Monthly Archives: January 2013

Getting More Mileage Out of the Mousetrap Cars

Earlier in the year, in Physics, I had the students create mouse-trap cars.  The students found it very fun and we got to measure acceleration and use  the kinematics equations to our heart’s content.  However, it took a reeeeeally long time.  I appreciate that students probably picked up some practical mechanical skills when tinkering with how to setup a mousetrap car and practiced problem solving many times over when they encountered various hiccups in their work, however, whether it was worth the time is still up for debate.

I could have more confidence in my students’ abilities to do work at home, and assigned them the task of completing their mousetrap cars at home.  However, I also know that many of my students live a good ways from campus (some about an hour away) and that the ability to just “come over to each other’s houses” just wasn’t there.

Despite that, they had fun, and I promised them that we would use the mouse-trap cars again because I knew we would (eventually) get to energy and that spring potential energy is a big component of any decent Physics course.

So now the goal I’ve given them is to (1) improve their mousetrap car, and show me that they have measurably improved it (we talked a little bit about what that means), and (2) get them to figure out the angle a ramp needs to be so that their mousetrap car can run to the top of it and knock over, say, a domino without the mousetrap car going over itself.  I think it’s a difficult challenge, largely because messy things like friction despite having wheels comes into play (wheels are supposed to be frictionless in a steril Physics thought-experiment, right?).  We’ll see if it’s too difficult for them (and me!).

What about your Physics classroom?  What kinds of hands-on problems that require various types of mechanical and/or potential energy do you use?  I suppose I’m trying to teaching using modeling without (a) having taken the summer course and (b) not having any modeling curriculum, so I’ve been flying by the seat of my pants, not always doing a good job, I admit.  I really want to take a summer course in modeling, but I’ve already got this summer full of stuff.

Pictures below are of my students taking apart the mousetrap cars they created a few months ago and are in the process of improving them, using what they now know about springs, forces, and kinematics.

Photo 2013-01-28 02.44.15 PM

Photo 2013-01-28 02.48.03 PM

Photo 2013-01-28 02.48.57 PM

Photo 2013-01-28 02.51.00 PM


Leave a comment

Filed under Teaching

A Better Law of Sines/Cosines Project

A while back I had students finding distances on our school’s campus using the Law of Sines and Cosines, and I made the point that I thought students appreciated finding things out that related to their lives a little more.  However, this activity still seemed superficial to me because of (1) the ease with which students could look online to find these distances (using Google maps and a latitude/longitude distance calculator can be surprisingly precise!–see below), (2) after finding 1 or 2 distances it got old fast, and (3) I’m pretty sure this is not how surveyors do it in the real world.

I was talking with the father of a student in my Precalculus class, who happened to be a farmer, and “finding the area of his land” came up somehow.  Now a good chunk of the students live on the reservation and so it is very, very rural.  One thing they have, however, is land, and a lot of it.  I realized that breaking polygons into triangles is a cool theorem, and one that has practicality in finding the area of a plot of land if, say, you wanted students to use the Law of Sines, Cosines, and the Trig Area formula for a triangle.

I’m going to start with the following warm-up and hope that students recognize the connection between the project and the warm-up (I may have to spell it out for some of them).

I decided to turn this into an individual project for the students and use it in place of a test, since this would probably interest them significantly more and would demonstrate a deeper understanding of how to use the equations than “apply it to this triangle”.  I’m going to hand them this sheet below, show them how to find distances on Google Maps via Wolfram Alpha, and then let them go.

I’m hoping that students will solve this problem in a number of different ways.  One way that came to my mind immediately was, after breaking the land into triangles, find all the distances using Google Maps, then use Law of Cosines to find an angle, and lastly use the trig area of a triangle formula which involves two sides and the included angle.  Of course, if students are familiar with Heron’s formula, they could jump to that, hence the requirement they use 2 of the 3 formulas (is that too false a requirement?).

Lastly, you’ll notice I’ve made accommodations for the “urban” and suburban students as well: they can measure the square footage of their house/apartment or even a room as long as it isn’t a rectangle.

Let me know what you think, and in return I hope to show off some students’ work!


Instructions for finding Distance using Google Maps and Wolfram Alpha

1) First you should find the place in Google Maps.  Right-click and select “What’s here?”  You should see a green arrow now on the location.  In the search bar it will leave some coordinates, which are the very precise latitude and longitude of the place.  Copy these coordinates.


