Final project write-up
1) My name is Nelly Ortega.2) The class in which I envision using this sketch is
elementary school, middle, and even high school. That is because area of a
circle and circumference are used throughout all of the grades, but when
introducing this new concept it would be a good idea to provide a visual since
lower grades. 3) The topic being studied is: circumference and area of a
circle. 4) The mathematics behind this sketch involves: basing the
construction on properties of circles so that for a given radius of 1 unit,
when the animation starts, the circumference of the circle is 2 pi, a whole
unit circle/revolution. Also the inscribed polygon and circle allows for the
area of the circle to be calculated, as radius changes arbitrarily. 5) The usual way it is taught is at least from what I
remember, students are given the formula c=d*pi and A=pi*r^2. 6) This sketch will enhance that way of learning, by
allowing students to see a visual representation of what part of the circle
accounts for the circumference and what part for the area. This can allow students to differentiate
between the two, and see how area works with respect to a circle. They can
manipulate the input as well. 7)I would imagine using the sketch in the following way:
show students using overhead, projector; that way they they engage by looking
at the animation. Then I would have them make their won construction, since it
is not that difficult to make. I would have them make 3 constructions for . The
two for circumference would be 1: like mine with radius=2, and 2: change
radius, 3: Area like mine. 8) Act out how you would introduce the lesson and what you
would expect to happen: Start off by showing them, without them having access
to the technology, in order to have their undivided attention. Then have them use technology to replicate
and try it our on their own, play around with mine. I predict confusion will arise, but I would walk around for
assistance and clarifications needed. 9) This activity covers the following 2 common core
standards for Mathematical Practice: #7: Look for and make use of structure.#5: Use appropriate tools strategically
That is because they make use of the structure of circle and its components i.e. they look for radius, diameter, circumference, inscribed polygon, area, etc. Also, they use tools to construct a circle with radius they choose and find the circumference and area accordingly. 10) The new functions of Geogebra that I used in this sketch
are: circular arc and inscribed polygon,
one for the circumference to unravel as you pressed the go button. 11) One thing that I learned about Mathematics from making
this is that there are many ways to try and explain a certain topic to
students. Also the use of technology to bring math problems/topics to life is
useful. By creating a mental image of what actually takes place when
calculating circumference and area of a circle, one can learn better, rather
than just memorizing a formula. 12) One thing that I learned about Pedagogy from making this
is: that incorporating technology to teach students is a great alternative to
teach mathematical concepts. Not only can the teacher utilize this, but rather
it’s simple enough for students to use.