## Saturday, August 3, 2013

### Not Ratios again!

Students either seem to "get" ratios or they don't.  I don't know what to do about it.  I made a really detailed ratio and proportion lesson based on beats per minute and the fastest guitar player in the world for my algebra 1 students.  3 students that I used it on loved it and understood everything just fine, 1 student could not get it no matter what I tried.

I drew a picture of a person and said that he was 6 ft tall but a shrink-ray shrunk him to 2 ft.  If his legs were 3 ft long originally how long are they now?  My student thought for a second and then said "-1 feet?"  I tried pictures of triangles, I tried explaining that scale factors worked with multiplication and division, not addition and subtraction, I tried just showing him the math steps based on fractions in a last ditch attempt to get him to walk out of the class with something.  But none of it worked because he didn't have an internal sense for proportion.  He could do the mechanism of cross-multiplication, but a "sense" for proportion just eluded him.

I'm now working on a lesson for geometry introducing ratio and proportion and I'm getting a little cold and clammy because I have nothing.  My experience is just kids see it or they don't and if they don't, I don't know what to do.  Sheer perseverance and drill have helped these students eventually reach an "aha" moment, but it just seems to be based on time, not on cleverness of the activity (or I haven't found or thought of a sufficiently clever activity.)  I've been sitting in a coffee shop for an hour now and so far, I just have a warm-up:

1. Which pair of numbers is out of place?  Explain why you chose that pair.
1.    3 and 4
2.  5 and 6
3.  9 and 12
4.   27 and 36
2. Which pair of numbers is out of place?  Explain why you chose that pair.
1.    9 and 12
2.   12 and 15
3.   20 and 25
4.   32 and 40
3. You got a part time job at The Pizza Hub.  You just found out that your co-worker makes more money.  Which statement would make you angrier?  Why?
1.    Your coworker makes \$10 more than you.
2. Your coworker makes double what you make.
If there's anything out there to follow this warm up with, I'd love to hear about it.

Update [8/4/2013]  Here's the lesson I eventually came up with.  I think it does a decent job.

And here's an "I notice, I wonder" activity that could be used to get students thinking about ratio and proportion.  Both of these are PDFs to preserve formatting, but if you go to my scribd profile you can find the .docx versions.