Last year was my first year ever teaching pre-calculus. Most of the year, my goal for each lesson was to 1) come up with a clear and concise interactive notebook page and 2) teach the content well. I definitely did not always hit #1, and I’d like to think I hit #2 most of the time, but I left myself a lot of notes in my lesson plan spreadsheet to improve for this year.
However, with this being my 7th year teaching Algebra 1 and my 6th year teaching Algebra 2, both of those classes feel nicely dotted with “fun” activities – card sorts, question stacks, puzzles, mazes, row games, scavenger hunts, Desmos activities, etc. Pre-Calc felt pretty lackluster last year. Mostly textbook assignments alternated with notes, interspersed with quizzes. Not that there’s anything wrong with that if it’s done well in a classroom, but I wanted to try this year to spice up pre-calc a bit and incorporate some of the practice structures that I find students enjoy more. Reminding myself that Algebra 1 has become full of these activities over SEVEN YEARS, I am starting slowly and trying to find or create at least one “more interesting” practice activity per chapter this year.
Currently, we are working on Chapter 3 of the Demana, Waits, Foley, Kennedy Precalculus textbook: Exponential, Logistic, and Logarithmic Functions. In our district’s curriculum, we focus solely on the exponential and logarithmic functions here. Section 3.5 of the book covers exponential and logarithmic modeling, aka what do we actually use these types of functions for? There are a couple problems about earthquakes, a couple about pH, and a couple about Newton’s Law of Cooling. I think this content is really interesting to work with, but 6 textbook problems just isn’t going to pique that interest in students.
Last year on twitter, I saw and saved this image from…SOMEONE. SOMEWHERE. Honestly, I’ve tried searching twitter for “pH lab logarithm” and so many other search terms, I’ve tried reverse image searching…nothing. If you know where this image was posted, I’d love to give the teacher credit for the idea!
Now looking at it again, I’m getting more ideas for next year because I see they used colored pencils to show the color their pH strip turned…
Anyways, I asked our science teachers if they had any materials to test pH of things, and my friend Jess Hughes kindly supplied me with some pH test strip rolls that she wasn’t sure even worked, so I went home and stuck them in some vinegar and things and they did!
I put some coffee, Maalox, vinegar, and distilled water in containers and brought them to school. I grabbed a bar of soap (which you have to dunk in water to get the pH strips to work), and filled another container with drinking fountain water from school. Here’s where you can find the worksheet I gave students along with this. Make a copy in your own Drive if you want to edit it!
Then, I swear I had seen a teacher do a lab with Newton’s Law of Cooling and a murder on twitter, so I went to find it. I found this from Jasmine Castanon, this (and this) from Cassandra Valenti, and this from Rebekah Mozdeh (via Sarah Carter). All great ideas, but failing to find something ready made that satisfied everything I wanted it to be, I decided to write my own story. I only have 5 students in my Pre-calc class, so it wasn’t too much effort to come up with a plot line that included each of them. They had so much fun reading the story and laughing about what would maybe be true in 30 years and what they hoped definitely wouldn’t be.
Here is a version of the story with my students’ names removed. I highlighted the information that is actually relevant to Newton’s Law of Cooling, because the rest of the story is just about who did it. I made up the temperatures and have no idea how accurate they are to actual cooling dead bodies – I started doing research on that and realized that it would take me a long time to figure out and decided it wasn’t worth it!
Students definitely enjoyed this more than just a textbook assignment and I think it got the point across how logarithms are actually used in our society.