Signed Numbers

Recently in Trig, we've embarked on the task of graphing sine and cosine curves. Before this, we constructed the unit circle and students became familiar with the exact values of sin and cos at the special angles. To introduce the parent graphs, I used an activity that I found at Kate' s blog last year (who I'm sure got it from somewhere else, but I don't know where). To first see the "unwrapped" unit circle that is the sine (and later, cosine) function, students used yarn to mark intervals along the circumference of a unit circle, then used spaghetti to measure the y (later, x) value at each place. They then transfered these lengths of spaghetti to an x-y plane with x intervals of length matching the circumference intervals. This was a great picture for them of where the shape of the sine function comes from. One student even explained it (works much better in ASL), as though you've taken the bottom half of the unit circle and spun it around to make up ...

I stole Mr. Sweeney's catapult project and tweaked it (more like, added to it) for Calculus class. It was fun! We not only calculated the equation of the parabolic motion of the projectile, but at the end we talked about how fast it was going using the limit definition of the derivative at different points during its flight. It was a really great discovery point of how the velocity is zero at the maximum height. We were also able to then talk about why that "makes sense". The next goal was for my calculus student to help my Algebra 2 students with the project while I was at a conference...stay tuned to hear how that went! (I started writing this post 1 1/2 weeks ago...and the other one has been started, too...just waiting for some TIME to finish up!)