Signed Numbers

Highlight of the Day: Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test. Problem: what is  ; Me (typical first question): So....what should we do? Student: Substitute the 2 in for t to find the answer Me: Why would we want to do that? Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer. Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo! Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.

Hello friends. This is what I've been doing this afternoon. It's a Geometer's Sketchpad file that I hope to use with my calc class when we talk about volumes of revolution. I tried to upload it using Javasketch for those of you that don't have GSP, but found out that JavaSketch doesn't support function plots, or pretty much anything I used to create the sketch. Typical. Anyway, I'm looking for feedback. Play with the sketch, press the buttons, see what you think. Ideally, I'd like this to be along the lines of a Dan Meyer "What Can You Do With This" type activity, but I don't think I'm there yet. It's not finished, mainly because I don't quite know how to create functions for the last 1.5 pictures. Any help is appreciated! Thanks, friends. ** UPDATE ** A new version is posted here . Thanks to iTeach in the comments section ( @PersidaB on twitter) for coming up with cubic regressions for the lasat 2 pictures. I didn't th...

Thursday we had a staff meeting led by our school Superintendent and the Human Resources director. The topic? Next year's budget cuts. As of the last governor's proposed budget, our school was scheduled to have $1.5 million cut from our budget for next year. The new governor has not approved a budget yet, so we're not sure if that number will remain, or increase. Currently we have about 50 students in the deaf department high school. Twelve or thirteen will be graduating. Currently we have five 8th grade students. Our numbers in the high school are going to be dropping. Our numbers in general are dropping. Next year we will have 66 students in the deaf department. That is, 66 students from preschool through 12th grade. Not very many. After telling us these numbers, HR discussed how the administration has been planning to deal with the budget cuts. They will be leaving vacant positions open, trimming utility and technology expenditures as much as possible, and decreasing...

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 ...