March 31, 2012

Measuring by Magic: Shadows and Mirrors

We had some unusually warm weather a week ago and the kids were all clamoring to go outside; I said "next week" not realizing the temperature would drop so dramatically. I should have known - I've lived in New England my entire life - but I certainly wasn't going to start having class outside just because it was warm out in March! Imagine the begging I would hear in June... So, we measured using shadows when the thermometer read 30-something and opted to use mirrors in the lobby, where there was heat and high ceilings (the entryway spans all three floors).

Indirect Measurement

Before we headed outside, we looked at the diagrams and determined why this method would work. Similar triangles was an obvious answer since that's the unit we are on, but they know better than to just assume triangles are similar. Important facts: pick something that is at 90 degrees to the ground and on level ground (our flag pole is on an impossible to measure cliff), hold the meter stick vertical, the sun is reeaallly far away (doing this inside with a lamp would not work) and finally when looking in the mirror you must stand up perfectly straight. We neglected to mention accurate measurements, which I discovered when we got back to the classroom and some students were calculating in terms of feet with no spare inches. I'm pretending that's due to rushing in the cold (yes, I know the mirror activity was inside, fine, I'll note their inaccuracy when I comment on their work) and will be sure to mention it with my other classes next week. Overall it's a fun activity that gets kids looking at applications of math in a non-contrived way. I even went on a little tangent about just how hard it is to measure trees- tall, hard to climb, branches everywhere so even if you reach the top, how do you know how high you are?? Problems like these also encourage students to estimate and check how reasonable their solution is. We know the lamppost is taller than them but shorter than the building so the answer had better fit in that range.

March 26, 2012

Favorite Phrases

I seem to have an influx of visitors (Thanks Mimi and MathyMcMatherson!) so now seems like a great time to conduct the poll I've been planning.  All teachers have a few key phrases that they use on a regular basis.  They are verbal cues that your students learn to react to.  I don't remember deciding on any of these, but they are the ones that I find myself saying over and over.  A month or so ago I was visiting a friend who is an elementary school teacher and she had a sheet full of really corny call and response ideas to use with kids.  As silly as they seem, I have no doubt they work.  I wouldn't mind adding a bit of fun to my transitions or classroom repertoire, but none on the list felt right to me.  That's where you come in!

Most Heard Phrases in my classroom:
"I need eyes up here and voices quiet" (by the time I say quiet, I'm speaking quietly)
"defend your answer" (the first few times I tell them to pretend to be lawyers providing evidence)
"use nice words" (when I hear anything that doesn't fit my definition of respectful)
I've used these three often enough that kids can both anticipate and complete them.  I'm sure I have others, but these are the only ones that jump out as phrases where I use the exact same wording every time.

My co-worker uses a call and response where she says/sings "red robin" and they say "yummm" (and their mouths have to stay closed on the mmm sound).  If the shoe fits...  I hope those students don't arrive in my classroom next year expecting me to sing to them every day though, since that's really not me!

What are your favorite phrases?  Did you pick them on purpose or did they happen organically?

March 21, 2012

Pi Day

This week is English MCAS (state test) week in Massachusetts. That means for 3 hours Tuesday, 3 hours Wednesday and 2 hours Thursday all the sophomores have to sit for exams that determine their eligibility for graduation. Then, they get sent off to class. Since I have almost all sophomores we postponed pi day by a week and celebrated on the 3 hour test days. I bribe my students with pie, but they do real math and we spend the 45 minutes productively, so I'm fine with it. Plus, they deserve the reward!

I started celebrating pi day at my first school, where it was actually a collaborative effort with a veteran English teacher. He had developed the method with some colleagues, but I wrote the worksheet to emphasize student thinking rather than providing all the steps and creating a mindless plug and chug activity.

Pi Day

Photo run through SketchUp App
 Since we only had 45 minutes to both calculate pi and eat pie, I found we needed to do numbers 1 and 2 as a class. With more time I would give students the independence to figure it out themselves and work with them individually as needed. After question 1 I tell students to imagine that they are mathematicians in ancient times: they have noticed these equations seems to hold true for some constant, but they don't know that 3.14... is the correct value, how would they find this mystery number?

