Thursday, January 13, 2011

Measurement Unit: Episodes 1, 2, 3 (Conversions and Unconventional Measurement Methods)

I have been enjoying the beginnings of the Measurement Unit! I wrote about it briefly back in November, but basically it's an entire unit on conversions and hands-on measurements of various properties of an object.

This is what we did on Day 1 of Measurement Unit (following a mini review of how to do basic conversions):

We were exploring the idea What different types of quantities can you measure?

As usual, even activities as simple as this allows me to catch little gaps in understanding, such as the fact that many 9th-graders need a little nudge in the right direction to figure out how many months old they are. (Most of them just want to multiply their age by 12, and they neglect the fact that their birthday wasn't within the last month!) Also, many of them think that 7 hours and 15 minutes is the same as 7.15 hours. (Naturally, I had seen these issues last year during the same lesson, but had forgotten about them until this week.)

In order to measure their own reaction times, kids followed a fun mini reaction time lab I had found on the interweb (you know, that one where kids drop rulers and their partners need to catch the rulers as quickly as possible). Notice that we're working on estimations as well as actually measuring things and converting things! It made me giggle (and in some cases, made the kids giggle) when they estimated their own reaction times as 1 whole second. I told them that means that when someone punches them in the face, it'd take them 1 whole second to say, "OUCH!"

The kids loved it, as they did last year. Really simple intro to the unit. For homework, they needed to do a sheet of basic conversions:

Then, on Day 2 of the Measurements Unit, I had kids start by brainstorming how we can measure the height of a building! Following that, we talked about setting up ratios using shadows (kids did most of the talking, I just gave them probing hints/questions here and there) until the kids figured out as a class how to find the height of an object using shadows and similarity concept. Then, I explained that it's logistically difficult for us to do a shadows lab, since our period rotates hours each day and it's hard for me to pick items that have clearly visible shadows at all hours of the day. I drew this picture on the board:

And I reminded them that reflected angles are congruent on both sides (like we had seen in the previous mini-golf hole-in-one project) and I asked what lengths they would need to measure, in order to figure out the length of the tree. The kids figured it out collectively. I didn't have to do any talking at all! Brilliant. :)

The rest of the period, we went outside and used their mirrors and metersticks to measure a 3-floor building (~1000 cm tall), a second-floor balcony (~450 cm), and a tree (~300 cm). It was really lovely, and we all enjoyed being outside (especially because, you know, El Salvador is in its warm, dry season)!

As homework, kiddies needed to do this:

One of the things I had wanted to change for this unit from last year was inserting more practice days in between activity days, so that the quizzes didn't come so much as a shock. So, today (Day 3), I spent half of the class reviewing and giving kids time to work on mixed practice problems, including a recipe conversion problem! It was an idea I got from a physics teacher, who used to make his kids bake in class using cups and teaspoons, but given only metric units. I don't have the connections here to get into the kitchen, but the kids still got into the problem. (It was pretty funny because I had to give them a little background on baking, and how you usually use cups to measure things like flour and sugar and butter, and only use teaspoons for the trace amounts of ingredients.)

After the little mixed practice, I told kids about how last year, I had found myself needing to figure out the exact height of my balcony in preparation for an Algebra 2 Bungee Jump project. I asked the kids how they thought we could measure the balcony besides the mirror/similarity method (which is a little imprecise). One kid in each class had the idea of keeping a string taut between the two floors, and then measuring the string. "Brilliant!" I said. That's what we did the rest of the class: we tied water bottles (as weights) to strings and lowered them to the ground from the second floor. They marked the places on the strings where they thought matched the height of the balcony, pulled the water bottle (weight) back up and measured the string. In the end, the group (in each class) that got the results closest to mine got a few extra points. So there was a friendly little competition, and the kids were super into it!

We talked afterwards about how tape measures is kind of the same idea. Wouldn't it be difficult if you had to measure your waist-line using a straight ruler?

Anyway, I'll write more later. I hope you guys will enjoy hearing about my measurement unit as much as I enjoy teaching it (and the kids enjoy learning it)! We will be going into 3-D measurements next!!!

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