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.  

Ratio and Proportion Lesson for Geometry by ezmoreldo

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.

Ratio and Proportion- I Notice I Wonder PDF by ezmoreldo

Parallel Lines and Transversals

I wanted to share this document I made because I used this lesson on Tuesday with my geometry class and it worked really nicely.  I did it with them on a doc camera and shared their answers over the doc camera as well.  We all really enjoyed especially the last problem which was written about a student.  He really enjoyed the problem even though it poked fun at him.  I did a terrible job after this lesson though with reinforcing all the angle relationships and their names.  I just went over all the vocab- alternate interior/exterior etc. and had them do problems out of the book.  In my defense, I just didn't have time to do anything more exciting.  But at least we had a good intro to the topic I think.

The pictures came from  world.mitrasites.com  and bookbuilder.cast.org.   By the way, I'm still pretty new to this so is it best to cite pictures as I did above, in fine print below the picture, or should I try to restrict myself to only using pictures I myself have taken?
  Parallel Lines and Transversals Worksheet

Geometry Test on Congruent Triangles

By the way, here is the test I was going to give.  About half I wrote myself and half I pillaged from other geometry textbooks and test question banks.  Sorry for the goofy font.  I've tried to change the font back to a more professionally mathy font, but my students rebelled.  They insist that the font makes math less stressful for them.  If that's all I have to do to make math less stressful, count me in.Geometry Test over Triangle Congruence

Rain Day! And Proofs in Geometry

We have a day off today.  Oregon is flooding.  We would have much preferred the snow storm that was predicted but it is Oregon after all.  The funny thing is the rain doesn't seem to be coming down that hard, and if there's one thing us Oregonians should be used to by now it's the constant drizzle.  Here's the bridge in the town I teach (picture from the local newspaper: The Sheridan Sun)



I think the river has risen high enough that the water is already spilling over it's banks but I'm not sure.  It's only running a few feet below the bridge and as the weather prediction is more rain, water will over take the bridge.  Since I need this bridge to get to work, I'm probably not going to work for a while.  We'll see.

We were supposed to have a geometry test today over congruent triangles.  The first thing one of my students did when she learned of the school cancellation was to give me a call and bemoan the fact that she couldn't take her test because she was going to rock it.  Odd  but awesome phone call to receive.

This brings me to something I've been worrying about.  I decided to use Harold R. Jacob's Geometry: seeing, doing and understanding text book, but my school could only afford the 2nd edition.  I've been happily teaching out of it though because I love it.  Recently, to aid in test writing I got the 3rd edition to help me find test questions so that tests didn't take me a million years to write and much to my dismay I saw that he took a whole bunch of the proofs out of the 3rd edition.  He doesn't stress them nearly as heavily in this newer edition, while I, blindly, have been battering my students over the head with the rigorous proof based curriculum of the second edition.  I promised my students the proofs were important, engaging, that knowing how to do them would aid in understanding higher level math, and that learning to do proofs taught them much needed critical thinking skills.  Has all my pleading, wheedling and dragging all been in vain?  Do people not do proofs as much in geometry anymore?  When I was doing higher level math in college, it took me forever to catch on that if and only if statements had to be proved both ways because no one in high school ever mentioned conditional statements.  All of math is couched in the language of conditional statements and proofs.  Isn't it still important to teach this stuff?  But maybe the content of geometry itself is more important.  It is true that while trying to help my students truly understand proofs, our progress through the curriculum has slowed down.  But as a college prep school I don't know if I could live with myself if I didn't help students feel more prepared for college than I felt and I felt the lack of having done proofs keenly.

Well, I guess I'll use my day off to have all sorts of fun- like plan my next algebra 1 unit... Yay.