I think I have a lot more fun watching kids roll circular objects down the hall than they do crawling or crouching for 100 feet, but it gets them moving and maybe experiencing circumference helps them understand it? I also enjoy writing silly messages on the start, half way and finish lines (blue painters tape- easy to see and remove).  One issue that comes up in every class is units.  We have tiles that are 1 foot long so it was easiest for me to make the track 100 feet.  In class I allow students to use cm or inches at their whim, so long as they are consistent with themselves throughout the activity, so many students measured diameter in cm.  You can guess how well their value of pi came out!

Photo run through SketchUp App
When students finished their work they traded in their worksheet for a slice of pie (donated by our local grocery store- Shaws). This turned out to do much more than make sure each kid only got one slice of pie; it meant there was very little copying (I had the completed sheets) and I could direct students with questions to find a student who already had pie (an easy identifier).

While they were calculating and eating I played my favorite pi music.

March 10, 2012


I hate giving detention. I invite students to stay after school on a regular basis (notes on low test scores, weekly invite lists based on average grades, missing assignments or lack of progress on a long term project) but the consequence for not attending is merely that they continue to not understand or owe assignments. Giving detention for poor behavior makes me sad, because it says that my students don't respect me or their peers enough to change their behavior on their own. It says that students are acting appropriately because they don't want to stay after school, not because it's the right thing to do. Reaching this point makes me really disappointed in my kids, but also in myself- how could I have allowed students to get this far without establishing a relationship based on respect?

Here is the strange thing- I teach on a block schedule so we have classes A-D on Red days and E-H on White days, then the next day is a red day and so on. My red day classes are awesome. We can get serious, joke around, have conversations while we work, get off topic and then refocus. We have reached the sweet spot in the year when we all understand each other and class runs smoothly. My white day classes? If I give them a centimeter (not even an inch) they take a mile. They can't refocus or settle down or work independently. My regular geometry classes are at the same time of day - one red day, the other white day - but if someone observed one class and another person observed the other class they would have completely different impressions of my teaching and ability to run a class.

I realized last week that my F block was really getting out of hand so Friday I started class with a new seating arrangement and the prompt "Silently make a list of the characteristics of an A student." It did not happen silently but we started making a good list and almost had a good discussion about being born smart vs. working hard, but yet again a few kids kept shouting increasingly irrelevant things out while we were in the middle of a discussion. It ruins the momentum of any conversation when I have to stop to refocus students. I ended the conversation by telling everyone to pretend that they're an A student in class today. Somehow, class only got worse from there. Every other class I've used this prompt with has given me at least one good day. Apparently I need to cut back on the freedoms I allow them and start doling out consequences until we can get back to a state where the priority is learning, not random outbursts.

What do you do with a class that doesn't know what to do with a little bit of freedom and responsibility? I clearly need some help.

March 5, 2012

Miniatures in Proportion

I started doing this project back when I taught pre-algebra, but it's such fun that I continue to use it in my lower geometry class to review solving proportions before we get into similarity.  My co-teacher and I scour our homes for miniature objects and end up with a pile of stuffed animals, toy cars, model trains, keychains etc.  Students get to pick any object that they want to measure.  Then, using just one dimension of the 'real life' object they have to calculate the other dimensions by assuming their miniature is proportional to the real thing.  I started with slide 3, then when most people had several measurements I went through the example.

This year I happened to have the laptops in my room during the project, so we had them look up the 'real life' dimension (in the past I've just provided it on an index card).  This allowed us to discuss what a reputable website was.  I was disappointed to discover that my sophomores don't all know how to scan a google search and pick a good resource, but it did make me glad that my co-teacher had suggested including this step!  The journal question at the end of class asked "How can you tell if a website is reputable?" and I've gotten some interesting responses.  They vary from "if the website name isn't goofy" to "if you check the information with several sources" to "why would anyone post fake information about a fish?!"  Internet research may be a topic we need to discuss again.  That or I tell their history teacher to take care of it ;).