2) Next, go to Wolfram Alpha, and paste the coordinates as follows (and shown in the picture below):

distance from (35.528149 N,108.654796 W) to (35.52855 N, 108.656035 W)

Make sure you change +/- to N/S or E/W otherwise Wolfram Alpha will simply plot them as points and find the distance.  You’ll have to go back to Google Maps to select the other point and find the other set of coordinates.


One cool thing that Wolfram Alpha does is gives the distance is a number of different measurements.  And I’m not just talking about m, km, feet, inches, etc., but it gives crazy ones like “times the traditional length of Noah’s Ark” or “about the height of the world’s tallest tree” or “Light travel time in a vacuum” or “Maximum distance visible from that height”.  Crazy cool, right?


Filed under Teaching

How the Mathtwitterblogosphere is Helping Me Grow

I found the Mathtwitterblogosphere because my 4th grade teacher found out I was teaching Physics among other things, and referred me to Aaron Titus, a High Point University Physics professor who helps teachers, who referred me to a physics forum somewhere (I forget where at the moment) which was talking about having a “physicstwitterblogosphere” kinda like the “math people” do.  At this point, I said “What, I’m teaching math–I need to look into this!”, and found the above website that Sameer Shah put together.  He was also just starting a New Blogger Initiation, which I promptly joined because of all the good things all the other teachers had to say about blogging.  And I haven’t made a smarter career decision as a teacher.

Because of this group of people, I’ve re-learned to love mathematics and teaching mathematics, I’ve completely changed every single quiz I’ve ever given, I’ve done creative projects with my Precalculus students that I would have never thought of in a million years, I’ve learned how to more effectively use my iPads, I’ve used Standards Based Grading for the first time, I’ve put a giant “Board of Remediation” in the back of my classroom for students to work on skills they need, I’ve revolutionized the way I go over tests and quizzes (I don’t!), I’ve found websites where students can practice their pattern-recognition skills with minimal effort on my part, and I’ve learned how to send all of my students nightly HW reminders via text on their phones anonymously (that was learned via the Global Math Department on Tuesday Nights at 9pm EST–a place where every time I leave, I’ve enjoyed the experience and gotten something that I took back to my class and used very soon afterwards!).

But more than that, this group of people have given me a community that has rekindled my desire to be a really good teacher.  I think that through blogging and participating in this environment I have improved in three main ways:

  1. I am reflecting.  Simply through blogging, I am thinking more about what I’ve taught and how I can improve it.  This is something I did not do my first two years of teaching outside of thinking “what should I teach next?”.  I cannot explain all the little ways that thinking about what you’ve done when you’ve stepped outside of a situation can help you improve doing whatever it is you want to do better.  In my case, it is teaching and while at school, or thinking about what I want to teach next, I cannot reflect and so I cannot grow anywhere near as close as how quickly I’ve grown these past 6 months.  Included in this reflection is thinking about how ideas, such as SBG or Dan Meyer’s 3 Acts, compares and contrasts with my own teaching philosophy, and I have only improved through reading and thinking about these ideas.
  2. I found a place to discover new ideas for lesson plans.  As a teacher, you simply cannot figure out how to teach everything in even a single course (let alone 4 right now) from the ground up.  You must look elsewhere and be good at seeing what someone else has done and adapting it to fit your children, your classroom, your pace/planning guide.  As you can see from above, so many lesson plans that I’ve done this year have come from this group of people.  I will never forget one of the things that Fawn Nguyen said in one of her posts (sorry that I can’t find the exact post at the moment!).  It was basically along the line of “finally, after teaching for 10 (?) years, I’m keeping roughly 60 or 70% of the lessons from the previous year”.  Wow.  And to think that before I got into teaching, I though: “Once you’ve done a lesson the first year, you can tweak it a bit, but it’s still good, right?”  Wrong!  Because of her comment, and seeing so many good lessons out there, I’ve begun to change any and every possible lesson I saw as “boring” for something that engages students and drives curiosity and problem-solving skills over memorizing and drill-and-kill skill training.
  3. I have striven to become a better teacher because I care what these people think of me.  Is this pride?  Sure.  Do I have a bunch of people visiting my blog regularly?  Nope.  Average is probably about 6-10 a day (thank you to each of you!!).  But I have worked more carefully on creating specific quizzes because I knew I wanted to put them up here.  I have taken care to grade with more comments so I could write a careful blog post about the experience.  I have worked and re-worked lesson plans, activities, and worksheets just so that I can put them on this blog and feel proud about what I’ve done.  And if each of these things are done better, and the students get more out of my teaching, then it has been worth it, no matter the motivation.

