So I have this idea.
My College Algebra students don’t get logarithms. I’ve got a bunch of ideas for improving the mathematical flow of our study of logarithms this semester, mostly having to do with lots of “find the exponent” tasks.
And I also want to provoke them to ask some questions of their own about logarithms. No small task, I assure you. Logarithms are abstract beasts.
So I’m thinking about where in the real world one encounters logarithms. The Richter scale and pH are my go-to examples. The Richter scale, while interesting (and of-the-moment), doesn’t suggest to me ways to bring it into the classroom to make things problematic for my students. I’m unsure how to get them wondering about the Richter scale.
So I’m going the pH route.
Here’s the setup: Orange juice concentrate. We have various mixtures of orange juice (which is acidic, so low pH). We will examine the pH of several of these mixtures and the question will be What is the pH of the concentrate?
So today I got some pH strips from our Chemistry department (props to Sara the CLA by the way-very helpful!) and bought some grapefruit juice in the College Store and mixed it up with water in various concentrations, testing each one with my strips.
Surprised by my results, I ran some computations.
So here’s the question for all you algebra teachers. Answer from your gut, not from computations. You have 10 seconds after reading the question to formulate the answer.
I can find it algebraically, and I know you can too, so no need to show off. Commit yourself to an answer.
(Readers who are not algebra teachers will find the answer in the comments section, but not a worked out solution.)
My grapefruit juice has pH=4 and my water has pH=7. I mix them in a 50-50 ratio. What is the pH of the resulting mixture?
Remember, answer from your gut. Then calculate.
The task goes into full production tomorrow. Because of the surprising (to me, anyway) results of my grapefruit experiment, I now know for sure that pH strips are not good enough for my task. I need a pH meter and I’ll need to make special arrangements in the Chem Lab to make it happen.
Update: Special permission in chemistry obtained. Storyboard made. Filming scheduled for Thursday afternoon.