A stupidly simple mnemonic for acceleration graphs

When working with position/time graphs of accelerated motion, it is easy to confuse the dire
ction of velocity with the direction of acceleration. for example, look at the two graphs below:

Many students will instinctively say that the first graph is positive acceleration, while the second graph is negative. In fact, these are the same graph, as you can see here:

It is a single parabola, representing positive acceleration.

So how do I get kids to recognize positive and negative acceleration? Using the following, stupidly simple trick:

Positive face

Negative face

It’s really that simple. Any part part of the smile, be it a corner of the mouth smirk or a full on grin, still looks positive. Any part of the frown still looks negative. And that’s it.

Desmos is another great math tool

Yesterday I wrote about g(Math), a tool for adding formulas and graphs into Google docs, like an equation editor on steroids. Today I’m going to talk about Desmos, a full-featured, web-based standalone graphing calculator.

Desmos can be run from the website, or installed as an app in Chrome. You don’t need an account to use it, but if you create an account you can save your work – even saving a copy to Google Drive, which is nice. The interface is clean, with the list of functions down the left side, and a large central grid (which can be switched between Cartesian and polar) to display functions. It responds well to double touch, so using it on an interactive whiteboard is easy.

There are many, many saved examples on the Desmos site which highlight it’s capabilities – including animation and drawing pictures with multiple equations.

I’ve started using it to illustrate the parabolic functions of acceleration, finding the roots, intersection of functions (solving two equations and two unknowns), and illustrating standing waves and beat frequency. I’ve just scratched the surface – there is a lot more that can be done with it, I just need to find the time to figure out what all else it can do. But for teaching transformations of functions? Just throw in a function with sliders and watch what happens. It is a very user-friendly interactive tool.

It’s teacher friendly, student friendly, works beautifully on the interactive white board, it runs animations, and it’s fun. What’s not to like?