Last semester I used the Statue of Me activity to teach proportional change with moderate success. More recently I incorporated it into our Measurement Project, and again we were somewhat successful. However, despite our efforts, student struggle with proportional change when it is expressed as a scale or ratio (and visualizing these changes) year after year. So I thought I'd use toy cars, like Matchbox Cars or Hot Wheels (both owned by Mattel), and real cars to help my students visualize these changes.
Objectives: Students will: measure the dimensions of a toy car and use a given scale to determine the size of the real car; measure the dimensions of a real car, determine the dimensions of a toy car of the same scale, and compare the results; convert between different units of measurement; determine the reasonableness of their solutions
Materials Needed: The cars cost about $5 for a pack of 5, although if you have children you might be able to "borrow" some for free.
- a package of Matchbox or Hot Wheels toy cars (enough for students to work in pairs)
- yard sticks
- computer with Internet access and an LCD projector (for the video)
In this video, a Mattel toy car designer explains the process of creating a toy car, from measuring the dimensions to the scale (1/64) used to create realistic looking cars.
After the video ended, I asked about what type of math the designer was talking about (proportions, measurement, scale), and what was the scale they used. Then I showed them my toy cars, and explained that we would use this information to find out the size of the real car.
Guided Practice: Students worked in pairs to measure length, width and height (from the ground to the highest point) of a toy car to the nearest eighth of an inch. I asked a volunteer group to share their results, and we discussed how we would use the scale (1/64) to figure out the size of the real car. They debated over dividing or multiplying and by what, before settling on multiplying by 64 (if they decide on something else, have them try it out and discuss the reasonableness of their results).
Since the measurements were in inches, I told them we'd convert it into feet so it would be easier to visualize and model how big the car would be (and figure out whether our results were reasonable). We discuss how to do that (divide by 12) and then I used the yard sticks to model the dimensions we had found.
Some students were skeptical of our results, so the next step of our lesson would help us get some answers.
Independent Practice: We took our yard sticks out to the faculty parking lot, where I had students measure the height, width and length of my filthy '97 Honda Civic (one student wrote "wash me plz" on the hood) in inches. I also had them carefully and covertly measure a longer car closer to that of the real-life version of the toy car.
We returned inside and ran out of time, but we would have figured out the dimensions of a toy car version of my Civic, discussed the reasonableness of our earlier results, and looked at some standardized test-style questions as an assessment.
The students really enjoyed this activity, especially because it was so rare for us to just get up and walk out the front door of the school. The novelty of having the toy cars and watching the relevant video was icing on the cake.
Some of the students came up with results to their conversions that made no sense, so we discussed them and they quickly discovered and corrected their mistakes. These discussions are as important as anything.
It might take two 45-55 minute classes to finish, which is fine. This is a memorable activity, and it's okay to take extra time.