Picturing the Possibilities - Project-based Learning Video Lecture | What is Project Based Learning (PBL)? - Professional Skills

so do you agree that these two cylinders
have the same surface area yes my
question for you today is which one has
the larger volume Megan Pacheco is a
math teacher at New Tech High School in
Napa California she's always on the
lookout for real-world applications that
connect her math content to her students
lives I don't just think of oh this
would be fun to do I'm looking at my
State Standards and part of my State
Standards are surface area and volume so
I try and think okay where is that used
in a real-world application and I go
from there on one level so how many
levels would fit in here
math doesn't have to be dry and boring
you know there's applications for math
that's why math exists and so what I'm
trying to do is make those connections
with those kids so they can see where
this is really being used
I plan to be an engineer when I grow up
so I'm just going to work harder do more
challenges and help and that's something
that you're gonna want to say in your
report that you know mathematically we
found that it could be this but
obviously there's gonna be some spaces
between the cookies so I've reduced it
by 20 a lot of my project ideas I would
just look in like text books but I
looked for the application problems you
know a lot of books do have good
sections ideas for like many projects
that I would just take and expand on a
larger scale and it does take a lot of
research upfront that's the whole basis
this there's your triangle right there
so you're dealing with a triangular
pyramid the current project is to design
a line of packaging for mini Oreos to
teach the concepts of surface area and
volume I'm doing a rectangular prism so
I decided to do six by six by four and
my volume was 144 inches cubed because
there's never just one right answer to a
project-based problem
Megan students think individually and
together as they search for solutions it
has to be something that this group
could come up with one thing this could
come up with something different but
they're still learning the material and
as long as they've defended their answer
then that's what I want
27.5 and we need to find the height
which goes straight through it how can
we find that knowing that this is seven
point five five would you use five two
point five right teachers help students
build on their prior knowledge and
experiences without giving them the
answers in one of my projects they had
to design a new expansion to the school
and a lot of them understand or should
understand the concepts of area they do
that in middle school and elementary
school so they can begin to work on the
project and lay out a floor plan and
think about okay if I have a rectangular
room they can calculate that area but
then as I get in more advanced shapes
like a polygon or trapezoid or a circle
they might not know those formulas and
so that's when I come in and we talk
about how do we you know calculate areas
of those different shapes and we do some
examples together we had to design this
and find the area perimeter of
everything full of stuff in it and then
at the end is like wow I actually I
really did a good job and my group
members really came through so take your
inches and divide by 144 and that will
give you square feet okay for each
project Megan gives her students the
rubric which she uses to assess their
work the rubric clarifies her
expectations so there are no surprises
in addition students are involved in
peer and self-assessment they know what
content they need to hit and they know
that that's what they're being graded on
it's not how cool their video was it's
did you show me the mass kills did you
understand the concepts area this it's
high times radius squared and then you
times that by the height and then you
get the volume inside it's important to
let students work out questions by
themselves these are both 70 degree
angles that's why this triangle looks so
perfect and this triangle and
it'll fit once we're done but with the
with the circle it doesn't work like I
know you have to use like a
circumference of a circle sometimes I
really have to hold myself back I have
to just you know step back and let them
work it out as a group and they'll be
talking and no it should be this way no
it should be that way or this is how you
do it and and I have to really you know
as teachers we want to just jump in and
help them and solve the problem so it
takes them restraint on my part ongoing
reflection is a vital part of each
project so what challenges or problems
did you encounter when you were working
today the fact that the calculations
won't really come to life I mean
supposedly 44 mini orders will fit in my
little three by two by two and really
only like 24 actually fit in it I always
do a debrief at the end what did we
learn from this and it can be what did
we learn about the content what did we
learn about working in groups what did
we learn about time management so every
time even if they struggled is the
project they're learning something
because we learned most when we're
struggling well I wanted to share with
you this project that I wrote for
geometry math has almost always been
taught in very traditional ways at this
meeting of the minds math teachers in
the new tech Network get together to
share projects refine ideas and reflect
on their experiences with project-based
learning having someone to bounce ideas
off of is really key and I think
anything you do is worth it because the
students are going to start enjoying
themselves and they're gonna start
learning or seeing the real-life
applications of things I think it is a
good thing I'm personally a really big
math person I've always loved math my
whole life and I'm also really hands-on
person so plus with all the projects you
know the stories behind it it really
makes math really interesting and fun to
do