Mariah Smith
Video Critique 1
Reflections on “Introduction to Vectors”
on February 14, 2014
The lesson’s objective was to
introduce the new subject of vectors. This unit was the first unit that I took
complete control of and was recently added to the curriculum for tenth graders.
The base lesson of how to represent vectors as directed line segments is
important because the students’ books don’t contain the subject. Therefore, I
must be clear in my explanations and make sure that the students understand the
topic.
At the beginning of the class it
took me a while to get the focus of the students and I find myself speaking
over the students. It would be more effective if I waited until everyone has
their notebook out and is prepared to learn. I began the lesson by referring to
the recently covered topic of complex numbers. This is a great method to review
part of the previous topic and to move into this new subject. Its important to
point these connections out between the different topics found in mathematics. While
writing down the graph of the complex number, I should have labeled the
horizontal axis of the argand diagram with Re(z) and the vertical axis with
Im(z). I asked an open-ended question of what is this line (the graph of the
complex number) but I was looking for a specific answer of vector. I should
have used the phrase “a vector is a directed line segment” from the beginning
of the lesson. The total time that took to begin the class was about three
minutes being two minutes shorter than planned.
I like that I explicitly told them
that they will need to write down notes because the topic is not in their
books. I have accomplished my teaching goals of providing real-life examples
for students to relate personally to the subject. Even though students can see
what I am pointing to on the board such as the head and the tail of the vector,
I should explain what I am pointing at so students can see and hear it. While I
am measuring the length of the vector, it should not take so long to do this. I
think it is important when describing the magnitude of a vector to explain how
it is a length and not use a confusing formula (distance formula) right away. I
think it was important to give examples on whether two vectors are equal or
not. When the student asked, “why do we call it (the zero vector) a vector”, I
did a great job of thinking on my feet of an explanation of why we do have a
zero vector. To support these types of questions, I would advise myself to say
to the student that the question was a great question. This first part of the
powerpoint turned out to be about nine minutes, which is what I planned for.
While handing out the worksheet, I
should smile and talk to the students. The clarification of the directions on
the class work helped the students begin with the paper. I have many ESL
students in my class therefore I should prepare myself on which words that I
should explain such as westerly. To avoid a lot of confusion, it would have
been useful to read all of the problems and clarify what direction the vectors
would be going. While I am going over the third question with the students, I
need to ask specific students for the answer instead of addressing the whole
class. The reason why I didn’t do this well is because I didn’t know all of
their names. I believe it is one of the most important strategies to include
students in the classroom. When the student yelled out that they need to be in
the same direction and I said that the vectors just need to parallel, I should
have asked him if he understood the difference. At the end of this problem, I
should have verbally pointed out this fact that parallel vectors don’t have the
same magnitude and the direction are the same or opposite. It took about nine
minutes to do this part of the lesson of which I planned ten minutes.
The given wait time for writing
notes was correct and the students didn’t need to rush to keep up with me. I am
surprised by the statement a student made that eluded to the magnitude of the
sum of two vectors is the same of the sum of the magnitudes of the vector. It
brought is into the perfect prompt-to of explaining its not true. I wish I had
taken this moment to go into more depth of explaining the triangle-inequality
theorem. Giving the students a few examples before they began with the
worksheet is a good method of demonstrating. I get a bit confused when asking
them which way I should draw the vector. I decided to do another example with
the students because I noticed that this was needed before they were able to do
it on their own. The reason why I did this is because a student said that it
needed to be a triangle and I pointed out the next situation did not form a
triangle. The planned time was less than the time I actually took to do this
part of the lesson.
While the students were working, I
would look for things that need to be addressed to the entire class such as
question that ends up with the zero vector. I really like how as we are doing
the vector geometry problem I was asking if the students were seeing a pattern.
This was a great way to scaffold their learning of vectors in the sense of
geometry. Sadly, the last part of the video was cut off for some reason but the
rest of the lesson consisted of the students working on the given worksheet. I
walked around the class offering help for the students and making sure the
students understood the topic.
In all, the lesson went well and the
students learned the lesson objectives that I created for the lesson.
LESSON PLAN
Intro to
Vectors
Date: Friday, Day 3, Period 4, February 14th
Grade/Class: Grade 10, Advanced Mathematics, MYP Year 5
Duration: 45 minutes
Background Information: The students had an investigation in test conditions
the previous math class. This was an assessment for the ratios between similar
figures and shapes. We also just finished up with complex numbers, which
included graphing a complex number on the Argand Diagram. Therefore the
students have seen a bit of vectors and how a vector could be drawn on a
Cartesian Plane.
Goals for Teaching: One goal is to be quick with my introduction of
vectors but to cover the basics needed for using vectors effectively. I also
want to begin a new subject with interest and motivation for the students to
learn about the subject of vectors. Give some real-life examples for students
to relate personally to the subject.
Objectives:
·
Students will be
able to identify vectors that are equal, have the same magnitude, and that are
parallel.
·
Students will be
able to represent vectors, scalar vectors, and sum of vectors using directed
line segments.
Materials:
·
Mathematics Higher Level Core Fabio Cirrito
·
PowerPoint
·
Worksheet
Procedure:
5 minutes
·
Ask students to
sit down and pull out math notebook.
·
Begin with class
on how to plot the complex number 6-2i
on an Argand Diagram.
·
The graph of the
complex number is a vector.
10 minutes
·
Do PowerPoint
and have students write notes on vector basics (naming a vector, magnitude of a
vector, equal vectors, negative vectors, zero vector)
10 minutes
·
Students do
questions 1-3 on worksheet
5 minutes
·
Explain with
power point on how to find the sum of two vectors.
·
Do question 4a
and 4b from worksheet
5 minutes
·
Students finish
question number 4 on their own.
10 minutes
·
Show example
problem on PowerPoint of vector geometry. Ask students for the answers.
·
Students work on
the rest of the worksheet.
Evaluation:
·
Formative/Ongoing
Assessment: Throughout the presentation of new material, I will be asking
questions that will assess if students are following and understanding.
·
Summative/End of
Lesson Assessment: The worksheet that will be looked at the next day will
provide whether the student understood or not.
Extra Class Work:
·
If needed students
can do the bearing questions on the back of the worksheet.
Click here to view the lesson plan and the worksheet used in the lesson.
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