danaleeling

In algebra and trigonometry this term I opted not to take the i and j component approach presented in section 10.8 of the OpenStax textbook this term. I learned during the summer that getting the students up to speed in component notation was a steep climb. One can add vectors using trigonometry without resorting to breaking the vectors in orthogonal components. I also opted to look at the special case of perpendicular vectors, simplifying the process further. I rode inbound with the ball from the LRC.  Earlier in the day I ran trial runs along the east side of the learning resource center to take advantage of the natural T in the covered walkway on a rainy day. I did not have enough "set-up" time to get stabilized in terms of speed and stability on the RipStik by the time I hit the speed trap and ball release point. The speed trap was 300 cm long starting from where Melsina is holding the stopwatch for timing the RipStik. At the upper left Mattstan holds the rada...

For twenty years, since 1997, MS 101 Algebra and Trigonometry has been taught in the A204 math science computer laboratory permitting the use of desktop computers in the course. Due to a scheduling conflict one section of the course was scheduled outside of the computer laboratory this term. The class was assigned to a classroom known as B201. B201 second floor, left end of B building By coincidence the college had just installed a new directional WiFi antenna that lit B201. New antenna atop south faculty building seen against the sky to the right of building center On the first day of class 14 of 21 registered students attended the class. I found that nine of the fourteen students had mobile technology - either a smartphone, tablet, or laptop. I also found that only five of the fourteen had a copy of the textbook, a textbook that retails for $294 dollars at the bookstore. Knowing that we needed graphing technology provided by Desmos , I saw the obvious solution. Have tho...

With the first use of Desmos in my summer algebra and trigonometry course, I opted to end the term with having the students put together their own creation in Desmos. I provided minimal guidance to the students. I wanted this to be as wide open as possible. I too am still learning all that Desmos can do. I did set up a preliminary marking rubric for the exercise and made this visible in Schoology . --> Criteria 4 3 2 1 Presentation mechanics:Presentor delivered clearly, concisely, demonstrated familiarity with the Desmos creation. Exceeds expectations: Well delivered exhibiting preparation and knowledge of their Desmos creation. Spoke clearly and always towards the audience. Meets expectations: Presentor showed evidence of preparation and some familiarity with the Desmos creation. Usually faced the audience. Does not meet expectations: Presentor was only able to vaguely explain their work, sometimes with their back to the audience. Severe does not meet expectations: Little...

In the algebra and trigonometry class I transition into vectors using a projectile motion demonstration on the lawn.  A ball is thrown into a parabolic trajectory. The launch angle is tracked with a protractor, a radar gun for sports is used to obtain the speed of the ball. Back in the classroom the horizontal and vertical components of the velocity are used to work out the distance the ball travels and the height to which the ball rises. As an exercise in Desmos , I put together a demonstrator that takes any angle and speed as inputs, calculates the distance and height, and plots the arc on the graph. I then added a ball that "flies" along the arc. The Desmos projectile motion demonstrator is available online .

In an earlier post I noted that Desmos did not directly plot polar coordinates. Not only was I incorrect, but Desmos responded to my blog to correct me! Although I had at some point seen that one could define a function f(x)=3x+5 and then have Desmos calculate f(6), I had not absorbed how this might be used to plot polar coordinates. The above works beautifully . Realizing that I could effectively program Desmos, I applied this thinking to demonstrating how to add two vectors when given the magnitudes m and the direction angles theta. The graph calculates the i and j components for the two vectors and then adds the vectors, graphically displaying the result while also providing information on the magnitude and direction of the vector sum. m1 and theta1 are the magnitude and direction angle for one of the two vectors, m2 and theta2 are the magnitude and direction for the other vector. All four are dynamically interactive and can be changed. The diagram purports to illustra...

Vectors and chapter 10.8 of the OpenStax Algebra and Trigonometry text would land on the same day as the planetary distances exercise in physical science. This meant juggling gear for the back-to-back one and half classes. A surveyor's wheel, the "sun" ball, BBs, a variety of marbles, along with 13 Planets and planetary distances were all for physical science. The RipStik, tape measure, radar gun, four square ball, chalk, and stopwatch (not shown) were for the vector exercise in algebra and trigonometry. In algebra and trigonometry I opted to use a 500 cm run for the RipStik. Due to rain, I fired the four square ball perpendicular to my rolling path towards the building. The covered walkway provided shelter from the rain. More equipment deployed in the vector exercise, the broom was used to sweep rocks from my rolling path. A look at the layout of the experiment. The 500 cm start point. The ball would be released at the second line. The...

The current regular algebra and trigonometry text in use during the regular term does not include polar coordinates nor polar graphing. Both are topics that are often a black-box mystery to students, hard to envision and perhaps even harder to graph. Polar graph paper helps, but there are an awful lot of calculations on a scientific calculator before one can "see" the graph. The OpenStax Algebra and Trigonometry text in experimental use this summer includes polar coordinates and graphing. These topics fit rather well into the summer curriculum which also includes a look at vectors - vectors underpin so much of physics and the physical sciences, as well as being important in computer graphics. The x = r cos θ and y = r sin θ that the class first met in generating SVG coordinates using trigonometric functions return as conversion functions from Cartesian to polar coordinates . This pair of functions will appear again in the section on vectors . In section 10.3 Desmos w...

The summer algebra and trigonometry course is a first encounter with radians for many if not almost all of my students. I like to start out on the lawn with a big circle. Starting at the generator, Madona held a line with a radius of 44 feet, Suzanne walked behind her with the surveyor's wheel. At 90° the wheel had measured 70 feet or about 1.59 radians. Afilina was the center of the circle, Patty and Herder on the right. Coming up to 180° in the morning class. The weather was sunny, already hot, but cooperative. The grass was still wet, but not overly so. At 180° the arclength was 144 and for 3.27 radians (against 3.14 theoretic). Madona passes David out near 180°. 180° Coming down to 270° the arclength was 218 feet or 4.95 radians. The surveyor's wheel measures feet, in algebra and trigonometry leaving measurements in feet is easier. Reading the measurement on the wheel. Headed back to 0 radians. Zero radians. 298 feet. 6.77 rad...