So thank you to anyone who has written a post I’ve read, spoken (or chatted) during the Global Math Dept, tweeted a helpful tweet, commented on my blog, or even just stopped by to read an entry.  Thank you each and every one of you for making me a better teacher.  I still have a long way to go, because I still consider myself a “bad” teacher, i.e. I always see ways to significantly improve my lessons and my teaching style.  However, even that is an improvement over the time I used to teach and think “hey, that lesson went just fine” (when it really didn’t!).

Thank you!


Filed under Teaching

[SBG] My First Attempt at SBG

I have read up a fair bit on SBG (Standards Based Grading) and first heard about it after the start of this school year.  I didn’t feel right changing my syllabus on my students, and I was unsure of SBG at first, which are some of the reasons I didn’t use SBG this year.  I am still skeptical about certain aspects and implications of SBG.  However, I had adapted my quizzes to test only one topic each, as well as clearly define for students on quizzes what they should know in order to earn a certain grade.  In addition to that, I have allowed for students to retake quizzes and have changed the way I look at grading.

All of this has been done because of what I’ve read about SBG, but none of it is actually SBG.  Enthusiasts of the grading system will tell you “SBG is more than retesting“, so I am excited to try SBG for real for the first time this.

The class is a very specific, special class: it is 5 students who failed my chemistry class the previous year.  A few days into the new semester, after no-one had (or had been) signed up for “General Science”–the remedial, generic science class I teach just for the purpose of doling out credits, my principal approached me and asked about the possibility of teaching remedial chemistry, so that the 5 students who failed last semester would have a chance at passing.  At first I was frightened of the prospect of trying to teach the same thing over again when students didn’t understand it the first time.  However, after I thought about it, I realize this was the perfect opportunity to use SBG.  All the students have to do, to get a passing grade where they didn’t the first time around, is to show me that they understand what I thought they didn’t.  And so I’m not lecturing to the students at all.  I’m not creating activities or labs or anything for the students (because I did that all last semester for them), I’ve simply asked them to show me that they know what they’re supposed to for chemistry.

I’ve given the students 7 standards (I called them “learning targets”) for the students to demonstrate to me, and I’ve given them about 10 or so options for them to do this.  The favorite, so far, has been making videos using Doceri on the iPad, which I appreciate too because you really get to see how much they know.  I lastly gave them about half a dozen ways for them to learn the material if they didn’t understand it in the first place, so I think that, right off the bat, they recognize and understand that they need to understand in order to advance in this setting.

I decided to go with Shawn Cornally’s Blue Harvest feedback program because I had heard it was specifically designed for SBG.  What I didn’t realize was just how awesome it was for communicating with students and having a conversation about what they understand and where they are.  Students can submit work and comments in the exact same avenue that I can submit grades, feedback, and mark whether they are proficient or not.  It even plays well with iPads!  It has a few graphs containing information, and doesn’t have the fancy multiple info-graphs that, say, Khan Academy has, but it is perfect for SBG and I really think Shawn hit the nail on the head when it comes creating a program for students trying to learn and understand material.

The one downside to this process, so far, has been time.  I have spent just as much time on feedback and assessment on these 5 students as I have in my larger classes of about 20, and so I don’t know if that says something about the way I’m going about with the 5 students or with the 20, but I know I couldn’t do this specific, good feedback to a class of 20 students, let alone 6 classes of that many.

I look forward to this experiment in SBG (for me) and hope that I can find a way to use it in my other classes in the future, for the students’ sake.

Leave a comment

Filed under Teaching

Augmented Reality Apps — How Can Educators Use Them?

Last semester, I discovered the world of Augmented Reality Apps.  If you want to see what these are, go to my other posts where I have links to a handful of these apps for iPads/iPhones and pictures & videos of students using them in the classroom.  Basically, they are apps where you can observe a 3-D object by using the camera on the iDevice and looking at a marker (usually a sheet of paper).  You can see the object from various angles by moving your iDevice around and, in some cases, even interact with the objects!

