180). Then we built up what the sum of all the "lines" angles were (8 * 180). Then we thought and discovered and here's what they taped in their notebooks:

Then as always I ran out of time and was rushed and couldn't do any practice problems, so my resolution of stopping class 1 minute before the bell so they could pack up was not put into place today!

Monday, January 02, 2012

What I Did on Vacation...

What's a vacation without lots of surfing on old and new favorites:
(I thought I'd share so that I'm not the only one losing many hours of my day)
(sorry, or you're welcome, whatever the case may be)