this video is sponsored by texas instruments i-35 runs to the heart of texas a self-driving rover
delivering texas instrument calculators leaves san antonio at noon it's headed north at two
miles per hour another self-driving rover leaves dallas fort worth at the same time at its south
going 1.5 miles per hour which town will have a front row seat to the unfortunate collision
of our two rovers and when can the town expect to see said collision hopefully that was a little
more engaging than just reading the classic train word problem today let's see how we
can bring mathematics to life in our classrooms with our texas instruments calculators and ti
innovator rovers this lesson is ideal for an algebra 1 classroom where you're learning
intersection of lines and systems of equations but you can differentiate if you teach a higher
level mathematics which i'll talk about later in the video and stick around to the end of
the video where i'm going to tell you how you can actually win a couple of these rover sets
for your classroom for free and this was actually really fun for me to do because i have only taught
fifth sixth seventh grade math and i got up to pre-algebra and so i never really taught algebra
one or anything after that a lot of these algebra one concepts i haven't seen since high school or
college and so some of these things i actually had to stop and think wait how exactly would i do this
again but it was really fun for me to rediscover some of these mathematical concepts in a really
conceptual and tangible way and realizing when i learned it myself i really just learned oh this
number means you start here on the graph and a really big number here means you've got a steeper
slant and so i share that because you might be thinking like i don't know about these robots and
these innovator hubs and electronics and stuff like that but i encourage you to have a growth
mindset about this this could be a super fun learning experience for both you and your students
and who knows maybe it will illuminate some of the mathematics for you too i'll be working
through a lesson document that i've created to help you and your students work through this
activity so these rovers are made up of three different elements the ti 84 plus ce you can
have the one with python or without python it'll work with either you can also do this with the ti
inspire cx or cx2 you've also got the ti innovator hub which your calculator connects to and then
this hub connects to the actual rover which for the most part is pretty assembled when you get it
you just have to slide in the hub and then attach the calculator and then plug in a few cables on my
lesson document i'm going to have links on how to actually assemble this so if you and your
students are doing this for the first time you can easily follow those directions there is a specific
program that you need to install on the calculator for this specific activity and on that document i
also have a link on what software you need to download to your computer in order to install
the appropriate program as well as a link to the program i recommend assembling the rovers and
installing the programs onto them before you do any of the work with this activity and so that way
you're not making all this momentum in the word problem and then saying okay now let's stop for 30
minutes and start assembling these and downloading the programs and all that the first thing you need
to do is create a number line to serve as your highway it's a vertical number line for a couple
of reasons first i-35 is north and south and runs right through the heart of texas i'm working with
texas instruments i live in austin texas all of it kind of just came together too nicely in that
regard but the bigger reason is that this number line is going to be representing our y axis later
on when we get to the graphing portion of the activity and it's going to be a lot easier for
our students to make the connection of a vertical number line being the y-axis versus working on a
horizontal number line but then thinking about it later as the y-axis each unit on the number line
is representing one mile in the word problem and it has to be 10 centimeters apart on the actual
physical number line that you draw in order for the program to run correctly obviously the cities
on my number line are much further than one mile apart but i just wanted to put a lot of the big
cities in texas on the number line you could also do this with a north south street in your town and
just use street names as your benchmarks i think customizing it to a road that your students are
familiar with will help contextualize it and make it a little bit more real for them a little bit
more tangible for them i wrote the question with everything in relation to austin and so austin is
problem and you probably want to customize it for cities and towns and streets in your area and then
show them the number line and then that's it just let them see what they can figure out don't worry
about any equations or functions or graphs or anything like that right now what can they figure
out based on the information given and the number line that they are presented with a few questions
you can ask students if they're struggling to get started are where is the first rover starting on
our number line what direction is it headed how fast is it going where is it going to be after
one hour what about after two hours can you write that down okay so what about the second rover
once they have a guess and they have an idea like okay i think the collision is going to happen
at this place on the number line after this many hours they can run the test with the actual rovers
you can put the rovers on the number line and you just match the front of the rover with the spot on
the number line that they're starting and then on their calculators they'll just run the program and
the program is going to ask him a few questions before it actually runs and this is where they
basically put their guesses in the first question is what's the velocity we know the velocities from
the original word problem so with our first rover the velocity was 2 miles per hour in the context
of this demonstration miles per hour are actually going to be units per second so two miles for
