Friday the thirteenth falls on a Friday this month.

The Friday Five stands in respect of this “stition” indeed, yet carries on with its work nonetheless. Algebra, Calculus, and Trigonometry are the lucky courses this Friday the 13th.

## Understanding Compound Inequalities

The title of Jennifer Vadnais’s activity doesn’t give much clue about the
playful opportunities that lurk within. Make the circles blink on and off by
naming intervals on the *x*-axis with inequalities. Finish off with an
invitation to blinking artistic experimentation, and pretty soon, your
accumulated fun units are substantially greater than zero.

## Area between Two Curves

Andrew Knauft uses Desmos’s brand-spanking-new Math Input as he has Calculus students work on finding the area between two curves. A classic technique of integral calculus beautifully Desmos-ified.

## Line of Best Fit

Dan Meyer gives us a simple set up,
but a difficult challenge. Eyeball a line of best fit. Which of several points
should that line go through? Predict where that line will be way down the
*x*-axis. Now zoom out and see the consequences of small errors, and the
power of careful predictions.

## Music and Money

Imagine you paid per song you streamed on Spotify. What would be a fair price? What do you imagine the artist gets for that? What should the artist get? Michael Fenton’s latest modeling activity doesn’t resolve these tricky modern questions, but it gets useful information in the hands of algebra students and asks them to analyze it. During and after the lesson, it’d be great to hear what students think is fair here—fair for listeners, fair for musicians, fair for the people who make and code the software that delivers the music. Great food for thought.

## Sine Transformations

The Friday Five wraps up with something for the Trig teachers. Jeremy Babel combines slider work and reflection questions in this solid and straightforward treatment of transformations of the sine curve. (It’s in degree mode, but go ahead! Duplicate and edit if you need radians!)