Unit 3 - Velocity on an Incline --> Acceleration!

So now we're taking our velocity model & turning it on its side.  Kind of literally, in fact.  What happens if the object is rolling down a ramp instead of being pushed on a flat surface?

The unit started off with a paradigm lab.  We had a car on a ramp & we had to graph what the position looked like (the horizontal axis was time).  This was a bit of a challenge & required some rhythm on the part of the data collectors.

We predicted correctly that the the position would increase in a parabolic fashion (a smiley graph).  We set the ramp up at a height of 2 Arons, put the motion detector at the top, & released the cart from the top.  I also released a huge steel marble.  The steelie took longer to go the 2 meters.  The equation for the cart's graph (from the Vernier LabQuest) was x=28t^2.

Then we had to use that data to graph velocity over time.  This involved subtracting the 1st position from the 2nd & dividing by the time elapsed (5 seconds in all cases, thanks to the metronome), then subtracting the 2nd from the 3rd, etc etc.  Our times ended up being on the "quarter-second" marks (0.25, 0.75, 1.25, etc) since really all we were doing was finding the midpoint of each segment.  We correctly predicted that the velocity would increase linearly.  The equation was v=51.6t, which we calculated from the graph & verified with the LabQuest.

So this added something new to our model so far.  We discussed the relationship between the position & velocity graphs & determined that the coefficient doubled.  (Ours went from 28 to 51.6, which is pretty close.)  At the top of the ramp, where the force diagram was just a dot (since the cart wasn't moving), that was not complex enough.  Why did it start moving?  Just like we did in the last unit, we looked at the graphed the slope of the velocity line & called that acceleration (after a bit of discussion about what its proper name was).  Since velocity is linear, acceleration is constant.  So on the motion map we added in acceleration, either on its own dot right under the velocity dot or on a "fat" dot that was big enough for 2 arrows.  (I am pretty consistent about putting putting the velocity arrow on top & the acceleration arrow on bottom but I don't know if that's the convention.)

As you can see in our model so far picture, we've got a motion graph (on a hill) with both velocity & acceleration arrows, a position-vs-time graph (x=__t^2), a velocity-vs-time graph (v=__t), & an acceleration-vs-time graph (a=constant).

Next we did the lab extension worksheet to help solidify & expand our thinking.  The cart was in various positions on the track, as was the sonic ranger.  In the last couple, the cart started at the bottom, was given a push to go up the track, & was caught again at the bottom.  After we did the worksheet, each group was assigned one of the problems to do in real life.  We whiteboarded these & discussed.  Even with the model so far on the wall right next to my desk, I still predicted that velocity & acceleration would change at the top of the hill, when the cart paused & started back downwards.  The cool thing is that we learned "symmetry is our friend" at this point, which I will totally use.  This also led into the velocity chart & dance (which sadly I didn't get video of), which I will also totally use (& totally blame Don for). :-)

Next Don did an engagement demo (that he probably wouldn't have done in class).  He asked us what would happen with a steelie on a ramp that flattened out.  What would happen with 2 steelies released at different times or locations?  Is non-constant acceleration possible? -- Draw a ramp that would show that.  The biggest thing I learned here is to be very careful with my language.  Spacing is not the same thing as speed.  (& drawing motion diagrams is terribly helpful.)

  

 

We practiced drawing motion diagrams & graphs for different ramp set-ups in worksheet 1 and going from one graph (say, velocity) to the others (in this case, position & acceleration) on the "stacks of curves" worksheet.  Stacking the graphs, & putting the dotted line of symmetry down thru the middle, is also terribly helpful.  We discussed the lines of evidence that support having 0 velocity but non-0 acceleration -- Sarah's rule (acceleration goes down the hill), motion map, acceleration graph, velocity graph.

We went back to the model so far to try to put variables in the blank spaces, but that was revealed only after we did the experiment.  Each group was asked to set up a ramp (either up or down) with the motion detector at the zero position & the cart traveling in the positive direction.  We had to get a quadratic equation for position, a linear equation for velocity, & a constant for acceleration.

