Saturday, September 29, 2007

Lesson Idea: Proportions and Ratios using Statues and Action Figures

My students had a lot of trouble with applying proportions and ratios to geometric figures and other problem situations, and I believed that the problem was in their inability to visualize the idea of scaling something up or down. I gave innumerable examples, of course, but being able to see in your mind what is described in a word problem is probably the most difficult skill needed to master Algebra I and pass the 9th grade math TAKS test (our state standardized test). They also had trouble doing measurement problems.

So I came up with a simple idea last year: why not have the students measure themselves and figure out the dimensions of a giant statue of themselves? They would have to make measurements, use measurements, and understand and solve proportions and ratios. Students would have to get up out of their chairs to make the measurements, do their own calculations with their own numbers, and would be forced to visualize a real life proportion problem.

After a successful trial during tutoring last year, I brought back the idea for this year's class. The only supply needed is yardsticks (ask the science teachers). Here's the plan:
  1. I introduced the activity by asking students to imagine that it's the far future, and they're all doctors, lawyers, engineers, scientists, and Presidents of the United States. They're so famous that their hometown wants to honor them with a giant statue in the middle of town. In order to make the statue lifelike, they need to use proportions to make sure that you don't look like a telephone pole or worse, Eric Cartman.
  2. Students make three measurements (in inches): height, shoulder width, and shoe length. They have to work together to get the measurements done quickly and easily.
  3. Optionally, they can measure a partner to give them something to compare their measurements to.
  4. Students return to their desks to make calculations; the teacher gives examples and then monitors independent work.
The questions are rather straightforward but require multiple calculations. I also included at this point in the lesson the idea of shrinking my students down to action figure size. Here are the questions:
  1. If we wanted to build a 50 ft tall statue, how wide and long would it be?
  2. If we decided the statue would be a ratio of 5:1 bigger than you, what would the dimensions be?
  3. If we wanted to make a 4 in tall action figure, how wide and long would it be?
  4. If we were making an action figure that was a ratio of 1:10 smaller than you, what would the dimensions be?
As an assessment you could give them standardized test-style questions with similar triangles (and other polygons) and word problems requiring application of proportions and ratios. I included a similar question on our weekly quiz which is linked in the resources at the end of this post.

Pitfalls and suggestions:
  • When I originally tried this activity, I displayed the questions via document camera (fancy replacement for an overhead projector) with the idea that I would write in examples and how to set up the proportions and ratios so we could do it together. I lost their attention after so effectively gaining it with the initial part of the activity. I corrected this in later classes by including a clear graphic organizer.
  • While getting them out of their desks once and a while is a good idea, you need to manage the activity effectively. Make sure you have enough yardsticks for pairs or groups of three. Give them a time limit and hold them to it. Most importantly, make sure their are no yardstick fights!
  • Many of my students had trouble setting up proportions themselves because they wanted to do something with all three dimensions at the same time. Thus, it might make sense to start with a two-dimensional idea (giant painting, miniature cut-outs) and then add the third after you are sure they have mastered it.
  • This activity is meant to be done after you have taught solving proportions, what ratios are and converting ratios to fractions.
  • This can be a very difficult concept to grasp, and thus this activity might be better suited for later in the year when you are targeting students to help them pass standardized and end-of-year exams.
Statue of Me documents available at The TeachForever Notebook:
  1. Statue of Me initial activity - introduction and questions for display on overhead
  2. Statue of Me Follow-Up Activity - Complete activity with graphic organizer that helps spell out what to do with their measurements
  3. Weekly Quiz - Covers proportions, ratios, rates and percents. Included is an example problem connected to the Statue of Me activity.
I think this idea could use a lot of work, so I appreciate any suggestions and ideas you have. Please post a comment or email me (remove NOSPAM)!