This is rather ironic because I actually had my students complete this activity earlier in the year. I had them create a real life application for proportions using indirect measurement. They had to write their own problems and provide an illustration. I found this to be extremely beneficial. If your school subscribes to united streaming there is also a very good clip that shows how Lance Armstrong and his team rely on indirect measurement to help them calculate distances and race. I used this as a basis for my discussion along with the scenario of finding the height of a very tall apartment building that the students can see from the windows in my classroom. I hold a 25 foot measuring tape in my hand and ask them how we can calculate the height of the building. I pray for a sunny day so that we can see the shadows! We then measure the height of a student, their shadow, and the buildings shadow. Next, setup a proportion being sure to keep everything in order and solve using cross multiplication.
Another activity that we do is called “left handed learns.” In this scenario we talk about sampling and how we can get a rough idea of the number of left handed, right handed, and ambidextrous students in the school. The students have a couple of days to sample students in each grade. We set up proportions using the data they have found and I provide them with the number of students in each grade. They must then calculate the left, right, and ambidextrous students for each grade. Since the numbers often differ by a little bit, this is a great chance to ask them how the polled the other students and talk about biased sampling. (note: They are not allowed to sample students that are in the same math class) This is a great activity that opens the door to sampling in the real world. Students discuss where sampling can be applied elsewhere along with why and how it is done outside the classroom.
Justin, similar to your “shadow” idea, I use a photograph of a student (or me) standing next to our 2-story building. We then use a proportion equation to calculate the height of the school. The kind of thinking you are asking your kids to do will benefit them way beyond the classroom. – Dawn
I like your sampling activity because you are actually using the students in your school. I talk about sampling, but never thought to actually have the kids try it within the population of our school.
THANKS!
Leslie
Justin,
Your “left handed learns” lesson is an excellent way to have students experience and understand proportions as well as sampling. When students experiment with their own data the learning has much more meaning!!
Judy