Don wrote all the numbers that different groups got below the blanks & then we looked for patterns.  We arrived at the standard velocity & acceleration formulas from experimental data only -- no algebra, no calculus.  The more experienced physics teachers were all agog, but isn't that how it should work?  If there's multiple ways to get to anything (& this is especially true in calculus), shouldn't you be able to get to these equations experimentally?  [Please see the picture for the formulas -- This blogging program doesn't do subscripts or superscripts, at least not that I've found.]  Don introduced the terms derivative & integral but I don't think we'll use them.  & honestly, I'm not sure my students will have had calculus when we're doing physics.  I need to get the typical sequence of classes from our counselor.  I got a handle on which science class they take when but I don't really know about the other classes.

Next, we figured out how to find the displacement in a couple different ways -- We drew the graphs & counted boxes but we also used geometric area formulas.  Then we worked on worksheets 2 & 4, which were all about creating graphs & calculating displacement/ velocity/ acceleration.  (Story problems, with bears!)

Then we started the challenge (getting the constant acceleration "pull-back" truck to collide with the constant velocity tumble buggy, using the same set-up as before ... without using a timer!) but we had an end-of-day break.

Before we continued with the challenge, we talked about the 2 reading we did for this unit -- a section in Arons (about acceleration, mostly) & a paper by Etkina about the role of models.  Apparently Etkina has written a physics textbook that's recommended for AP Physics.  I'm not so worried about that yet (& I'd rather do AP Bio anyways).  Both these readings reinforce what we're doing during the workshop.  I chatted in my group about doing the readings beforehand versus doing the readings afterwards & I think I kinda like doing them afterwards.  Things make more sense.  (Altho my table partners talked about reading first, doing the class stuff, then re-reading.  I can't expect anyone but my most motivated students to do that.  Sure, it might work, but...)

So for our challenge, I'm a bit afraid we cheated a little (& we had to put a "sail" on our accel-truck for the motion detector to see it for any distance), but we only had a near-miss, not an actual collision.  Sadly, my video is no longer in my phone so I cannot share it here.  It was an exciting near-miss, tho -- The buggy grazed the edge of the sail on the truck.

Then we had an inquiry lab, where different groups changed different aspects of the cart-on-a-ramp experiment to see if they could change the acceleration.  My group changed the initial velocity; other groups changed the angle of the ramp, the mass of the cart, or the initial position of the cart.  The only variable that changed the acceleration was the angle of the ramp.  That was really interesting during the whiteboard discussion, because one group had asked to do the change-in-mass option specifically because they thought it would change the acceleration.  (My group correctly predicted that acceleration wouldn't change.  I probably wouldn't have gotten fooled by adding mass, either, since I'd played with the 1" ball bearing, but maybe.)

Our last activity was trying to figure out what happened if the ramp the object rolled down was straight up & down.  So we didn't use a ramp -- Instead Don gave us bean bags, saying "If you're going to drop things on your motion sensor, they'd better be soft."  Getting this to work right was a bit of a challenge.  To get up-&-down data, the bean bag had to stay in view of the sensor the whole time & the tosser had to get their hand out of the way quickly.  We also tried it with our tallest person standing on a chair with the sensor & the bean bag & just dropping it.  My group got 10.5 m/s/s & when all the groups results were averaged, the class got 9.7 m/s/s.

The funny thing is that AP Physics now suggests that students use 10 m/s/s (instead of the textbook standard of 9.8 m/s/s) to make the math easier ... & since we as students aren't trying to land humans on Mars.  Don drew a stick person (tethered for safety) dropping a ball off a building & called this the free fall acceleration.  He had us use the 9.7 that we got, the 9.8 from a textbook, & the 10 recommended to figure out the velocity at 4 points.  He stressed that it was not a constant & that we weren't considering air resistance, etc.  We have not called it gravity yet.  It is free fall acceleration.

So that was Unit 4 -- Hello, acceleration!  I asked & it'd be really hard to do this without a sonic ranger/ motion detector/ whatever you want to call it.  I'm pretty sure my school doesn't have one (I need to go look around in the science storage area, now that I know what stuff looks like), which means I need to check with the ISD.  Wonder if that's something I could borrow from the Battle Creek Math & Science Center, or whoever made those traveling kits.  My budget for last year was $450 -- There's no way I could get a classroom set of equipment.  Luckily I don't have Physics until winter trimester so maybe I can write a grant request.  The question is, to whom...


