I have found myself in a pretty lucky situation in
Pre-Calculus. For a variety of reasons I am a little ahead of where I need to
be in the curriculum so I am able to slow things down a bit while we are remote
learning. I am grateful because the particular chapter we are covering is very
challenging for most students. Polar coordinates, Complex Numbers in Polar form
and Vectors are never easy in the best of times but I want to make sure that
the students can still master these very important concepts.
Pre-Calculus. For a variety of reasons I am a little ahead of where I need to
be in the curriculum so I am able to slow things down a bit while we are remote
learning. I am grateful because the particular chapter we are covering is very
challenging for most students. Polar coordinates, Complex Numbers in Polar form
and Vectors are never easy in the best of times but I want to make sure that
the students can still master these very important concepts.
Polar coordinates are
a brand new concept to the students. They are used to graphing on a rectangular
a brand new concept to the students. They are used to graphing on a rectangular
coordinate system using ordered pairs (x, y). The polar coordinate
system looks like the figure below and the ordered pairs are now (r, θ)
where r is the length of a radius and theta is the angle.
For most students, polar coordinates are completely bizarre
and seem to have no relevance to real life. However, when I was developing the
Trigonometry curriculum for the new Math Program, I came across a Desmos
Classroom activity for introducing polar coordinates. This activity uses images and situations students have seen in the movies
for navigation on submarines and aircraft to put this coordinate system into
perspective.
and seem to have no relevance to real life. However, when I was developing the
Trigonometry curriculum for the new Math Program, I came across a Desmos
Classroom activity for introducing polar coordinates. This activity uses images and situations students have seen in the movies
for navigation on submarines and aircraft to put this coordinate system into
perspective.
For those who don’t already
know, Desmos started as an online graphing calculator but it has developed into
so much more in recent years. A teacher can set up an activity and invite their
students to join and the students can proceed through a series of screens that
have different tasks and questions. The teacher can monitor all of this from a
teacher dashboard and when the teacher wants to share out student work, the
students’ names can be anonymized by substituting in the names of famous
mathematicians! I have used this several times in class already (this will be
the subject of a different blog post) but I wasn’t sure how this would work in
a remote classroom.
know, Desmos started as an online graphing calculator but it has developed into
so much more in recent years. A teacher can set up an activity and invite their
students to join and the students can proceed through a series of screens that
have different tasks and questions. The teacher can monitor all of this from a
teacher dashboard and when the teacher wants to share out student work, the
students’ names can be anonymized by substituting in the names of famous
mathematicians! I have used this several times in class already (this will be
the subject of a different blog post) but I wasn’t sure how this would work in
a remote classroom.
The students started the activity by watching a short
movie clip showing a tense battle in a submarine with the sonar operator
shouting out the location of “bogeys” that were attacking the sub. The students
then advanced to a screen that set up the activity.
movie clip showing a tense battle in a submarine with the sonar operator
shouting out the location of “bogeys” that were attacking the sub. The students
then advanced to a screen that set up the activity.
I was able to watch
their progress as they moved through the screens.
their progress as they moved through the screens.
After a series of
screens where students learned how to use polar coordinates, the students were
put to the test!
screens where students learned how to use polar coordinates, the students were
put to the test!
The students were
racing to see who could finish first. I was able to watch the students work in
real time and was announcing over our zoom meeting who was the closest to clearing
all the bogeys.
racing to see who could finish first. I was able to watch the students work in
real time and was announcing over our zoom meeting who was the closest to clearing
all the bogeys.
The activity also gave me a
great opportunity to check for understanding.
great opportunity to check for understanding.
In the end I was able
to get some final feedback. I highlighted a
couple of fun comments.
to get some final feedback. I highlighted a
couple of fun comments.
I think the class enjoyed this and I am going to
be looking for more Desmos activities for us to do in the future!
be looking for more Desmos activities for us to do in the future!