# Your Friday Five for the Fourth Friday in February

This week’s title leaves us wondering if there are ever FIVE Fridays in February. Gotta be, right? Will any of us ever live to see such a February? Can you answer this question with Googling it? Please show your work.

Either way, here’s your Friday Five, including exponential functions, dilations, calculus, composition, and regressions.

## Abe and Ben’s Repair Shop

In this twist on a classic activity (written up in Activity Builder by our very own Michael Fenton), students compare linear and exponential growth in the context of daily payments. One plan increases by \$100 each day, while another grows by doubling the previous day’s payment.

Bonus points must be awarded to students who spontaneously offer Abe and Ben’s identities.

## Working with Dilations

Here, Mr. Rothe has students exploring a little bit of coordinate geometry by using Desmos sliders to dilate triangles and consider the consequences. Also it ends with the admonition to students, “Go nuts!”

## Mean Value Theorem

More calculus from the Desmos Teaching Faculty! That and the title are all you need to know. If you’re teaching the mean value theorem, click on through and have a peek.

## Composing Functions Exploration

This is precisely what it claims to be. Use function notation and compose some functions. The particular functions being composed have an important relationship—they are inverses. Plus the activity’s author Bree gives us some of the more creative illustrations we’ve seen in Activity Builder. If you teach Algebra 2 or Precalculus, go have a look.

## Regression: Matching Given Data

Stephanie Girvan takes you from matching a dataset with sliders to regressions, with the overarching questions being “What best fits the data?” and “Can we do better?” This is an intuition-building exercise, combined with some technical skills for precision; great fodder for classroom conversation.