Lesson Reflection: Measuring Error

New to our Integrated Algebra standards last year was percent error in measurements. Last year I did a miserable job of it. "Copy notes followed by practice problems" miserable. This year was better.

Things to keep in mind:

1. They already have learned how to calculate "percent error" in science labs.
   
2. This concept is a hybrid of "greatest possible error" and "percent error".
   

I started this year with a slide and a discussion:



They all said "5.4 cm". To which I replied, "Are you sure it's not really 5.38 cm? 5.41 cm? 5.40236 cm? We discussed the mechanics of measuring something, how you end up visually rounding to the nearest marking on the measuring device. They talked about their digital scales in science class, and how you can set the readout to the nearest tenth or hundredth, and we discussed that the little onboard computer is doing the rounding, even though you can't see it. (For next year: at this point, have them measure several different items to the nearest _______th, to ensure everyone groks the "visual rounding" idea.) Then, I got them to conclude verbally, stated several different ways, that any measurement could really be up to half a unit smaller or larger than the stated value.

Then a few problems:



Then brought in area:



The next day, we tie greatest possible error to percent error, and calculate measuring error (greatest possible area divided by measurement).

On the assessment, 83% of the students scored a 4 or 5 on the question compared to 26% last year. I think the difference was in the introduction.

For next year: take 5 minutes and have them measure some stuff to the nearest whatever. Measure your desk/textbook/etc to the nearest inch, nearest centimeter, nearest 16th of an inch, nearest millimeter, etc. Perhaps borrow a few of those digital scales from science.

Also, it's still pretty dry. Any suggestions to make it more engaging? Other NY teachers (and anywhere else you cover this topic), what are you doing?