every one hour is actually going to be two units on the number line each unit being 10 centimeters
every second the next question it asks the students is what's the position of the rover
where on the number line in relationship to zero is our rover the next question is what is the
time of intersection how many hours or in the demonstration how many seconds is it going to take
until these two rovers collide what this number is doing is it's telling the rover how long to go
at the velocity that they had written earlier and so if they do everything right the two rovers
should basically come together and stop right when they collide or maybe right before they collide or
just a little bit after they collide some students may say the time of intersection is seven seconds
when in our example it's actually going to be four seconds and they'll think they got it right
because the collision happened in the place that they thought it would happen but the wheels are
continually turning even after the collision so one way to kind of point this out to them is say
in an effort to ensure that the collision does not destroy the whole town that they collide in
the rovers must stop upon collision if your wheels are still going after the collision you've done
something wrong in your calculations and the last question is asking the students for a delay
this is a situation where one of the rovers leaves later than the other one it's on a one or two or
three hour delay or in this case one two or three second delay in relation to the other rover the
original problem said they left at the same time so our delay is actually zero for both of them
but don't tell the students this right off the bat if they ask you what it means say well what do you
think delay means they love it when you do that and have them refer back to the original problem
if you teach a higher level mathematics you can change the problem up so one of the rovers does
leave later than the other rover and then this can become an exploration of a transformation of
functions and then after that both students will have to hit enter at the same time and then see if
they were correct did the two rovers collide when and where the students had predicted if not they
can continue trying until they figure it out so now we want to get them to see how this connects
to linear functions and systems of equations ask students to draw a vertical number line similar
to the one that you made for them and then have them show you what happened they'll probably say
something like oh well rover one started down in san antonio and headed up north and rover
two started up in dallas fort worth and headed south and they collided and belt in after four
seconds and asked them how did you notate that it took them four seconds until they collided they
may kind of just stare at you for a second we're trying to get them to see that right now they are
only seeing one dimension the change in distance of these rovers but how do we see that change in
distance happening over time some students will start making these connections depending on how
much you've done with linear functions to this point for those that aren't have them then draw a
horizontal line through austin through r0 and say this line is now representing time so what would
zero time mean well zero time means nothing has happened yet and what about our first rover where
does it start well starting down in san antonio which is gonna be negative five okay so zero time
we're at san antonio negative five what about one hour or one second in the demonstration well it
was going north and so after an hour it had gone two miles and so it was in san marcos okay so
let's write that and what about hour number two what about our number three have them continue
to plot this out so then we want to create our function ask them if i give you time but it's
represented by variable t would you be able to figure out the location of the rover how far
away it is from where it started and students may likely say yeah so after one hour i know i just
multiply one hour by the two miles per hour so so it's just two times the amount of hours or two
times t so after one hour then it should be in the location of two two miles north of austin because
two times one is two and they're like well no i mean it started down in san antonio it didn't
start in austin oh so how do we actually show that we're not starting at zero we're starting way down
in san antonio of negative five oh we just have two t minus five and then that will actually get
us to our final destination after however many hours so our function for distance from austin
when time t is our variable would be y equals 2t minus 5. you can decide how much of the function
notation you want to introduce to them at this point and then have them do this entire same thing
with the other rover they should be graphing both lines and then that graph should be representing
the experience that they had that after four seconds or four hours in the word problem the
place where the two rovers met was three miles north of austin you may be tempted to start
with the linear functions and then have them figure out where the point of intersection is
by having a graphing and working on the systems of equations and then introducing the rovers and the
word problem and all sorts of things like that but i implore you start with something concrete
that they can see and feel and understand and then let that lead into the mathematics let
math be used to explain the situation instead of creating this situation to explain the math
if you'd like the google doc that i created to walk you and your students through this activity
you can get it emailed to you using the link down in the description and that will also add
you to the new edtech classroom newsletter you'll want to be a part of that newsletter
because that's how you're going to find out when we're going to do our big giveaway with
texas instruments and sending a bunch of these rovers and calculators and hubs to teachers like
you so thanks so much for watching and let me know if you have any questions about the lesson
document and once you get the lesson document stay tuned for the email about the big giveaway