As soon as I saw this, I became too excited to go to sleep that night.  My wife just laughed at my childish excitement, but my mind began moving to all the possibilities this technology holds for people in the future.  Just imagine the possibilities:

  1. Movie theaters where the movies are full-immersion experiences.  You have a device (or better yet, glasses) where you can focus on the action, but can also look side to side and see what else is going on around your other favorite characters.
  2. Video games where you can look at a map and see, in real (augmented) 3-D where things are.
  3. Art galleries where you can observe famous works of art without the hassle of moving the art or the worry of them being stolen.
  4. The Augmented Reality company is advertising their app as a way to view furnature and other home remodeling before making the leap to purchase the product.
  5. With the new wave of (relatively) cheap 3D printers (which I reeeeeeally, reeeeeeeally want), you could examine your object before wasting the precious “ink” producing the 3D object.
  6. You can make any building in the world look like it was remodeled by Disney for some big celebration.
  7. You can make portals to other secret worlds.

There were dozens of other ideas that I thought about, but can’t remember at the moment.  However, you’ll notice that of all the things above, none of them are easily lifted to go into the classroom.  Sure, we can force this technology into the classroom, and use it for things that could have just as easily been accomplished without augmented reality.  But there have got to be things that we can now do in the classroom that couldn’t have been done without it.  Just look at the list above!   There’s GOT to be some way to significantly improve students’ interaction with concepts that couldn’t be done without augmented reality, and I want to explore that.

If you have ideas, please, please comment below.  I think that of the math classes, Geometry stands the best chance of using this immediately (when exploring 3D solids) just because it’s the most obvious connection.  To that end, I had started making your basic 3D shapes for the Augmented Reality app in hopes that some geometry teacher would come along and want to try this out, but I didn’t get very far and ran out of time.  If you’d like for me to keep making them, please let me know and I’d be happy to finish them!

To me, this seems like a whole new frontier when it comes to human interaction with computing.  Perhaps that’s why Google is taking their time with Google Glass–they want it to be big in the way that the iPhone was when it first came out: it changed the face of computing and the way a significant number of people interact with computers for a significant amount of the time.  The possibilities are out there and I really want education to be on the front of this wave rather than 10 years behind the curve as it has been in the past when it comes to technology.


Filed under Teaching

Law of Sines/Cosines “Mapquest”

I was kinda proud of this activity last year, having created in during my first year of teaching this course, while being swamped under tons of other stuff.  The students actually enjoyed the activity because they got to see and talk about our school’s campus, and it was probably neat for them to think about how trig relates to distances and look at an overhead view of the campus.

The materials for this include (1) protractor/ruler, (2) worksheet below (you’d have to adjust it for your school’s campus), and (3) a map of campus.  I got my map from Google maps (seen below), but if your school is basically one big building, then I think it’d be just as fun to get a blueprint of the school and talk about “how far is it from Mrs. Smith’s classroom to Mr. Jones’s”.

The idea is to create triangles so students use the one length they know (in this case, the length of a soccer field) and then use the Law of Sines or Cosines (typically the Law of Sines) to find the other distances after they’ve measured the angles.  While this is probably not exactly what real surveyors do, it is perhaps the closest thing we can get to while learning/practicing these two trig laws.  And the students find it much more interesting than a bunch of unrelated triangles.

One idea that I want to explore some time later is how much students eventually “get off” with poor measurements.  Each time they measure an angle, if it is off by a little, then their measurements get off by a little more each time.  It would be much more accurate to always use the soccer field, but it is much more fun to build triangles that march across the campus, each attached to the previous, so you are using your previous answer to come up with the next distance (which is what I instruct students to do).  I think last year I even used Google maps and a distance calculator to find the actual measurements and gave an award (candy) to the group that got the closest.

Here’s the worksheet and map (for our campus) as an example:


Filed under Teaching

Visual Patterns

Just wanted to give props to Fawn Nguyen (@fawnpnguyen) with her work on  It’s a great website with 60+ visual patterns and it even comes with a nice half-sheet you can print out and give to students that is basically self-explanatory.  Even my Precal students enjoyed it as a “back-from-break-warmup” to get them thinking, and I KNOW they benefited from it, even though I think it is intended to target a younger audience.

I’ve printed out several of those sheets and now that I’m offering participation points for them, students are hungry to do more, which is wonderful!


Filed under Teaching