Costs:

http://www.vernier.com/products/lab-equipment/dynamics/vds-ec/
The motion encoder set contains the track (1.2 m or 2.2 m), a regular cart, a "plunger" cart, a motion encoder receiver, a "double the mass" block, & various connectors.  The cost is $424 (or $534 for the long track).

http://www.vernier.com/products/interfaces/labq2/
The LabQuest 2 handheld data collector/ processor, which connects with ChromeBooks & comes with standard connecting cables & free software upgrades, costs $329.

http://www.vernier.com/products/interfaces/labq2/
The "sonic ranger" comes in 3 varieties, depending on what you want to connect it to, & ranges in price from $79 to $109.

http://www.amazon.com/Inch-Chrome-Steel-Bearing-Balls/dp/B007B2AA0K/ref=pd_sim_328_6?ie=UTF8&refRID=0TZVP2NHKYDRMS49AH6E
1" steel ball bearings, 10 for $15.

Unit 2 - Velocity ... aka, Playing with Tumble Buggies

This unit consisted of 2 labs, a couple of worksheets, & 2 readings.  & discussions, of course.  Lots of "model so far" discussions.

To be honest, it's leading (or guiding) the discussions that worries me the most.  I know I'll get better at it but that feels like the shakiest ground right now.  Maybe I should look for a "unlocking your inner Socrates" self-help book. :-)

So here's the video of lab # 1, where we tried to figure out if a toy car actually moved at a constant speed.  (Don took this video & posted it on Vine -- Thanks, Don!)

https://vine.co/v/eiMtMnvdF3L

The intro to this lab was "hey, look at this toy car, what do you observe?", making a big list of all the facts, & then crossing out everything but "constant speed".  We had a few minutes to discuss in our groups how we'd figure out the speed, then we reported out.  Don said one way was too easy (measuring how long it took for the car to travel a meter) so all the groups had to do it the hard way, marking out how far the car traveled in x number of seconds.  (We chose 2 seconds -- Trying to do a mark a second was a bit much.)

Once we had that done (& we did 3 trials, because human error is a big issue in this lab -- saying the seconds on time, marking the distance traveled on time, those are hard to get right), we got part 2 of the lab.  We had to turn our car around on our starting line & go 10 seconds in the opposite direction.  (Every group had a different part 2: Start from the end point & go back, try it with a blue car, start at 1 meter, etc.)

& then of course we made a whiteboard:

There was a big discussion & Don asked why some slopes were negative, why we said "position" instead of "distance", & what were the "for every" for the slopes.  (The blue cars were half-powered & went painfully slow.  I'm kind of glad we didn't have one.)  This discussion uncovered the difference between speed & velocity, so then of course we graphed the velocity for both our experiments:

More discussion, especially about how negative slopes on the distance-vs-time graphs become lines below the horizontal axis on the velocity-vs-time graphs.  & also just good discussion about the nature of both types of graphs -- What do they really show?  One group presented a great critical competitor:

This graph got us into the difference between graphing speed vs graphing velocity.  They fixed their graph (the labels) to be accurate.  This will be a trick with moody teenagers -- discussing things so that classmates see their errors & fix them rather than snarking at people for being obtuse.  I sure hope I've got a good group of kids to practice discussions with next year!

& then it was time to go home, do a worksheet, read a section of the Arons book (http://www.amazon.com/Teaching-Introductory-Physics-Arnold-Arons/dp/0471137073), & blog/ tweet as appropriate.

We started the next day off with a discussion of the Arons section, which was the intro to why he wrote the book -- how students don't really understand the concepts (what really is area, what really is a ratio), they're not asked to explain their reasoning so instead they've only got shallow algorithmic understanding, etc etc.  (Sorry, I forgot to snap a picture of our whiteboard with likes, dislikes, & questions.)  He was writing in the '90s citing data from the '70s ... & it's now 20 (or 40!) years later & these issues are still problems.  I need to take better discussion notes, altho really this is all stuff we discussed in my Woodrow Wilson Teaching Fellowship classes.  [Side note; I wish we got the hardcover edition of this book, like Don & Laura both have -- It'd be easier to handle.]

& back into the physics!  We pulled out our whiteboards from the buggy labs & figured out that the area under the curve (more accurately, the area between our line & the horizontal axis) on the velocity-vs-time graph was the displacement of the buggy (as opposed to the distance traveled by the buggy).  Then we built "the model so far" on the front board.  I really need to take much better discussion notes -- what are the transitions like, what sorts of questions do Don & Laura ask, how do they lead us to realize contradictions & weaknesses in our thinking?  Of course, that's hard to do while I'm also taking notes on the actual physics...

