Credit Cards & Recursive Geometric Formulas

This is my first lesson post with materials, so please comment if you need more information, or if things don’t work.

Learning Targets:
1. Students will be able to write a recursive formula with a percent increase or decrease.
2.  Students will know how a credit card balance is calculated (hindsight:  they need to know how a credit card works)
3.  Students will know about credit card fees, APR, interest and monthly payments.

Background: Our textbook (Discovering Advanced Algebra) uses recursion to build into linear functions and exponential functions.  Our district decided at the beginning of the year that we could take the geometric recursive sequences and teach them at the intro to exponential functions.  The student teacher I’m working with had the idea that we could use credit cards to make a real-world connection.  Unfortunately he got saddled with all of the lesson planning for PreCalculus and never got to flesh out the idea.  So I hopped on that train and made it into a groupwork jigsaw activity.
What makes it a groupworthy task:  credit card calculations involve a lot of separate pieces of information, and you don’t need to be an expert on every aspect to grasp the whole, but you do need the basics.  By dividing up the resources of content knowledge, the final group has a reason to seek a contribution from each member.

Activate Prior Knowledge: We opened with the warm-up to make sure students were all clear on percentages, and finding increase and decrease.  In years past this was tricky, but it was smooth sailing this year.  The discussion questions at the end of the warm-up helped a ton to prepare them for presenting their work to the rest of the class.
Grouping: Each group of four students were assigned individual expert tasks.  They split to meet with their matching experts from other groups & work through their sheets.  The FEES experts have an actual credit card offer on the back of their sheet.

Products: After completing their requisite tasks, they head back to their original groups, and get the overall Task Card.  In a 100 minute period, this is where we had to stop and we’ll continue on Monday.

The final product will be a public vote tally on which credit card is “better.”  I haven’t figure out how to guide that into a mathematical argument.  Perhaps each vote needs to put up 2 reasons for the vote, and discussion will ensue?  I have to see it play out once and then decide what can be added.




Reading Process

We devoted an entire 100 minute class to practicing this process (it’s on three chart papers on the wall now).  It was myself, a student teacher and a literacy coach in a class of 32 students.  We chose a problem in a future section, and told students to base their reading off solving this problem.
We gave all of the students 3 minutes of private quiet think time to read the problem and assess their level of understanding.  They held up fingers (1-4) and we grouped the students by their level of understanding.  I re-explained the rest of the process and how they should expect to repeat it multiple times.
I sat down and worked with the small group of 1’s to get them started on understanding the question.  I pretty much kept repeating the two questions:  “What do you understand?”  “What information are you looking for?”  Even the IDKers could say what information they were looking for.  If it was from before the section, I directed them to the index after they couldn’t find it in the index.
  1. Read the problem (or example)
  2. Assess your level of understanding (this is on a second poster)
    1. I don’t understand the question –> I’m reading to understand the question (you may need help from a classmate or teacher)
    2. I kind of understand the question, but can’t start the problem -> I’m reading to find an example
    3. I understand the question, but I need an example –> I’m reading to see possible solutions
    4. I understand the question and know what to do –> Go for it!
  3. Prepare to read (this is on a third poster)
    1. What information do you know?
    2. What information do you need? (just one thing at a time)
    3. Run your eyes over the section of the textbook and find several places where that might be located
    4. Choose one location
  4. Read
  5. Did that answer your question?  Yes – solve the problem.  No – repeat!

We (the student teacher and I) need to devote another 40-50 minutes in a month or so to reinforce this process.  But already we’ve learned a lot about where students get stuck reading and locating information.  Just breaking down the “prepare to read” was a huge eye opening experience for me.

Teaching reading

I didn’t sign up for this.  I come by this honestly to myself (even if I won’t admit it to anybody else), I intended to teach physics to the best and most interested students.  I intended to teach math to students that were willing to work.  I didn’t sign up to teach reading.  And yet here I am, thinking about reading nearly constantly for the past two weeks.

Our school was wise enough to spend some money on a literacy coach, and even smarter to devote several of her days to science and occupational ed teachers.  I get the best of the math and science worlds, so I had the pleasure of planning out an entire block period around reading a math textbook.  She’s incredible, and her depth of knowledge was evident because in a few minutes we had a very usable process that students can use to read a math textbook.  To make it even better, it’s a recursive process!

Now I feel like my eyes have been opened.  Everywhere I’m seeing students that don’t know how to read word problems.  Students that can’t get information from a text, just run their eyes over it and say “I don’t get it.”  And now that I finally recognize their struggle, I can find solutions.  I am finding solutions.

So I didn’t sign up to be a reading teacher, but for my students I’ll gladly take on the task.

p.s. If I remember to post before another 3 months elapses, the next post will have that reading process.