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Each year Peter Papulis asks his geometry students to apply abstract knowledge of proportions, similarity, and ratios to their own experience - through manipulating images in Smart Notebook. Students take snapshots of one another next to prominent places around school, pull the images into Notebook and estimate the height or length of their subjects. If you'd like kids to collect, annotate, or measure images, Smart Notebook might be your simplest solution.
"The pre-work makes the project work." - Peter Papulis
This is Peter's second year with this project, and he's noticed that preparing students with the necessary mathematical vocabulary and walking them through the process prior to entering the lab has made all the difference. Here's his pattern:
Students begin the unit looking at proportion word problems, gathering an understanding of the vocabulary of proportions and a sense of what proportion is all about.
Once vocabulary is in place, Peter surveys to see who has a iPhone or iPod Touch in the room, arranging the groups so that there's at least one in each group. He then asks the groups to download the free Multimeasure app and experiment with estimating. The app uses the same mathematics students are learning in this unit. One of Peter's goals is to demonstrate to students that mathematics isn't something that's just on paper. Math is used in tools and problems that surround us, and people can capitalize on that in order to make a profit - as the makers of this app (which has a for-cost counterpart) have.
After the hook with the app, it's back to the classroom for a "hands-on" approach to this idea. Using real rulers and example pictures, students work out how they can use proportion to estimate the height of common landmarks around the world.
After the practice, Peter takes a portion of one period (~45 minutes) for students to take pictures around the school using cameras checked out from the library. Each group had at least 3 pictures of a student (the reference height) standing in front of a portion of the building or other landmark on campus. They are given a rubric and tutorial before beginning the work
The next day in the lab, Peter oriented students to Smart Notebook (his instructions are here), and the final day is reserved for student work: uploading images, calculating proportions, and annotating their slides. The final product? A student-created estimate of the height or length of a place they walk by every day:
Students must position their cameras as close to "reality" as possible. A tilted shot will skew the estimation of the larger object.
When calculating the reference height of their peers, students must use the metric system rather than the English system of measurement (e.g. six feet, two inches should not be written 6.2, but converted into metric units - 188 cm).
Without the separate "Math Tools" plugin from Smart, ratios can be a challenge to draw on a PC, but Peter's students worked around this in a variety of ways.
Peter's unit is effective for many reasons. From the perspective of educational technology, he leverages tech to both hook his students (through their experiences with the app) as well as provide for personalization and choice (as students are able to travel around the campus and select their objects of choice). All the technology is fairly easy to use, moving tech into the background and allowing the curriculum to take it's rightful place: front and center.
If you or your students are looking for a way to gather and annotate images, Notebook is worth a look!