The worksheets so far (& I expect forever) tie directly into what we've just done & help to solidify concepts.  They're a bit vague & Don was noting the poor graphics.  Worksheets can either be homework or in-class assignments but so far they've all gotten whiteboarded.  (Is that really a verb?  O well, it is now.)  Even tho we work on the problems by ourselves, we put them on a board as a group.  Not every question, & sometimes groups write up the same questions as other groups, but everything gets discussed.  Here's the whiteboard we did:

Up to this point, things have been pretty basic.  I mean, it's only Unit 2, how complicated can it have gotten.  Well, now we introduce motion maps.  I'll have to figure out a different way to do this because the fake-strobe gave me a terrible headache.

After the strobe-motion demonstration, Don led a discussion about how to record what we saw & voila, he came up with the dots-&-arrows of the motion map.  We talked about them some, wrote out dots for the fast buggy & the slow buggy, & then had a reading from Unit 2.  This is the only content reading we've done so far, & it was just a couple pages about motion maps & some examples.  No, seriously.  All the other content we've learned has been thru experimentation & discussion.  & then we had a worksheet, which we whiteboarded & discussed, & then we wrapped up the unit with a challenge activity.

So, for the t-bone challenge, we took the 2 buggies & tried to make them collide on an X.  There's 2 start lines, both 2 meters away & orthogonal to each other (I love that word!  It just means at a right angle).  We couldn't test it out beforehand but we could figure out the speed for the buggies & make predictions, etc.  Here's all the instruction Don gave us (note the motion dots at the top of the discussion board):

So yes, vague enough to get started.  We calculated velocities, figured out displacement (via the area method), & whiteboarded that:

If we released both buggies at the same time, the fast buggy would've had to start 5 meters back from the X, which we figured just asked for a curvature error.  So we released them both at the 2 meter starting lines, only we released the fast buggy about 7 seconds after the slow buggy.  We only had one chance at this & sadly our buggies failed to collide.  (Our releaser was off by a second.  The 2nd time worked perfectly, when it didn't count.)  So here's our video:

After all that excitement, it was time to go home.  The readings over the weekend were kind of more of the same.  We read another bit of the Arons book, which focused on how teachers ought to lead students to explicitly state their thinking (because otherwise students won't crystallize their ideas & teachers can't see hidden misconceptions).  Seriously, there was a lot of "leading students" -- I don't think that's the right terminology.  "Guiding students" would be better, since it implies that the students are discovering the knowledge on their own.  (You can lead a student to physics but you can't make them think.  Ha ha!  [OK, I know, I'm not that funny...] )  & the Wells method paper answered a bunch of questions from the first reading.  It's very sad that he died of Lou Gehrig's disease.  But the original modeling protocol is, like, 20-some years old.  I'm sure it's changed since this paper was written.  Heck, it's changed since the worksheets in our binder were created (in 2006).  So these both are more historical background & perennial suggestions more than immediately helpful.

Here is the whiteboard for the Arons, from our discussion Monday morning:

So, 2 units (& 3 days) in...  I'm really happy to be refreshing my physics.  (I'd like to refresh my calculus too but that can wait.)  The modeling stuff we're learning goes hand-in-hand with what my WWTF professors stressed ... only this is an actual demonstration, not just "you should do this, it works".  I don't know how much of the equipment we have.  It'll cost ~$100 for a 5-group set of buggies (that includes shipping & batteries, the buggies themselves are like $8 each) & the LoggerPro software is only $250 for the whole school ... but this is only Unit 2 & I know there's essential equipment coming up in Unit 3 that's darned pricey.  I really wish I'd had this workshop before I had to turn in my "shopping list" in June.  I'm just going to have to go spend some time in the science storage area, which unfortunately is not attached to my room.  (But I shouldn't complain, I've got the biggest science room in the building.)

This is a great experience.  I'm trying to figure out how to do this for biology, but maybe I just ought to concentrate on the physics for the next few weeks.

Unit 1 - Relationships (in Physics)

So, Unit 1 was where we learned how to "whiteboard", how to circle up & have a scientific discourse (aka how to argue without arguing), & hopefully the best ways to drive to & from the Kent ISD building.  This was our training stage, & it took a day & a half.

So after we got our huge binders & our name tags (left out on the table where we signed in), our science notebooks were handed to us.  Both the presenters & previous workshop participants emphasized the importance of the notebook as a future reference so hopefully I take good & useful notes!

We spent the rest of the day doing labs about relationships.  The lab directions are purposefully vague ("vague enough to get started") & therefore open-ended, which means different groups approach things in different ways.  For instance, in the first lab, my group had 2 meter sticks so to find the relationship between inches & centimeters, we just put the 2 sticks together & looked at the lines.  (Actually, I'm pretty sure that was Kal's idea.)  Don came around & made a suggestion or 2 but other than that he was pretty hands-off.  Another group only had 1 stick & so they measured things -- a laptop, a book, etc -- in both units.  Here is the whiteboard with my group's results:

To make the whiteboard, we had minimal instructions: include the T-chart & graph, write a "for every" statement, & have the formula.  (O, & multiple colors.)  The discussion of this led to 1) what should go on the horizontal axis, & why, 2) the difference between in/cm & cm/in, 3) the process rather than just checking with Google, & 4) what should be included in future whiteboards.

Then our groups got rearranged.  This is a fantastic idea for cohort building (I know from experience people will end up with their favorites unless you move them around on purpose) -- I had a class last year where making a seating chart was really tricky because of all the interpersonal drama (yay, teenagers) so maybe I'll have to be more brave with group assignments next year.

Our next activity was a relationship smorgasbord -- how is the length of the string related to the time it takes a pendulum to swing, how is the mass of a cup filled with mystery items related to the number of items, etc.  A couple of the labs used "area-ometer" paper -- Even if we knew how to calculate the area of a circle, we had to draw the circle out on square-centimeter graph paper & *count* how many squares.  I don't think I've ever done area in real life before.

After we took all the data (my group didn't get to the 2 pendulum options, sadly -- my lab titles were pit-&-the-pendulum inspired, of course), we were assigned 2 to whiteboard.  & of course the choices of which ones to graph, etc weren't random -- Laura wanted us to uncover particular shapes of lines & particular equations.  (Major types were already on the board.)  The biggest thing here was trying out different graphing software.  I'm pretty sure my school doesn't have any of the Vernier software (http://www.vernier.com/products/software/lp/) so I was excited to find out about Plotly (https://plot.ly/).  Unfortunately, it's not as powerful or as useful as Excel, which my teacher laptop has but my students' ChromeBooks don't.  So that will either take some finagling of which experiments to ask for or some computer lab time.

[Aside: The price of Vernier's Logger Pro 3 is really pretty cheap.  I've sent an email to our IT guy & if it'll work with ChromeBooks, I might just donate it to the school.  The union rep where I interned said to never spend your own money on your classroom but honestly, I want good equipment, even if I have to pay for it.  If I had thought about this earlier, before I submitted my budget for the year... but o well.]

Ooo, & here's the whiteboards my group did.  I didn't even think to get pictures of all the action.  (Trying to balance the weight & the baseball was kind of challenging & might have been photogenic enough...)  To get the 10-fold increase for the circle's area, Don measured the clock on the wall -- at a student suggestion.  The need for that range will be something I stress...

< meter-stick balance with a baseball



diameter of circular lids vs area >











The final thing we did was read an article about the Force Concept Inventory, the pretest we all took that first morning.  (Hopefully we'll get our before-&-after scores back -- I'm sure this workshop will help me fill in gaps & misconceptions in my content knowledge.)  This test looks at how students conceptualize how the world works -- how gravity works, how air pressure works, how projectile motion works, etc.  Sadly, common sense & Newton don't agree on a lot, which is where the misconceptions come in.  Also sadly, most teaching methods (with the notable exception of modeling) don't do much to alter those misconceptions.

What's up next: Playing with tumble buggies!

Day 1 of Physics Modeling Workshop

Good morning, Vietnam!

No, really, hello way to discuss my physics modeling class.  Otherwise I'd probably never blog -- I'm such a luddite. :-)  I've already quintupled the amount of tweets I've sent out & it's only been the first day.  & other than me getting lost in Barry County on the way home (I figured the back roads would be nicer than going thru GR during rush hour), it's been a good day.

O, & I got 13 out of 24 right on Harvard's pretest.  Hope the posttest is better!